TSTP Solution File: SYN466-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN466-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:55:39 EDT 2022
% Result : Unsatisfiable 2.07s 1.57s
% Output : Proof 2.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN466-1 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 04:06:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 2.07/1.57 % SZS status Unsatisfiable
% 2.07/1.57 % SZS output start Proof
% 2.07/1.57 tff(c1_1_type, type, (
% 2.07/1.57 c1_1: $i > $o)).
% 2.07/1.57 tff(a111_type, type, (
% 2.07/1.57 a111: $i)).
% 2.07/1.57 tff(c0_1_type, type, (
% 2.07/1.57 c0_1: $i > $o)).
% 2.07/1.57 tff(a135_type, type, (
% 2.07/1.57 a135: $i)).
% 2.07/1.57 tff(hskp19_type, type, (
% 2.07/1.57 hskp19: $o)).
% 2.07/1.57 tff(c2_1_type, type, (
% 2.07/1.57 c2_1: $i > $o)).
% 2.07/1.57 tff(c3_1_type, type, (
% 2.07/1.57 c3_1: $i > $o)).
% 2.07/1.57 tff(ndr1_0_type, type, (
% 2.07/1.57 ndr1_0: $o)).
% 2.07/1.57 tff(hskp10_type, type, (
% 2.07/1.57 hskp10: $o)).
% 2.07/1.57 tff(a141_type, type, (
% 2.07/1.57 a141: $i)).
% 2.07/1.57 tff(hskp1_type, type, (
% 2.07/1.57 hskp1: $o)).
% 2.07/1.57 tff(hskp24_type, type, (
% 2.07/1.57 hskp24: $o)).
% 2.07/1.57 tff(hskp31_type, type, (
% 2.07/1.57 hskp31: $o)).
% 2.07/1.57 tff(hskp4_type, type, (
% 2.07/1.57 hskp4: $o)).
% 2.07/1.57 tff(a105_type, type, (
% 2.07/1.57 a105: $i)).
% 2.07/1.57 tff(hskp15_type, type, (
% 2.07/1.57 hskp15: $o)).
% 2.07/1.57 tff(hskp28_type, type, (
% 2.07/1.57 hskp28: $o)).
% 2.07/1.57 tff(a131_type, type, (
% 2.07/1.57 a131: $i)).
% 2.07/1.57 tff(hskp30_type, type, (
% 2.07/1.57 hskp30: $o)).
% 2.07/1.57 tff(a163_type, type, (
% 2.07/1.57 a163: $i)).
% 2.07/1.57 tff(a118_type, type, (
% 2.07/1.57 a118: $i)).
% 2.07/1.57 tff(a106_type, type, (
% 2.07/1.57 a106: $i)).
% 2.07/1.57 tff(a126_type, type, (
% 2.07/1.57 a126: $i)).
% 2.07/1.57 tff(a132_type, type, (
% 2.07/1.57 a132: $i)).
% 2.07/1.57 tff(hskp17_type, type, (
% 2.07/1.57 hskp17: $o)).
% 2.07/1.57 tff(hskp16_type, type, (
% 2.07/1.57 hskp16: $o)).
% 2.07/1.57 tff(hskp5_type, type, (
% 2.07/1.57 hskp5: $o)).
% 2.07/1.57 tff(a117_type, type, (
% 2.07/1.57 a117: $i)).
% 2.07/1.57 tff(a108_type, type, (
% 2.07/1.57 a108: $i)).
% 2.07/1.57 tff(a109_type, type, (
% 2.07/1.57 a109: $i)).
% 2.07/1.57 tff(hskp8_type, type, (
% 2.07/1.57 hskp8: $o)).
% 2.07/1.57 tff(hskp2_type, type, (
% 2.07/1.57 hskp2: $o)).
% 2.07/1.57 tff(a103_type, type, (
% 2.07/1.57 a103: $i)).
% 2.07/1.57 tff(hskp9_type, type, (
% 2.07/1.57 hskp9: $o)).
% 2.07/1.57 tff(a110_type, type, (
% 2.07/1.57 a110: $i)).
% 2.07/1.57 tff(hskp7_type, type, (
% 2.07/1.57 hskp7: $o)).
% 2.07/1.57 tff(hskp6_type, type, (
% 2.07/1.57 hskp6: $o)).
% 2.07/1.57 tff(a107_type, type, (
% 2.07/1.57 a107: $i)).
% 2.07/1.57 tff(a114_type, type, (
% 2.07/1.57 a114: $i)).
% 2.07/1.57 tff(hskp13_type, type, (
% 2.07/1.57 hskp13: $o)).
% 2.07/1.57 tff(hskp11_type, type, (
% 2.07/1.57 hskp11: $o)).
% 2.07/1.57 tff(a112_type, type, (
% 2.07/1.57 a112: $i)).
% 2.07/1.57 tff(a102_type, type, (
% 2.07/1.57 a102: $i)).
% 2.07/1.57 tff(a145_type, type, (
% 2.07/1.57 a145: $i)).
% 2.07/1.57 tff(hskp22_type, type, (
% 2.07/1.57 hskp22: $o)).
% 2.07/1.57 tff(a101_type, type, (
% 2.07/1.57 a101: $i)).
% 2.07/1.57 tff(hskp0_type, type, (
% 2.07/1.57 hskp0: $o)).
% 2.07/1.57 tff(a113_type, type, (
% 2.07/1.57 a113: $i)).
% 2.07/1.57 tff(hskp12_type, type, (
% 2.07/1.57 hskp12: $o)).
% 2.07/1.57 tff(a128_type, type, (
% 2.07/1.57 a128: $i)).
% 2.07/1.57 tff(hskp29_type, type, (
% 2.07/1.57 hskp29: $o)).
% 2.07/1.57 tff(a104_type, type, (
% 2.07/1.57 a104: $i)).
% 2.07/1.57 tff(hskp3_type, type, (
% 2.07/1.57 hskp3: $o)).
% 2.07/1.57 tff(1,assumption,(~hskp19), introduced(assumption)).
% 2.07/1.57 tff(2,plain,
% 2.07/1.57 (^[U: $i] : refl((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))),
% 2.07/1.57 inference(bind,[status(th)],[])).
% 2.07/1.57 tff(3,plain,
% 2.07/1.57 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.07/1.57 inference(quant_intro,[status(thm)],[2])).
% 2.07/1.57 tff(4,plain,
% 2.07/1.57 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(5,plain,
% 2.07/1.57 (^[U: $i] : 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) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))))),
% 2.07/1.57 inference(bind,[status(th)],[])).
% 2.07/1.57 tff(6,plain,
% 2.07/1.57 (![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> ![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.07/1.57 inference(quant_intro,[status(thm)],[5])).
% 2.07/1.57 tff(7,axiom,(![U: $i] : (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 2.07/1.57 tff(8,plain,
% 2.07/1.57 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[7, 6])).
% 2.07/1.57 tff(9,plain,
% 2.07/1.57 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[8, 4])).
% 2.07/1.57 tff(10,plain,(
% 2.07/1.57 ![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.07/1.57 inference(skolemize,[status(sab)],[9])).
% 2.07/1.57 tff(11,plain,
% 2.07/1.57 (![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[10, 3])).
% 2.07/1.57 tff(12,plain,
% 2.07/1.57 (^[U: $i] : refl((hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 2.07/1.57 inference(bind,[status(th)],[])).
% 2.07/1.57 tff(13,plain,
% 2.07/1.57 (![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(quant_intro,[status(thm)],[12])).
% 2.07/1.57 tff(14,plain,
% 2.07/1.57 (![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(15,plain,
% 2.07/1.57 (^[U: $i] : 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(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)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp24) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp24) <=> (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 2.07/1.57 inference(bind,[status(th)],[])).
% 2.07/1.57 tff(16,plain,
% 2.07/1.57 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp24) <=> ![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(quant_intro,[status(thm)],[15])).
% 2.07/1.57 tff(17,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp1) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 2.07/1.57 tff(18,plain,
% 2.07/1.57 (![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[17, 16])).
% 2.07/1.57 tff(19,plain,
% 2.07/1.57 (![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[18, 14])).
% 2.07/1.57 tff(20,plain,(
% 2.07/1.57 ![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(skolemize,[status(sab)],[19])).
% 2.07/1.57 tff(21,plain,
% 2.07/1.57 (![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[20, 13])).
% 2.07/1.57 tff(22,assumption,(~hskp10), introduced(assumption)).
% 2.07/1.57 tff(23,assumption,(~hskp31), introduced(assumption)).
% 2.07/1.57 tff(24,plain,
% 2.07/1.57 (^[U: $i] : refl((hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.07/1.57 inference(bind,[status(th)],[])).
% 2.07/1.57 tff(25,plain,
% 2.07/1.57 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(quant_intro,[status(thm)],[24])).
% 2.07/1.57 tff(26,plain,
% 2.07/1.57 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(27,plain,
% 2.07/1.57 (^[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)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp28) <=> ((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite(((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp28) <=> (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.07/1.57 inference(bind,[status(th)],[])).
% 2.07/1.57 tff(28,plain,
% 2.07/1.57 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp28) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(quant_intro,[status(thm)],[27])).
% 2.07/1.57 tff(29,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 2.07/1.57 tff(30,plain,
% 2.07/1.57 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[29, 28])).
% 2.07/1.57 tff(31,plain,
% 2.07/1.57 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[30, 26])).
% 2.07/1.57 tff(32,plain,(
% 2.07/1.57 ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(skolemize,[status(sab)],[31])).
% 2.07/1.57 tff(33,plain,
% 2.07/1.57 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[32, 25])).
% 2.07/1.57 tff(34,assumption,(hskp4), introduced(assumption)).
% 2.07/1.57 tff(35,plain,
% 2.07/1.57 (((~hskp4) | (~c1_1(a105))) <=> ((~hskp4) | (~c1_1(a105)))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(36,plain,
% 2.07/1.57 (((~c1_1(a105)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a105)))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(37,axiom,((~c1_1(a105)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 2.07/1.57 tff(38,plain,
% 2.07/1.57 ((~hskp4) | (~c1_1(a105))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[37, 36])).
% 2.07/1.57 tff(39,plain,
% 2.07/1.57 ((~hskp4) | (~c1_1(a105))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[38, 35])).
% 2.07/1.57 tff(40,plain,
% 2.07/1.57 (~c1_1(a105)),
% 2.07/1.57 inference(unit_resolution,[status(thm)],[39, 34])).
% 2.07/1.57 tff(41,plain,
% 2.07/1.57 (((~hskp4) | c3_1(a105)) <=> ((~hskp4) | c3_1(a105))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(42,axiom,((~hskp4) | c3_1(a105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 2.07/1.57 tff(43,plain,
% 2.07/1.57 ((~hskp4) | c3_1(a105)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[42, 41])).
% 2.07/1.57 tff(44,plain,
% 2.07/1.57 ((~hskp4) | c3_1(a105)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[43, 41])).
% 2.07/1.57 tff(45,plain,
% 2.07/1.57 ((~hskp4) | c3_1(a105)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[44, 41])).
% 2.07/1.57 tff(46,plain,
% 2.07/1.57 ((~hskp4) | c3_1(a105)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[45, 41])).
% 2.07/1.57 tff(47,plain,
% 2.07/1.57 ((~hskp4) | c3_1(a105)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[46, 41])).
% 2.07/1.57 tff(48,plain,
% 2.07/1.57 ((~hskp4) | c3_1(a105)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[47, 41])).
% 2.07/1.57 tff(49,plain,
% 2.07/1.57 ((~hskp4) | c3_1(a105)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[48, 41])).
% 2.07/1.57 tff(50,plain,
% 2.07/1.57 ((~hskp4) | c3_1(a105)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[49, 41])).
% 2.07/1.57 tff(51,plain,
% 2.07/1.57 (c3_1(a105)),
% 2.07/1.57 inference(unit_resolution,[status(thm)],[50, 34])).
% 2.07/1.57 tff(52,assumption,(~c1_1(a163)), introduced(assumption)).
% 2.07/1.57 tff(53,assumption,(hskp31), introduced(assumption)).
% 2.07/1.57 tff(54,plain,
% 2.07/1.57 (((~hskp31) | c3_1(a141)) <=> ((~hskp31) | c3_1(a141))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(55,axiom,((~hskp31) | c3_1(a141)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 2.07/1.57 tff(56,plain,
% 2.07/1.57 ((~hskp31) | c3_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[55, 54])).
% 2.07/1.57 tff(57,plain,
% 2.07/1.57 ((~hskp31) | c3_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[56, 54])).
% 2.07/1.57 tff(58,plain,
% 2.07/1.57 ((~hskp31) | c3_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[57, 54])).
% 2.07/1.57 tff(59,plain,
% 2.07/1.57 ((~hskp31) | c3_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[58, 54])).
% 2.07/1.57 tff(60,plain,
% 2.07/1.57 ((~hskp31) | c3_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[59, 54])).
% 2.07/1.57 tff(61,plain,
% 2.07/1.57 ((~hskp31) | c3_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[60, 54])).
% 2.07/1.57 tff(62,plain,
% 2.07/1.57 ((~hskp31) | c3_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[61, 54])).
% 2.07/1.57 tff(63,plain,
% 2.07/1.57 ((~hskp31) | c3_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[62, 54])).
% 2.07/1.57 tff(64,plain,
% 2.07/1.57 (c3_1(a141)),
% 2.07/1.57 inference(unit_resolution,[status(thm)],[63, 53])).
% 2.07/1.57 tff(65,plain,
% 2.07/1.57 (((~hskp31) | c1_1(a141)) <=> ((~hskp31) | c1_1(a141))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(66,axiom,((~hskp31) | c1_1(a141)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 2.07/1.57 tff(67,plain,
% 2.07/1.57 ((~hskp31) | c1_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[66, 65])).
% 2.07/1.57 tff(68,plain,
% 2.07/1.57 ((~hskp31) | c1_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[67, 65])).
% 2.07/1.57 tff(69,plain,
% 2.07/1.57 ((~hskp31) | c1_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[68, 65])).
% 2.07/1.57 tff(70,plain,
% 2.07/1.57 ((~hskp31) | c1_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[69, 65])).
% 2.07/1.57 tff(71,plain,
% 2.07/1.57 ((~hskp31) | c1_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[70, 65])).
% 2.07/1.57 tff(72,plain,
% 2.07/1.57 ((~hskp31) | c1_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[71, 65])).
% 2.07/1.57 tff(73,plain,
% 2.07/1.57 ((~hskp31) | c1_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[72, 65])).
% 2.07/1.57 tff(74,plain,
% 2.07/1.57 ((~hskp31) | c1_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[73, 65])).
% 2.07/1.57 tff(75,plain,
% 2.07/1.57 (c1_1(a141)),
% 2.07/1.57 inference(unit_resolution,[status(thm)],[74, 53])).
% 2.07/1.57 tff(76,plain,
% 2.07/1.57 (((~hskp31) | c0_1(a141)) <=> ((~hskp31) | c0_1(a141))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(77,axiom,((~hskp31) | c0_1(a141)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 2.07/1.57 tff(78,plain,
% 2.07/1.57 ((~hskp31) | c0_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[77, 76])).
% 2.07/1.57 tff(79,plain,
% 2.07/1.57 ((~hskp31) | c0_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[78, 76])).
% 2.07/1.57 tff(80,plain,
% 2.07/1.57 ((~hskp31) | c0_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[79, 76])).
% 2.07/1.57 tff(81,plain,
% 2.07/1.57 ((~hskp31) | c0_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[80, 76])).
% 2.07/1.57 tff(82,plain,
% 2.07/1.57 ((~hskp31) | c0_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[81, 76])).
% 2.07/1.57 tff(83,plain,
% 2.07/1.57 ((~hskp31) | c0_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[82, 76])).
% 2.07/1.57 tff(84,plain,
% 2.07/1.57 ((~hskp31) | c0_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[83, 76])).
% 2.07/1.57 tff(85,plain,
% 2.07/1.57 ((~hskp31) | c0_1(a141)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[84, 76])).
% 2.07/1.57 tff(86,plain,
% 2.07/1.57 (c0_1(a141)),
% 2.07/1.57 inference(unit_resolution,[status(thm)],[85, 53])).
% 2.07/1.57 tff(87,plain,
% 2.07/1.57 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 2.07/1.57 inference(bind,[status(th)],[])).
% 2.07/1.57 tff(88,plain,
% 2.07/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.57 inference(quant_intro,[status(thm)],[87])).
% 2.07/1.57 tff(89,plain,
% 2.07/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(90,plain,
% 2.07/1.57 (^[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))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 2.07/1.57 inference(bind,[status(th)],[])).
% 2.07/1.57 tff(91,plain,
% 2.07/1.57 (![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))) | (~c3_1(W))) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.57 inference(quant_intro,[status(thm)],[90])).
% 2.07/1.57 tff(92,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))) | (~c3_1(W))) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 2.07/1.57 tff(93,plain,
% 2.07/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[92, 91])).
% 2.07/1.57 tff(94,plain,
% 2.07/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[93, 89])).
% 2.07/1.57 tff(95,plain,(
% 2.07/1.57 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.57 inference(skolemize,[status(sab)],[94])).
% 2.07/1.57 tff(96,plain,
% 2.07/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[95, 88])).
% 2.07/1.57 tff(97,assumption,(~c3_1(a163)), introduced(assumption)).
% 2.07/1.57 tff(98,assumption,(~c2_1(a163)), introduced(assumption)).
% 2.07/1.57 tff(99,plain,
% 2.07/1.57 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)))),
% 2.07/1.57 inference(bind,[status(th)],[])).
% 2.07/1.57 tff(100,plain,
% 2.07/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.07/1.57 inference(quant_intro,[status(thm)],[99])).
% 2.07/1.57 tff(101,plain,
% 2.07/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(102,plain,
% 2.07/1.57 (^[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))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_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) | (~c1_1(U)) | (~c3_1(U)) | (~c2_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) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_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)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | 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)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | 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)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_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)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))))),
% 2.07/1.57 inference(bind,[status(th)],[])).
% 2.07/1.57 tff(103,plain,
% 2.07/1.57 (![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)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.07/1.57 inference(quant_intro,[status(thm)],[102])).
% 2.07/1.57 tff(104,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)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause192')).
% 2.07/1.57 tff(105,plain,
% 2.07/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[104, 103])).
% 2.07/1.57 tff(106,plain,
% 2.07/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[105, 101])).
% 2.07/1.57 tff(107,plain,(
% 2.07/1.57 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.07/1.57 inference(skolemize,[status(sab)],[106])).
% 2.07/1.57 tff(108,plain,
% 2.07/1.57 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[107, 100])).
% 2.07/1.57 tff(109,assumption,(~c2_1(a106)), introduced(assumption)).
% 2.07/1.57 tff(110,assumption,(c0_1(a163)), introduced(assumption)).
% 2.07/1.57 tff(111,plain,
% 2.07/1.57 (^[U: $i] : refl((hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 2.07/1.57 inference(bind,[status(th)],[])).
% 2.07/1.57 tff(112,plain,
% 2.07/1.57 (![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.07/1.57 inference(quant_intro,[status(thm)],[111])).
% 2.07/1.57 tff(113,plain,
% 2.07/1.57 (![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(114,plain,
% 2.07/1.57 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp8))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp8) <=> (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8) <=> (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 2.07/1.57 inference(bind,[status(th)],[])).
% 2.07/1.57 tff(115,plain,
% 2.07/1.57 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8) <=> ![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.07/1.57 inference(quant_intro,[status(thm)],[114])).
% 2.07/1.57 tff(116,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp19) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 2.07/1.57 tff(117,plain,
% 2.07/1.57 (![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[116, 115])).
% 2.07/1.57 tff(118,plain,
% 2.07/1.57 (![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[117, 113])).
% 2.07/1.57 tff(119,plain,(
% 2.07/1.57 ![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.07/1.57 inference(skolemize,[status(sab)],[118])).
% 2.07/1.57 tff(120,plain,
% 2.07/1.57 (![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[119, 112])).
% 2.07/1.57 tff(121,assumption,(~ndr1_0), introduced(assumption)).
% 2.07/1.57 tff(122,plain,
% 2.07/1.57 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(123,plain,
% 2.07/1.57 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(124,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause9')).
% 2.07/1.57 tff(125,plain,
% 2.07/1.57 (ndr1_0 | (~hskp24)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[124, 123])).
% 2.07/1.57 tff(126,plain,
% 2.07/1.57 (ndr1_0 | (~hskp24)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[125, 122])).
% 2.07/1.57 tff(127,plain,
% 2.07/1.57 (~hskp24),
% 2.07/1.57 inference(unit_resolution,[status(thm)],[126, 121])).
% 2.07/1.57 tff(128,plain,
% 2.07/1.57 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(129,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 2.07/1.57 tff(130,plain,
% 2.07/1.57 ((~hskp31) | ndr1_0),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[129, 128])).
% 2.07/1.57 tff(131,plain,
% 2.07/1.57 ((~hskp31) | ndr1_0),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[130, 128])).
% 2.07/1.57 tff(132,plain,
% 2.07/1.57 ((~hskp31) | ndr1_0),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[131, 128])).
% 2.07/1.57 tff(133,plain,
% 2.07/1.57 ((~hskp31) | ndr1_0),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[132, 128])).
% 2.07/1.57 tff(134,plain,
% 2.07/1.57 ((~hskp31) | ndr1_0),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[133, 128])).
% 2.07/1.57 tff(135,plain,
% 2.07/1.57 ((~hskp31) | ndr1_0),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[134, 128])).
% 2.07/1.57 tff(136,plain,
% 2.07/1.57 ((~hskp31) | ndr1_0),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[135, 128])).
% 2.07/1.57 tff(137,plain,
% 2.07/1.57 ((~hskp31) | ndr1_0),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[136, 128])).
% 2.07/1.57 tff(138,plain,
% 2.07/1.57 (~hskp31),
% 2.07/1.57 inference(unit_resolution,[status(thm)],[137, 121])).
% 2.07/1.57 tff(139,plain,
% 2.07/1.57 ((ndr1_0 | (~hskp30)) <=> (ndr1_0 | (~hskp30))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(140,plain,
% 2.07/1.57 (((~hskp30) | ndr1_0) <=> (ndr1_0 | (~hskp30))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(141,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 2.07/1.57 tff(142,plain,
% 2.07/1.57 (ndr1_0 | (~hskp30)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[141, 140])).
% 2.07/1.57 tff(143,plain,
% 2.07/1.57 (ndr1_0 | (~hskp30)),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[142, 139])).
% 2.07/1.57 tff(144,plain,
% 2.07/1.57 (~hskp30),
% 2.07/1.57 inference(unit_resolution,[status(thm)],[143, 121])).
% 2.07/1.57 tff(145,plain,
% 2.07/1.57 ((hskp31 | hskp30 | hskp24) <=> (hskp31 | hskp30 | hskp24)),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(146,plain,
% 2.07/1.57 (((hskp31 | hskp30) | hskp24) <=> (hskp31 | hskp30 | hskp24)),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(147,plain,
% 2.07/1.57 ((hskp31 | hskp30) <=> (hskp31 | hskp30)),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(148,plain,
% 2.07/1.57 (((hskp31 | hskp30) | hskp24) <=> ((hskp31 | hskp30) | hskp24)),
% 2.07/1.57 inference(monotonicity,[status(thm)],[147])).
% 2.07/1.57 tff(149,plain,
% 2.07/1.57 (((hskp31 | hskp30) | hskp24) <=> (hskp31 | hskp30 | hskp24)),
% 2.07/1.57 inference(transitivity,[status(thm)],[148, 146])).
% 2.07/1.57 tff(150,axiom,((hskp31 | hskp30) | hskp24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 2.07/1.57 tff(151,plain,
% 2.07/1.57 (hskp31 | hskp30 | hskp24),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[150, 149])).
% 2.07/1.57 tff(152,plain,
% 2.07/1.57 (hskp31 | hskp30 | hskp24),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[151, 145])).
% 2.07/1.57 tff(153,plain,
% 2.07/1.57 (hskp31 | hskp30 | hskp24),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[152, 145])).
% 2.07/1.57 tff(154,plain,
% 2.07/1.57 (hskp31 | hskp30 | hskp24),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[153, 145])).
% 2.07/1.57 tff(155,plain,
% 2.07/1.57 (hskp31 | hskp30 | hskp24),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[154, 145])).
% 2.07/1.57 tff(156,plain,
% 2.07/1.57 (hskp31 | hskp30 | hskp24),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[155, 145])).
% 2.07/1.57 tff(157,plain,
% 2.07/1.57 (hskp31 | hskp30 | hskp24),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[156, 145])).
% 2.07/1.57 tff(158,plain,
% 2.07/1.57 (hskp31 | hskp30 | hskp24),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[157, 145])).
% 2.07/1.57 tff(159,plain,
% 2.07/1.57 ($false),
% 2.07/1.57 inference(unit_resolution,[status(thm)],[158, 144, 138, 127])).
% 2.07/1.57 tff(160,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 2.07/1.57 tff(161,plain,
% 2.07/1.57 (((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp8 | hskp19 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp8 | hskp19 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(162,plain,
% 2.07/1.57 ((hskp8 | hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c0_1(a163))) <=> (hskp8 | hskp19 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(163,plain,
% 2.07/1.57 (((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp8 | hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp8 | hskp19 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163))))),
% 2.07/1.57 inference(monotonicity,[status(thm)],[162])).
% 2.07/1.57 tff(164,plain,
% 2.07/1.57 (((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp8 | hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp8 | hskp19 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 2.07/1.57 inference(transitivity,[status(thm)],[163, 161])).
% 2.07/1.57 tff(165,plain,
% 2.07/1.57 ((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp8 | hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c0_1(a163)))),
% 2.07/1.57 inference(quant_inst,[status(thm)],[])).
% 2.07/1.57 tff(166,plain,
% 2.07/1.57 ((~![U: $i] : (hskp8 | hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp8 | hskp19 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[165, 164])).
% 2.07/1.57 tff(167,plain,
% 2.07/1.57 (hskp8 | hskp19 | (~c0_1(a163))),
% 2.07/1.57 inference(unit_resolution,[status(thm)],[166, 160, 98, 97, 120])).
% 2.07/1.57 tff(168,plain,
% 2.07/1.57 (hskp8),
% 2.07/1.57 inference(unit_resolution,[status(thm)],[167, 1, 110])).
% 2.07/1.57 tff(169,plain,
% 2.07/1.57 (((~hskp8) | (~c3_1(a109))) <=> ((~hskp8) | (~c3_1(a109)))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(170,plain,
% 2.07/1.57 (((~c3_1(a109)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a109)))),
% 2.07/1.57 inference(rewrite,[status(thm)],[])).
% 2.07/1.57 tff(171,axiom,((~c3_1(a109)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 2.07/1.57 tff(172,plain,
% 2.07/1.57 ((~hskp8) | (~c3_1(a109))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[171, 170])).
% 2.07/1.57 tff(173,plain,
% 2.07/1.57 ((~hskp8) | (~c3_1(a109))),
% 2.07/1.57 inference(modus_ponens,[status(thm)],[172, 169])).
% 2.07/1.57 tff(174,plain,
% 2.07/1.57 (~c3_1(a109)),
% 2.07/1.57 inference(unit_resolution,[status(thm)],[173, 168])).
% 2.07/1.58 tff(175,plain,
% 2.07/1.58 (((~hskp8) | c1_1(a109)) <=> ((~hskp8) | c1_1(a109))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(176,axiom,((~hskp8) | c1_1(a109)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 2.07/1.58 tff(177,plain,
% 2.07/1.58 ((~hskp8) | c1_1(a109)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[176, 175])).
% 2.07/1.58 tff(178,plain,
% 2.07/1.58 ((~hskp8) | c1_1(a109)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[177, 175])).
% 2.07/1.58 tff(179,plain,
% 2.07/1.58 ((~hskp8) | c1_1(a109)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[178, 175])).
% 2.07/1.58 tff(180,plain,
% 2.07/1.58 ((~hskp8) | c1_1(a109)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[179, 175])).
% 2.07/1.58 tff(181,plain,
% 2.07/1.58 ((~hskp8) | c1_1(a109)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[180, 175])).
% 2.07/1.58 tff(182,plain,
% 2.07/1.58 ((~hskp8) | c1_1(a109)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[181, 175])).
% 2.07/1.58 tff(183,plain,
% 2.07/1.58 ((~hskp8) | c1_1(a109)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[182, 175])).
% 2.07/1.58 tff(184,plain,
% 2.07/1.58 ((~hskp8) | c1_1(a109)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[183, 175])).
% 2.07/1.58 tff(185,plain,
% 2.07/1.58 (c1_1(a109)),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[184, 168])).
% 2.07/1.58 tff(186,plain,
% 2.07/1.58 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c3_1(a109) | (~ndr1_0) | c2_1(a109) | (~c1_1(a109)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a109) | (~ndr1_0) | c2_1(a109) | (~c1_1(a109)))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(187,plain,
% 2.07/1.58 ((hskp19 | (~ndr1_0) | c3_1(a109) | c2_1(a109) | (~c1_1(a109))) <=> (hskp19 | c3_1(a109) | (~ndr1_0) | c2_1(a109) | (~c1_1(a109)))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(188,plain,
% 2.07/1.58 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a109) | c2_1(a109) | (~c1_1(a109)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c3_1(a109) | (~ndr1_0) | c2_1(a109) | (~c1_1(a109))))),
% 2.07/1.58 inference(monotonicity,[status(thm)],[187])).
% 2.07/1.58 tff(189,plain,
% 2.07/1.58 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a109) | c2_1(a109) | (~c1_1(a109)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a109) | (~ndr1_0) | c2_1(a109) | (~c1_1(a109)))),
% 2.07/1.58 inference(transitivity,[status(thm)],[188, 186])).
% 2.07/1.58 tff(190,plain,
% 2.07/1.58 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a109) | c2_1(a109) | (~c1_1(a109)))),
% 2.07/1.58 inference(quant_inst,[status(thm)],[])).
% 2.07/1.58 tff(191,plain,
% 2.07/1.58 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a109) | (~ndr1_0) | c2_1(a109) | (~c1_1(a109))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[190, 189])).
% 2.07/1.58 tff(192,plain,
% 2.07/1.58 (c2_1(a109)),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[191, 160, 1, 185, 174, 11])).
% 2.07/1.58 tff(193,plain,
% 2.07/1.58 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 2.07/1.58 inference(bind,[status(th)],[])).
% 2.07/1.58 tff(194,plain,
% 2.07/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.07/1.58 inference(quant_intro,[status(thm)],[193])).
% 2.07/1.58 tff(195,plain,
% 2.07/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(196,plain,
% 2.07/1.58 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c0_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 2.07/1.58 inference(bind,[status(th)],[])).
% 2.07/1.58 tff(197,plain,
% 2.07/1.58 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.07/1.58 inference(quant_intro,[status(thm)],[196])).
% 2.07/1.58 tff(198,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 2.07/1.58 tff(199,plain,
% 2.07/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[198, 197])).
% 2.07/1.58 tff(200,plain,
% 2.07/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[199, 195])).
% 2.07/1.58 tff(201,plain,(
% 2.07/1.58 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.07/1.58 inference(skolemize,[status(sab)],[200])).
% 2.07/1.58 tff(202,plain,
% 2.07/1.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[201, 194])).
% 2.07/1.58 tff(203,plain,
% 2.07/1.58 (((~hskp8) | (~c0_1(a109))) <=> ((~hskp8) | (~c0_1(a109)))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(204,plain,
% 2.07/1.58 (((~c0_1(a109)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a109)))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(205,axiom,((~c0_1(a109)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 2.07/1.58 tff(206,plain,
% 2.07/1.58 ((~hskp8) | (~c0_1(a109))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[205, 204])).
% 2.07/1.58 tff(207,plain,
% 2.07/1.58 ((~hskp8) | (~c0_1(a109))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[206, 203])).
% 2.07/1.58 tff(208,plain,
% 2.07/1.58 (~c0_1(a109)),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[207, 168])).
% 2.07/1.58 tff(209,plain,
% 2.07/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c2_1(a109)) | (~c1_1(a109)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c2_1(a109)) | (~c1_1(a109)) | (~c0_1(a163)))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(210,plain,
% 2.07/1.58 (((~ndr1_0) | c3_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109))) <=> (c2_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c2_1(a109)) | (~c1_1(a109)) | (~c0_1(a163)))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(211,plain,
% 2.07/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c2_1(a109)) | (~c1_1(a109)) | (~c0_1(a163))))),
% 2.07/1.58 inference(monotonicity,[status(thm)],[210])).
% 2.07/1.58 tff(212,plain,
% 2.07/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c2_1(a109)) | (~c1_1(a109)) | (~c0_1(a163)))),
% 2.07/1.58 inference(transitivity,[status(thm)],[211, 209])).
% 2.07/1.58 tff(213,plain,
% 2.07/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109)))),
% 2.07/1.58 inference(quant_inst,[status(thm)],[])).
% 2.07/1.58 tff(214,plain,
% 2.07/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c2_1(a109)) | (~c1_1(a109)) | (~c0_1(a163))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[213, 212])).
% 2.07/1.58 tff(215,plain,
% 2.07/1.58 ($false),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[214, 160, 185, 98, 97, 208, 174, 202, 110, 192])).
% 2.07/1.58 tff(216,plain,(hskp19 | c2_1(a163) | c3_1(a163) | (~c0_1(a163))), inference(lemma,lemma(discharge,[]))).
% 2.07/1.58 tff(217,plain,
% 2.07/1.58 (~c0_1(a163)),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[216, 1, 97, 98])).
% 2.07/1.58 tff(218,plain,
% 2.07/1.58 (^[U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 2.07/1.58 inference(bind,[status(th)],[])).
% 2.07/1.58 tff(219,plain,
% 2.07/1.58 (![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.58 inference(quant_intro,[status(thm)],[218])).
% 2.07/1.58 tff(220,plain,
% 2.07/1.58 (![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(221,plain,
% 2.07/1.58 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 2.07/1.58 inference(bind,[status(th)],[])).
% 2.07/1.58 tff(222,plain,
% 2.07/1.58 (![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp5) <=> ![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.58 inference(quant_intro,[status(thm)],[221])).
% 2.07/1.58 tff(223,axiom,(![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 2.07/1.58 tff(224,plain,
% 2.07/1.58 (![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[223, 222])).
% 2.07/1.58 tff(225,plain,
% 2.07/1.58 (![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[224, 220])).
% 2.07/1.58 tff(226,plain,(
% 2.07/1.58 ![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.58 inference(skolemize,[status(sab)],[225])).
% 2.07/1.58 tff(227,plain,
% 2.07/1.58 (![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[226, 219])).
% 2.07/1.58 tff(228,plain,
% 2.07/1.58 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(229,plain,
% 2.07/1.58 ((hskp5 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (hskp5 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(230,plain,
% 2.07/1.58 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163)))),
% 2.07/1.58 inference(monotonicity,[status(thm)],[229])).
% 2.07/1.58 tff(231,plain,
% 2.07/1.58 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 2.07/1.58 inference(transitivity,[status(thm)],[230, 228])).
% 2.07/1.58 tff(232,plain,
% 2.07/1.58 ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 2.07/1.58 inference(quant_inst,[status(thm)],[])).
% 2.07/1.58 tff(233,plain,
% 2.07/1.58 ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[232, 231])).
% 2.07/1.58 tff(234,plain,
% 2.07/1.58 (hskp5 | c3_1(a163) | c0_1(a163)),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[233, 160, 52, 227])).
% 2.07/1.58 tff(235,plain,
% 2.07/1.58 (hskp5),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[234, 217, 97])).
% 2.07/1.58 tff(236,assumption,(c1_1(a106)), introduced(assumption)).
% 2.07/1.58 tff(237,plain,
% 2.07/1.58 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a106) | (~ndr1_0) | c3_1(a106) | (~c1_1(a106)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a106) | (~ndr1_0) | c3_1(a106) | (~c1_1(a106)))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(238,plain,
% 2.07/1.58 ((hskp19 | (~ndr1_0) | c3_1(a106) | c2_1(a106) | (~c1_1(a106))) <=> (hskp19 | c2_1(a106) | (~ndr1_0) | c3_1(a106) | (~c1_1(a106)))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(239,plain,
% 2.07/1.58 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a106) | c2_1(a106) | (~c1_1(a106)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a106) | (~ndr1_0) | c3_1(a106) | (~c1_1(a106))))),
% 2.07/1.58 inference(monotonicity,[status(thm)],[238])).
% 2.07/1.58 tff(240,plain,
% 2.07/1.58 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a106) | c2_1(a106) | (~c1_1(a106)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a106) | (~ndr1_0) | c3_1(a106) | (~c1_1(a106)))),
% 2.07/1.58 inference(transitivity,[status(thm)],[239, 237])).
% 2.07/1.58 tff(241,plain,
% 2.07/1.58 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a106) | c2_1(a106) | (~c1_1(a106)))),
% 2.07/1.58 inference(quant_inst,[status(thm)],[])).
% 2.07/1.58 tff(242,plain,
% 2.07/1.58 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a106) | (~ndr1_0) | c3_1(a106) | (~c1_1(a106))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[241, 240])).
% 2.07/1.58 tff(243,plain,
% 2.07/1.58 (hskp19 | c3_1(a106)),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[242, 160, 236, 109, 11])).
% 2.07/1.58 tff(244,plain,
% 2.07/1.58 (c3_1(a106)),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[243, 1])).
% 2.07/1.58 tff(245,assumption,(~c0_1(a163)), introduced(assumption)).
% 2.07/1.58 tff(246,plain,
% 2.07/1.58 (hskp5 | c0_1(a163)),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[233, 160, 52, 97, 227])).
% 2.07/1.58 tff(247,plain,
% 2.07/1.58 (hskp5),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[246, 245])).
% 2.07/1.58 tff(248,plain,
% 2.07/1.58 (((~hskp5) | c1_1(a106)) <=> ((~hskp5) | c1_1(a106))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(249,axiom,((~hskp5) | c1_1(a106)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 2.07/1.58 tff(250,plain,
% 2.07/1.58 ((~hskp5) | c1_1(a106)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[249, 248])).
% 2.07/1.58 tff(251,plain,
% 2.07/1.58 ((~hskp5) | c1_1(a106)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[250, 248])).
% 2.07/1.58 tff(252,plain,
% 2.07/1.58 ((~hskp5) | c1_1(a106)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[251, 248])).
% 2.07/1.58 tff(253,plain,
% 2.07/1.58 ((~hskp5) | c1_1(a106)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[252, 248])).
% 2.07/1.58 tff(254,plain,
% 2.07/1.58 ((~hskp5) | c1_1(a106)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[253, 248])).
% 2.07/1.58 tff(255,plain,
% 2.07/1.58 ((~hskp5) | c1_1(a106)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[254, 248])).
% 2.07/1.58 tff(256,plain,
% 2.07/1.58 ((~hskp5) | c1_1(a106)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[255, 248])).
% 2.07/1.58 tff(257,plain,
% 2.07/1.58 ((~hskp5) | c1_1(a106)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[256, 248])).
% 2.07/1.58 tff(258,plain,
% 2.07/1.58 (c1_1(a106)),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[257, 247])).
% 2.07/1.58 tff(259,plain,
% 2.07/1.58 (hskp19 | c3_1(a106) | (~c1_1(a106))),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[242, 160, 109, 11])).
% 2.07/1.58 tff(260,plain,
% 2.07/1.58 (c3_1(a106)),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[259, 1, 258])).
% 2.07/1.58 tff(261,plain,
% 2.07/1.58 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 2.07/1.58 inference(bind,[status(th)],[])).
% 2.07/1.58 tff(262,plain,
% 2.07/1.58 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.07/1.58 inference(quant_intro,[status(thm)],[261])).
% 2.07/1.58 tff(263,plain,
% 2.07/1.58 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(264,plain,
% 2.07/1.58 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 2.07/1.58 inference(bind,[status(th)],[])).
% 2.07/1.58 tff(265,plain,
% 2.07/1.58 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.07/1.58 inference(quant_intro,[status(thm)],[264])).
% 2.07/1.58 tff(266,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 2.07/1.58 tff(267,plain,
% 2.07/1.58 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[266, 265])).
% 2.07/1.58 tff(268,plain,
% 2.07/1.58 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[267, 263])).
% 2.07/1.58 tff(269,plain,(
% 2.07/1.58 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.07/1.58 inference(skolemize,[status(sab)],[268])).
% 2.07/1.58 tff(270,plain,
% 2.07/1.58 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[269, 262])).
% 2.07/1.58 tff(271,plain,
% 2.07/1.58 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(272,plain,
% 2.07/1.58 ((hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a163) | c1_1(a163) | c0_1(a163)) <=> (hskp2 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(273,plain,
% 2.07/1.58 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163)))),
% 2.07/1.58 inference(monotonicity,[status(thm)],[272])).
% 2.07/1.58 tff(274,plain,
% 2.07/1.58 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163))),
% 2.07/1.58 inference(transitivity,[status(thm)],[273, 271])).
% 2.07/1.58 tff(275,plain,
% 2.07/1.58 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a163) | c1_1(a163) | c0_1(a163))),
% 2.07/1.58 inference(quant_inst,[status(thm)],[])).
% 2.07/1.58 tff(276,plain,
% 2.07/1.58 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[275, 274])).
% 2.07/1.58 tff(277,plain,
% 2.07/1.58 (hskp2 | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a163)),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[276, 160, 52, 98, 109, 270])).
% 2.07/1.58 tff(278,plain,
% 2.07/1.58 (hskp2),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[277, 260, 258, 245])).
% 2.07/1.58 tff(279,plain,
% 2.07/1.58 (((~hskp2) | c1_1(a103)) <=> ((~hskp2) | c1_1(a103))),
% 2.07/1.58 inference(rewrite,[status(thm)],[])).
% 2.07/1.58 tff(280,axiom,((~hskp2) | c1_1(a103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 2.07/1.58 tff(281,plain,
% 2.07/1.58 ((~hskp2) | c1_1(a103)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[280, 279])).
% 2.07/1.58 tff(282,plain,
% 2.07/1.58 ((~hskp2) | c1_1(a103)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[281, 279])).
% 2.07/1.58 tff(283,plain,
% 2.07/1.58 ((~hskp2) | c1_1(a103)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[282, 279])).
% 2.07/1.58 tff(284,plain,
% 2.07/1.58 ((~hskp2) | c1_1(a103)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[283, 279])).
% 2.07/1.58 tff(285,plain,
% 2.07/1.58 ((~hskp2) | c1_1(a103)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[284, 279])).
% 2.07/1.58 tff(286,plain,
% 2.07/1.58 ((~hskp2) | c1_1(a103)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[285, 279])).
% 2.07/1.58 tff(287,plain,
% 2.07/1.58 ((~hskp2) | c1_1(a103)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[286, 279])).
% 2.07/1.58 tff(288,plain,
% 2.07/1.58 ((~hskp2) | c1_1(a103)),
% 2.07/1.58 inference(modus_ponens,[status(thm)],[287, 279])).
% 2.07/1.58 tff(289,plain,
% 2.07/1.58 (c1_1(a103)),
% 2.07/1.58 inference(unit_resolution,[status(thm)],[288, 278])).
% 2.07/1.58 tff(290,assumption,(~c3_1(a103)), introduced(assumption)).
% 2.07/1.58 tff(291,plain,
% 2.07/1.58 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(292,plain,
% 2.07/1.59 ((hskp19 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103))) <=> (hskp19 | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(293,plain,
% 2.07/1.59 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103))))),
% 2.07/1.59 inference(monotonicity,[status(thm)],[292])).
% 2.07/1.59 tff(294,plain,
% 2.07/1.59 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)))),
% 2.07/1.59 inference(transitivity,[status(thm)],[293, 291])).
% 2.07/1.59 tff(295,plain,
% 2.07/1.59 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)))),
% 2.07/1.59 inference(quant_inst,[status(thm)],[])).
% 2.07/1.59 tff(296,plain,
% 2.07/1.59 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[295, 294])).
% 2.07/1.59 tff(297,plain,
% 2.07/1.59 (hskp19 | c2_1(a103) | (~c1_1(a103))),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[296, 160, 290, 11])).
% 2.07/1.59 tff(298,plain,
% 2.07/1.59 (c2_1(a103)),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[297, 289, 1])).
% 2.07/1.59 tff(299,plain,
% 2.07/1.59 (((~hskp2) | c0_1(a103)) <=> ((~hskp2) | c0_1(a103))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(300,axiom,((~hskp2) | c0_1(a103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 2.07/1.59 tff(301,plain,
% 2.07/1.59 ((~hskp2) | c0_1(a103)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[300, 299])).
% 2.07/1.59 tff(302,plain,
% 2.07/1.59 ((~hskp2) | c0_1(a103)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[301, 299])).
% 2.07/1.59 tff(303,plain,
% 2.07/1.59 ((~hskp2) | c0_1(a103)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[302, 299])).
% 2.07/1.59 tff(304,plain,
% 2.07/1.59 ((~hskp2) | c0_1(a103)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[303, 299])).
% 2.07/1.59 tff(305,plain,
% 2.07/1.59 ((~hskp2) | c0_1(a103)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[304, 299])).
% 2.07/1.59 tff(306,plain,
% 2.07/1.59 ((~hskp2) | c0_1(a103)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[305, 299])).
% 2.07/1.59 tff(307,plain,
% 2.07/1.59 ((~hskp2) | c0_1(a103)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[306, 299])).
% 2.07/1.59 tff(308,plain,
% 2.07/1.59 ((~hskp2) | c0_1(a103)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[307, 299])).
% 2.07/1.59 tff(309,plain,
% 2.07/1.59 (c0_1(a103)),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[308, 278])).
% 2.07/1.59 tff(310,assumption,(c3_1(a106)), introduced(assumption)).
% 2.07/1.59 tff(311,plain,
% 2.07/1.59 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))))),
% 2.07/1.59 inference(bind,[status(th)],[])).
% 2.07/1.59 tff(312,plain,
% 2.07/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_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) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 2.07/1.59 inference(quant_intro,[status(thm)],[311])).
% 2.07/1.59 tff(313,plain,
% 2.07/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_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) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(314,plain,
% 2.07/1.59 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_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) | (~c1_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) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))))),
% 2.07/1.59 inference(bind,[status(th)],[])).
% 2.07/1.59 tff(315,plain,
% 2.07/1.59 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 2.07/1.59 inference(quant_intro,[status(thm)],[314])).
% 2.07/1.59 tff(316,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 2.07/1.59 tff(317,plain,
% 2.07/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[316, 315])).
% 2.07/1.59 tff(318,plain,
% 2.07/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[317, 313])).
% 2.07/1.59 tff(319,plain,(
% 2.07/1.59 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 2.07/1.59 inference(skolemize,[status(sab)],[318])).
% 2.07/1.59 tff(320,plain,
% 2.07/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[319, 312])).
% 2.07/1.59 tff(321,assumption,(hskp9), introduced(assumption)).
% 2.07/1.59 tff(322,plain,
% 2.07/1.59 (((~hskp9) | (~c1_1(a110))) <=> ((~hskp9) | (~c1_1(a110)))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(323,plain,
% 2.07/1.59 (((~c1_1(a110)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a110)))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(324,axiom,((~c1_1(a110)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 2.07/1.59 tff(325,plain,
% 2.07/1.59 ((~hskp9) | (~c1_1(a110))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[324, 323])).
% 2.07/1.59 tff(326,plain,
% 2.07/1.59 ((~hskp9) | (~c1_1(a110))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[325, 322])).
% 2.07/1.59 tff(327,plain,
% 2.07/1.59 (~c1_1(a110)),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[326, 321])).
% 2.07/1.59 tff(328,plain,
% 2.07/1.59 (((~hskp5) | c0_1(a106)) <=> ((~hskp5) | c0_1(a106))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(329,axiom,((~hskp5) | c0_1(a106)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 2.07/1.59 tff(330,plain,
% 2.07/1.59 ((~hskp5) | c0_1(a106)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[329, 328])).
% 2.07/1.59 tff(331,plain,
% 2.07/1.59 ((~hskp5) | c0_1(a106)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[330, 328])).
% 2.07/1.59 tff(332,plain,
% 2.07/1.59 ((~hskp5) | c0_1(a106)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[331, 328])).
% 2.07/1.59 tff(333,plain,
% 2.07/1.59 ((~hskp5) | c0_1(a106)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[332, 328])).
% 2.07/1.59 tff(334,plain,
% 2.07/1.59 ((~hskp5) | c0_1(a106)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[333, 328])).
% 2.07/1.59 tff(335,plain,
% 2.07/1.59 ((~hskp5) | c0_1(a106)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[334, 328])).
% 2.07/1.59 tff(336,plain,
% 2.07/1.59 ((~hskp5) | c0_1(a106)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[335, 328])).
% 2.07/1.59 tff(337,plain,
% 2.07/1.59 ((~hskp5) | c0_1(a106)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[336, 328])).
% 2.07/1.59 tff(338,plain,
% 2.07/1.59 (c0_1(a106)),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[337, 247])).
% 2.07/1.59 tff(339,plain,
% 2.07/1.59 (((~hskp9) | c2_1(a110)) <=> ((~hskp9) | c2_1(a110))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(340,axiom,((~hskp9) | c2_1(a110)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 2.07/1.59 tff(341,plain,
% 2.07/1.59 ((~hskp9) | c2_1(a110)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[340, 339])).
% 2.07/1.59 tff(342,plain,
% 2.07/1.59 ((~hskp9) | c2_1(a110)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[341, 339])).
% 2.07/1.59 tff(343,plain,
% 2.07/1.59 ((~hskp9) | c2_1(a110)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[342, 339])).
% 2.07/1.59 tff(344,plain,
% 2.07/1.59 ((~hskp9) | c2_1(a110)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[343, 339])).
% 2.07/1.59 tff(345,plain,
% 2.07/1.59 ((~hskp9) | c2_1(a110)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[344, 339])).
% 2.07/1.59 tff(346,plain,
% 2.07/1.59 ((~hskp9) | c2_1(a110)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[345, 339])).
% 2.07/1.59 tff(347,plain,
% 2.07/1.59 ((~hskp9) | c2_1(a110)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[346, 339])).
% 2.07/1.59 tff(348,plain,
% 2.07/1.59 ((~hskp9) | c2_1(a110)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[347, 339])).
% 2.07/1.59 tff(349,plain,
% 2.07/1.59 (c2_1(a110)),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[348, 321])).
% 2.07/1.59 tff(350,plain,
% 2.07/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a110) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c2_1(a110)) | (~c0_1(a110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a110) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c2_1(a110)) | (~c0_1(a110)))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(351,plain,
% 2.07/1.59 (((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c1_1(a110) | (~c0_1(a110)) | (~c2_1(a110))) <=> (c1_1(a110) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c2_1(a110)) | (~c0_1(a110)))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(352,plain,
% 2.07/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c1_1(a110) | (~c0_1(a110)) | (~c2_1(a110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a110) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c2_1(a110)) | (~c0_1(a110))))),
% 2.07/1.59 inference(monotonicity,[status(thm)],[351])).
% 2.07/1.59 tff(353,plain,
% 2.07/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c1_1(a110) | (~c0_1(a110)) | (~c2_1(a110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a110) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c2_1(a110)) | (~c0_1(a110)))),
% 2.07/1.59 inference(transitivity,[status(thm)],[352, 350])).
% 2.07/1.59 tff(354,plain,
% 2.07/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c1_1(a110) | (~c0_1(a110)) | (~c2_1(a110)))),
% 2.07/1.59 inference(quant_inst,[status(thm)],[])).
% 2.07/1.59 tff(355,plain,
% 2.07/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a110) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c2_1(a110)) | (~c0_1(a110))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[354, 353])).
% 2.07/1.59 tff(356,plain,
% 2.07/1.59 (~c0_1(a110)),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[355, 160, 349, 338, 258, 327, 109, 320, 310])).
% 2.07/1.59 tff(357,assumption,(c2_1(a103)), introduced(assumption)).
% 2.07/1.59 tff(358,plain,
% 2.07/1.59 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 2.07/1.59 inference(bind,[status(th)],[])).
% 2.07/1.59 tff(359,plain,
% 2.07/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 2.07/1.59 inference(quant_intro,[status(thm)],[358])).
% 2.07/1.59 tff(360,plain,
% 2.07/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(361,plain,
% 2.07/1.59 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~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))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_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))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_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))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 2.07/1.59 inference(bind,[status(th)],[])).
% 2.07/1.59 tff(362,plain,
% 2.07/1.59 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 2.07/1.59 inference(quant_intro,[status(thm)],[361])).
% 2.07/1.59 tff(363,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 2.07/1.59 tff(364,plain,
% 2.07/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[363, 362])).
% 2.07/1.59 tff(365,plain,
% 2.07/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[364, 360])).
% 2.07/1.59 tff(366,plain,(
% 2.07/1.59 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 2.07/1.59 inference(skolemize,[status(sab)],[365])).
% 2.07/1.59 tff(367,plain,
% 2.07/1.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[366, 359])).
% 2.07/1.59 tff(368,plain,
% 2.07/1.59 (((~hskp9) | (~c3_1(a110))) <=> ((~hskp9) | (~c3_1(a110)))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(369,plain,
% 2.07/1.59 (((~c3_1(a110)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a110)))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(370,axiom,((~c3_1(a110)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 2.07/1.59 tff(371,plain,
% 2.07/1.59 ((~hskp9) | (~c3_1(a110))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[370, 369])).
% 2.07/1.59 tff(372,plain,
% 2.07/1.59 ((~hskp9) | (~c3_1(a110))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[371, 368])).
% 2.07/1.59 tff(373,plain,
% 2.07/1.59 (~c3_1(a110)),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[372, 321])).
% 2.07/1.59 tff(374,assumption,(c0_1(a103)), introduced(assumption)).
% 2.07/1.59 tff(375,plain,
% 2.07/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | c3_1(a163) | c3_1(a110) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a110)) | c0_1(a110) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | c3_1(a163) | c3_1(a110) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a110)) | c0_1(a110) | c0_1(a163))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(376,plain,
% 2.07/1.59 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a110) | c3_1(a110) | (~c2_1(a110)) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (c1_1(a163) | c3_1(a163) | c3_1(a110) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a110)) | c0_1(a110) | c0_1(a163))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(377,plain,
% 2.07/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a110) | c3_1(a110) | (~c2_1(a110)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | c3_1(a163) | c3_1(a110) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a110)) | c0_1(a110) | c0_1(a163)))),
% 2.07/1.59 inference(monotonicity,[status(thm)],[376])).
% 2.07/1.59 tff(378,plain,
% 2.07/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a110) | c3_1(a110) | (~c2_1(a110)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | c3_1(a163) | c3_1(a110) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a110)) | c0_1(a110) | c0_1(a163))),
% 2.07/1.59 inference(transitivity,[status(thm)],[377, 375])).
% 2.07/1.59 tff(379,plain,
% 2.07/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a110) | c3_1(a110) | (~c2_1(a110)) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 2.07/1.59 inference(quant_inst,[status(thm)],[])).
% 2.07/1.59 tff(380,plain,
% 2.07/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | c3_1(a163) | c3_1(a110) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | (~c2_1(a110)) | c0_1(a110) | c0_1(a163)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[379, 378])).
% 2.07/1.59 tff(381,plain,
% 2.07/1.59 ($false),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[380, 160, 349, 374, 52, 97, 373, 290, 367, 245, 357, 356])).
% 2.07/1.59 tff(382,plain,((~hskp9) | (~c0_1(a103)) | c1_1(a163) | c3_1(a163) | c3_1(a103) | c0_1(a163) | (~c2_1(a103)) | c2_1(a106) | (~c3_1(a106))), inference(lemma,lemma(discharge,[]))).
% 2.07/1.59 tff(383,plain,
% 2.07/1.59 (~hskp9),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[382, 309, 52, 97, 290, 245, 298, 109, 260])).
% 2.07/1.59 tff(384,plain,
% 2.07/1.59 (^[U: $i] : refl((hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 2.07/1.59 inference(bind,[status(th)],[])).
% 2.07/1.59 tff(385,plain,
% 2.07/1.59 (![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.59 inference(quant_intro,[status(thm)],[384])).
% 2.07/1.59 tff(386,plain,
% 2.07/1.59 (![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(387,plain,
% 2.07/1.59 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp9) <=> (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 2.07/1.59 inference(bind,[status(th)],[])).
% 2.07/1.59 tff(388,plain,
% 2.07/1.59 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.59 inference(quant_intro,[status(thm)],[387])).
% 2.07/1.59 tff(389,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 2.07/1.59 tff(390,plain,
% 2.07/1.59 (![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[389, 388])).
% 2.07/1.59 tff(391,plain,
% 2.07/1.59 (![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[390, 386])).
% 2.07/1.59 tff(392,plain,(
% 2.07/1.59 ![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.59 inference(skolemize,[status(sab)],[391])).
% 2.07/1.59 tff(393,plain,
% 2.07/1.59 (![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[392, 385])).
% 2.07/1.59 tff(394,plain,
% 2.07/1.59 (((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp8 | hskp9 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))) <=> ((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp8 | hskp9 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(395,plain,
% 2.07/1.59 ((hskp8 | hskp9 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (hskp8 | hskp9 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(396,plain,
% 2.07/1.59 (((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp8 | hskp9 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp8 | hskp9 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163)))),
% 2.07/1.59 inference(monotonicity,[status(thm)],[395])).
% 2.07/1.59 tff(397,plain,
% 2.07/1.59 (((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp8 | hskp9 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp8 | hskp9 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 2.07/1.59 inference(transitivity,[status(thm)],[396, 394])).
% 2.07/1.59 tff(398,plain,
% 2.07/1.59 ((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp8 | hskp9 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 2.07/1.59 inference(quant_inst,[status(thm)],[])).
% 2.07/1.59 tff(399,plain,
% 2.07/1.59 ((~![U: $i] : (hskp8 | hskp9 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp8 | hskp9 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[398, 397])).
% 2.07/1.59 tff(400,plain,
% 2.07/1.59 (hskp8 | hskp9 | c0_1(a163)),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[399, 160, 52, 97, 393])).
% 2.07/1.59 tff(401,plain,
% 2.07/1.59 (hskp8),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[400, 383, 245])).
% 2.07/1.59 tff(402,plain,
% 2.07/1.59 (~c3_1(a109)),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[173, 401])).
% 2.07/1.59 tff(403,plain,
% 2.07/1.59 (c1_1(a109)),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[184, 401])).
% 2.07/1.59 tff(404,plain,
% 2.07/1.59 (c2_1(a109)),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[191, 160, 1, 403, 402, 11])).
% 2.07/1.59 tff(405,plain,
% 2.07/1.59 (~c0_1(a109)),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[207, 401])).
% 2.07/1.59 tff(406,plain,
% 2.07/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(407,plain,
% 2.07/1.59 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (c1_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(408,plain,
% 2.07/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163)))),
% 2.07/1.59 inference(monotonicity,[status(thm)],[407])).
% 2.07/1.59 tff(409,plain,
% 2.07/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))),
% 2.07/1.59 inference(transitivity,[status(thm)],[408, 406])).
% 2.07/1.59 tff(410,plain,
% 2.07/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 2.07/1.59 inference(quant_inst,[status(thm)],[])).
% 2.07/1.59 tff(411,plain,
% 2.07/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | c3_1(a163) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163)),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[410, 409])).
% 2.07/1.59 tff(412,plain,
% 2.07/1.59 ($false),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[411, 160, 309, 52, 97, 405, 402, 290, 367, 245, 298, 404])).
% 2.07/1.59 tff(413,plain,(hskp19 | c1_1(a163) | c3_1(a163) | c3_1(a103) | c0_1(a163) | c2_1(a106) | c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.59 tff(414,plain,
% 2.07/1.59 (c3_1(a103)),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[413, 1, 97, 245, 52, 109, 98])).
% 2.07/1.59 tff(415,plain,
% 2.07/1.59 (((~hskp2) | (~c3_1(a103))) <=> ((~hskp2) | (~c3_1(a103)))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(416,plain,
% 2.07/1.59 (((~c3_1(a103)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a103)))),
% 2.07/1.59 inference(rewrite,[status(thm)],[])).
% 2.07/1.59 tff(417,axiom,((~c3_1(a103)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 2.07/1.59 tff(418,plain,
% 2.07/1.59 ((~hskp2) | (~c3_1(a103))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[417, 416])).
% 2.07/1.59 tff(419,plain,
% 2.07/1.59 ((~hskp2) | (~c3_1(a103))),
% 2.07/1.59 inference(modus_ponens,[status(thm)],[418, 415])).
% 2.07/1.59 tff(420,plain,
% 2.07/1.59 (~hskp2),
% 2.07/1.59 inference(unit_resolution,[status(thm)],[419, 414])).
% 2.07/1.59 tff(421,plain,
% 2.07/1.59 (hskp2 | (~c3_1(a106))),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[276, 160, 236, 52, 98, 109, 270, 245])).
% 2.07/1.60 tff(422,plain,
% 2.07/1.60 ($false),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[421, 420, 244])).
% 2.07/1.60 tff(423,plain,(hskp19 | (~c1_1(a106)) | c1_1(a163) | c2_1(a163) | c2_1(a106) | c0_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.60 tff(424,plain,
% 2.07/1.60 (~c1_1(a106)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[423, 217, 52, 98, 97, 109, 1])).
% 2.07/1.60 tff(425,plain,
% 2.07/1.60 ($false),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[257, 424, 235])).
% 2.07/1.60 tff(426,plain,(hskp19 | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a106)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.60 tff(427,plain,
% 2.07/1.60 (hskp19),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[426, 109, 98, 97, 52])).
% 2.07/1.60 tff(428,plain,
% 2.07/1.60 (((~hskp19) | (~c3_1(a135))) <=> ((~hskp19) | (~c3_1(a135)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(429,plain,
% 2.07/1.60 (((~c3_1(a135)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a135)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(430,axiom,((~c3_1(a135)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 2.07/1.60 tff(431,plain,
% 2.07/1.60 ((~hskp19) | (~c3_1(a135))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[430, 429])).
% 2.07/1.60 tff(432,plain,
% 2.07/1.60 ((~hskp19) | (~c3_1(a135))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[431, 428])).
% 2.07/1.60 tff(433,plain,
% 2.07/1.60 (~c3_1(a135)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[432, 427])).
% 2.07/1.60 tff(434,plain,
% 2.07/1.60 (((~hskp19) | (~c2_1(a135))) <=> ((~hskp19) | (~c2_1(a135)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(435,plain,
% 2.07/1.60 (((~c2_1(a135)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a135)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(436,axiom,((~c2_1(a135)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 2.07/1.60 tff(437,plain,
% 2.07/1.60 ((~hskp19) | (~c2_1(a135))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[436, 435])).
% 2.07/1.60 tff(438,plain,
% 2.07/1.60 ((~hskp19) | (~c2_1(a135))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[437, 434])).
% 2.07/1.60 tff(439,plain,
% 2.07/1.60 (~c2_1(a135)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[438, 427])).
% 2.07/1.60 tff(440,assumption,(hskp19), introduced(assumption)).
% 2.07/1.60 tff(441,assumption,(hskp6), introduced(assumption)).
% 2.07/1.60 tff(442,plain,
% 2.07/1.60 (((~hskp6) | (~c0_1(a107))) <=> ((~hskp6) | (~c0_1(a107)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(443,plain,
% 2.07/1.60 (((~c0_1(a107)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a107)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(444,axiom,((~c0_1(a107)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 2.07/1.60 tff(445,plain,
% 2.07/1.60 ((~hskp6) | (~c0_1(a107))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[444, 443])).
% 2.07/1.60 tff(446,plain,
% 2.07/1.60 ((~hskp6) | (~c0_1(a107))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[445, 442])).
% 2.07/1.60 tff(447,plain,
% 2.07/1.60 (~c0_1(a107)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[446, 441])).
% 2.07/1.60 tff(448,assumption,(~c0_1(a107)), introduced(assumption)).
% 2.07/1.60 tff(449,plain,
% 2.07/1.60 (~c3_1(a135)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[432, 440])).
% 2.07/1.60 tff(450,plain,
% 2.07/1.60 (((~hskp19) | c0_1(a135)) <=> ((~hskp19) | c0_1(a135))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(451,axiom,((~hskp19) | c0_1(a135)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 2.07/1.60 tff(452,plain,
% 2.07/1.60 ((~hskp19) | c0_1(a135)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[451, 450])).
% 2.07/1.60 tff(453,plain,
% 2.07/1.60 ((~hskp19) | c0_1(a135)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[452, 450])).
% 2.07/1.60 tff(454,plain,
% 2.07/1.60 ((~hskp19) | c0_1(a135)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[453, 450])).
% 2.07/1.60 tff(455,plain,
% 2.07/1.60 ((~hskp19) | c0_1(a135)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[454, 450])).
% 2.07/1.60 tff(456,plain,
% 2.07/1.60 ((~hskp19) | c0_1(a135)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[455, 450])).
% 2.07/1.60 tff(457,plain,
% 2.07/1.60 ((~hskp19) | c0_1(a135)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[456, 450])).
% 2.07/1.60 tff(458,plain,
% 2.07/1.60 ((~hskp19) | c0_1(a135)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[457, 450])).
% 2.07/1.60 tff(459,plain,
% 2.07/1.60 ((~hskp19) | c0_1(a135)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[458, 450])).
% 2.07/1.60 tff(460,plain,
% 2.07/1.60 (c0_1(a135)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[459, 440])).
% 2.07/1.60 tff(461,plain,
% 2.07/1.60 (~c2_1(a135)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[438, 440])).
% 2.07/1.60 tff(462,assumption,(~c3_1(a135)), introduced(assumption)).
% 2.07/1.60 tff(463,assumption,(~c2_1(a135)), introduced(assumption)).
% 2.07/1.60 tff(464,plain,
% 2.07/1.60 (((~hskp6) | c2_1(a107)) <=> ((~hskp6) | c2_1(a107))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(465,axiom,((~hskp6) | c2_1(a107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 2.07/1.60 tff(466,plain,
% 2.07/1.60 ((~hskp6) | c2_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[465, 464])).
% 2.07/1.60 tff(467,plain,
% 2.07/1.60 ((~hskp6) | c2_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[466, 464])).
% 2.07/1.60 tff(468,plain,
% 2.07/1.60 ((~hskp6) | c2_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[467, 464])).
% 2.07/1.60 tff(469,plain,
% 2.07/1.60 ((~hskp6) | c2_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[468, 464])).
% 2.07/1.60 tff(470,plain,
% 2.07/1.60 ((~hskp6) | c2_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[469, 464])).
% 2.07/1.60 tff(471,plain,
% 2.07/1.60 ((~hskp6) | c2_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[470, 464])).
% 2.07/1.60 tff(472,plain,
% 2.07/1.60 ((~hskp6) | c2_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[471, 464])).
% 2.07/1.60 tff(473,plain,
% 2.07/1.60 ((~hskp6) | c2_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[472, 464])).
% 2.07/1.60 tff(474,plain,
% 2.07/1.60 (c2_1(a107)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[473, 441])).
% 2.07/1.60 tff(475,plain,
% 2.07/1.60 (((~hskp6) | c1_1(a107)) <=> ((~hskp6) | c1_1(a107))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(476,axiom,((~hskp6) | c1_1(a107)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 2.07/1.60 tff(477,plain,
% 2.07/1.60 ((~hskp6) | c1_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[476, 475])).
% 2.07/1.60 tff(478,plain,
% 2.07/1.60 ((~hskp6) | c1_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[477, 475])).
% 2.07/1.60 tff(479,plain,
% 2.07/1.60 ((~hskp6) | c1_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[478, 475])).
% 2.07/1.60 tff(480,plain,
% 2.07/1.60 ((~hskp6) | c1_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[479, 475])).
% 2.07/1.60 tff(481,plain,
% 2.07/1.60 ((~hskp6) | c1_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[480, 475])).
% 2.07/1.60 tff(482,plain,
% 2.07/1.60 ((~hskp6) | c1_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[481, 475])).
% 2.07/1.60 tff(483,plain,
% 2.07/1.60 ((~hskp6) | c1_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[482, 475])).
% 2.07/1.60 tff(484,plain,
% 2.07/1.60 ((~hskp6) | c1_1(a107)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[483, 475])).
% 2.07/1.60 tff(485,plain,
% 2.07/1.60 (c1_1(a107)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[484, 441])).
% 2.07/1.60 tff(486,assumption,(c0_1(a135)), introduced(assumption)).
% 2.07/1.60 tff(487,plain,
% 2.07/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(488,plain,
% 2.07/1.60 (((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163)) <=> (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(489,plain,
% 2.07/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c0_1(a135))))),
% 2.07/1.60 inference(monotonicity,[status(thm)],[488])).
% 2.07/1.60 tff(490,plain,
% 2.07/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))),
% 2.07/1.60 inference(transitivity,[status(thm)],[489, 487])).
% 2.07/1.60 tff(491,plain,
% 2.07/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))),
% 2.07/1.60 inference(quant_inst,[status(thm)],[])).
% 2.07/1.60 tff(492,plain,
% 2.07/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c0_1(a135))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[491, 490])).
% 2.07/1.60 tff(493,plain,
% 2.07/1.60 (~c3_1(a107)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[492, 160, 486, 485, 474, 52, 98, 97, 463, 462, 108])).
% 2.07/1.60 tff(494,plain,
% 2.07/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c0_1(a107) | (~ndr1_0) | c3_1(a107) | (~c2_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c0_1(a107) | (~ndr1_0) | c3_1(a107) | (~c2_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(495,plain,
% 2.07/1.60 (((~ndr1_0) | c3_1(a107) | (~c1_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a107) | c0_1(a107) | (~c1_1(a107))) <=> (c2_1(a135) | c3_1(a135) | c0_1(a107) | (~ndr1_0) | c3_1(a107) | (~c2_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(496,plain,
% 2.07/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a107) | (~c1_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a107) | c0_1(a107) | (~c1_1(a107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c0_1(a107) | (~ndr1_0) | c3_1(a107) | (~c2_1(a107)) | (~c1_1(a107)) | (~c0_1(a135))))),
% 2.07/1.60 inference(monotonicity,[status(thm)],[495])).
% 2.07/1.60 tff(497,plain,
% 2.07/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a107) | (~c1_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a107) | c0_1(a107) | (~c1_1(a107)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c0_1(a107) | (~ndr1_0) | c3_1(a107) | (~c2_1(a107)) | (~c1_1(a107)) | (~c0_1(a135)))),
% 2.07/1.60 inference(transitivity,[status(thm)],[496, 494])).
% 2.07/1.60 tff(498,plain,
% 2.07/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a107) | (~c1_1(a107)) | (~c2_1(a107)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a107) | c0_1(a107) | (~c1_1(a107)))),
% 2.07/1.60 inference(quant_inst,[status(thm)],[])).
% 2.07/1.60 tff(499,plain,
% 2.07/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c0_1(a107) | (~ndr1_0) | c3_1(a107) | (~c2_1(a107)) | (~c1_1(a107)) | (~c0_1(a135))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[498, 497])).
% 2.07/1.60 tff(500,plain,
% 2.07/1.60 ($false),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[499, 160, 486, 485, 474, 463, 462, 448, 202, 493])).
% 2.07/1.60 tff(501,plain,((~hskp6) | (~c0_1(a135)) | c2_1(a135) | c3_1(a135) | c0_1(a107) | c1_1(a163) | c2_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.60 tff(502,plain,
% 2.07/1.60 ($false),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[501, 461, 460, 441, 449, 448, 52, 98, 97])).
% 2.07/1.60 tff(503,plain,((~hskp19) | (~hskp6) | c0_1(a107) | c1_1(a163) | c2_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.60 tff(504,plain,
% 2.07/1.60 ($false),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[503, 447, 441, 440, 52, 98, 97])).
% 2.07/1.60 tff(505,plain,((~hskp6) | (~hskp19) | c1_1(a163) | c2_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.60 tff(506,plain,
% 2.07/1.60 (~hskp6),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[505, 427, 52, 98, 97])).
% 2.07/1.60 tff(507,assumption,(~hskp5), introduced(assumption)).
% 2.07/1.60 tff(508,plain,
% 2.07/1.60 (c0_1(a163)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[234, 507, 97])).
% 2.07/1.60 tff(509,plain,
% 2.07/1.60 (c0_1(a163)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[246, 507])).
% 2.07/1.60 tff(510,plain,
% 2.07/1.60 (hskp19),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[216, 509, 97, 98])).
% 2.07/1.60 tff(511,plain,
% 2.07/1.60 (~c3_1(a135)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[432, 510])).
% 2.07/1.60 tff(512,plain,
% 2.07/1.60 (c0_1(a135)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[459, 510])).
% 2.07/1.60 tff(513,plain,
% 2.07/1.60 (~c2_1(a135)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[438, 510])).
% 2.07/1.60 tff(514,assumption,(hskp28), introduced(assumption)).
% 2.07/1.60 tff(515,plain,
% 2.07/1.60 (((~hskp28) | c3_1(a118)) <=> ((~hskp28) | c3_1(a118))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(516,axiom,((~hskp28) | c3_1(a118)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 2.07/1.60 tff(517,plain,
% 2.07/1.60 ((~hskp28) | c3_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[516, 515])).
% 2.07/1.60 tff(518,plain,
% 2.07/1.60 ((~hskp28) | c3_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[517, 515])).
% 2.07/1.60 tff(519,plain,
% 2.07/1.60 ((~hskp28) | c3_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[518, 515])).
% 2.07/1.60 tff(520,plain,
% 2.07/1.60 ((~hskp28) | c3_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[519, 515])).
% 2.07/1.60 tff(521,plain,
% 2.07/1.60 ((~hskp28) | c3_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[520, 515])).
% 2.07/1.60 tff(522,plain,
% 2.07/1.60 ((~hskp28) | c3_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[521, 515])).
% 2.07/1.60 tff(523,plain,
% 2.07/1.60 ((~hskp28) | c3_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[522, 515])).
% 2.07/1.60 tff(524,plain,
% 2.07/1.60 ((~hskp28) | c3_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[523, 515])).
% 2.07/1.60 tff(525,plain,
% 2.07/1.60 (c3_1(a118)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[524, 514])).
% 2.07/1.60 tff(526,plain,
% 2.07/1.60 (((~hskp28) | c2_1(a118)) <=> ((~hskp28) | c2_1(a118))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(527,axiom,((~hskp28) | c2_1(a118)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 2.07/1.60 tff(528,plain,
% 2.07/1.60 ((~hskp28) | c2_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[527, 526])).
% 2.07/1.60 tff(529,plain,
% 2.07/1.60 ((~hskp28) | c2_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[528, 526])).
% 2.07/1.60 tff(530,plain,
% 2.07/1.60 ((~hskp28) | c2_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[529, 526])).
% 2.07/1.60 tff(531,plain,
% 2.07/1.60 ((~hskp28) | c2_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[530, 526])).
% 2.07/1.60 tff(532,plain,
% 2.07/1.60 ((~hskp28) | c2_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[531, 526])).
% 2.07/1.60 tff(533,plain,
% 2.07/1.60 ((~hskp28) | c2_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[532, 526])).
% 2.07/1.60 tff(534,plain,
% 2.07/1.60 ((~hskp28) | c2_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[533, 526])).
% 2.07/1.60 tff(535,plain,
% 2.07/1.60 ((~hskp28) | c2_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[534, 526])).
% 2.07/1.60 tff(536,plain,
% 2.07/1.60 (c2_1(a118)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[535, 514])).
% 2.07/1.60 tff(537,plain,
% 2.07/1.60 (((~hskp28) | c1_1(a118)) <=> ((~hskp28) | c1_1(a118))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(538,axiom,((~hskp28) | c1_1(a118)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 2.07/1.60 tff(539,plain,
% 2.07/1.60 ((~hskp28) | c1_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[538, 537])).
% 2.07/1.60 tff(540,plain,
% 2.07/1.60 ((~hskp28) | c1_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[539, 537])).
% 2.07/1.60 tff(541,plain,
% 2.07/1.60 ((~hskp28) | c1_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[540, 537])).
% 2.07/1.60 tff(542,plain,
% 2.07/1.60 ((~hskp28) | c1_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[541, 537])).
% 2.07/1.60 tff(543,plain,
% 2.07/1.60 ((~hskp28) | c1_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[542, 537])).
% 2.07/1.60 tff(544,plain,
% 2.07/1.60 ((~hskp28) | c1_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[543, 537])).
% 2.07/1.60 tff(545,plain,
% 2.07/1.60 ((~hskp28) | c1_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[544, 537])).
% 2.07/1.60 tff(546,plain,
% 2.07/1.60 ((~hskp28) | c1_1(a118)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[545, 537])).
% 2.07/1.60 tff(547,plain,
% 2.07/1.60 (c1_1(a118)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[546, 514])).
% 2.07/1.60 tff(548,plain,
% 2.07/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(549,plain,
% 2.07/1.60 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163)) <=> (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(550,plain,
% 2.07/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 2.07/1.60 inference(monotonicity,[status(thm)],[549])).
% 2.07/1.60 tff(551,plain,
% 2.07/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.07/1.60 inference(transitivity,[status(thm)],[550, 548])).
% 2.07/1.60 tff(552,plain,
% 2.07/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))),
% 2.07/1.60 inference(quant_inst,[status(thm)],[])).
% 2.07/1.60 tff(553,plain,
% 2.07/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[552, 551])).
% 2.07/1.60 tff(554,plain,
% 2.07/1.60 ($false),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[553, 160, 547, 536, 525, 486, 52, 98, 97, 463, 462, 108])).
% 2.07/1.60 tff(555,plain,((~hskp28) | (~c0_1(a135)) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.60 tff(556,plain,
% 2.07/1.60 (~hskp28),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[555, 513, 52, 98, 97, 512, 511])).
% 2.07/1.60 tff(557,assumption,(~hskp28), introduced(assumption)).
% 2.07/1.60 tff(558,assumption,(hskp15), introduced(assumption)).
% 2.07/1.60 tff(559,plain,
% 2.07/1.60 (((~hskp15) | (~c1_1(a117))) <=> ((~hskp15) | (~c1_1(a117)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(560,plain,
% 2.07/1.60 (((~c1_1(a117)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a117)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(561,axiom,((~c1_1(a117)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 2.07/1.60 tff(562,plain,
% 2.07/1.60 ((~hskp15) | (~c1_1(a117))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[561, 560])).
% 2.07/1.60 tff(563,plain,
% 2.07/1.60 ((~hskp15) | (~c1_1(a117))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[562, 559])).
% 2.07/1.60 tff(564,plain,
% 2.07/1.60 (~c1_1(a117)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[563, 558])).
% 2.07/1.60 tff(565,plain,
% 2.07/1.60 (((~hskp15) | c0_1(a117)) <=> ((~hskp15) | c0_1(a117))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(566,axiom,((~hskp15) | c0_1(a117)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 2.07/1.60 tff(567,plain,
% 2.07/1.60 ((~hskp15) | c0_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[566, 565])).
% 2.07/1.60 tff(568,plain,
% 2.07/1.60 ((~hskp15) | c0_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[567, 565])).
% 2.07/1.60 tff(569,plain,
% 2.07/1.60 ((~hskp15) | c0_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[568, 565])).
% 2.07/1.60 tff(570,plain,
% 2.07/1.60 ((~hskp15) | c0_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[569, 565])).
% 2.07/1.60 tff(571,plain,
% 2.07/1.60 ((~hskp15) | c0_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[570, 565])).
% 2.07/1.60 tff(572,plain,
% 2.07/1.60 ((~hskp15) | c0_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[571, 565])).
% 2.07/1.60 tff(573,plain,
% 2.07/1.60 ((~hskp15) | c0_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[572, 565])).
% 2.07/1.60 tff(574,plain,
% 2.07/1.60 ((~hskp15) | c0_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[573, 565])).
% 2.07/1.60 tff(575,plain,
% 2.07/1.60 (c0_1(a117)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[574, 558])).
% 2.07/1.60 tff(576,plain,
% 2.07/1.60 (((~hskp15) | c3_1(a117)) <=> ((~hskp15) | c3_1(a117))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(577,axiom,((~hskp15) | c3_1(a117)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 2.07/1.60 tff(578,plain,
% 2.07/1.60 ((~hskp15) | c3_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[577, 576])).
% 2.07/1.60 tff(579,plain,
% 2.07/1.60 ((~hskp15) | c3_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[578, 576])).
% 2.07/1.60 tff(580,plain,
% 2.07/1.60 ((~hskp15) | c3_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[579, 576])).
% 2.07/1.60 tff(581,plain,
% 2.07/1.60 ((~hskp15) | c3_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[580, 576])).
% 2.07/1.60 tff(582,plain,
% 2.07/1.60 ((~hskp15) | c3_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[581, 576])).
% 2.07/1.60 tff(583,plain,
% 2.07/1.60 ((~hskp15) | c3_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[582, 576])).
% 2.07/1.60 tff(584,plain,
% 2.07/1.60 ((~hskp15) | c3_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[583, 576])).
% 2.07/1.60 tff(585,plain,
% 2.07/1.60 ((~hskp15) | c3_1(a117)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[584, 576])).
% 2.07/1.60 tff(586,plain,
% 2.07/1.60 (c3_1(a117)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[585, 558])).
% 2.07/1.60 tff(587,plain,
% 2.07/1.60 (^[U: $i] : refl((hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.07/1.60 inference(bind,[status(th)],[])).
% 2.07/1.60 tff(588,plain,
% 2.07/1.60 (![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.60 inference(quant_intro,[status(thm)],[587])).
% 2.07/1.60 tff(589,plain,
% 2.07/1.60 (![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(590,plain,
% 2.07/1.60 (^[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)) | hskp31) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp31))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp31) <=> (hskp31 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) <=> (hskp31 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) | hskp28) <=> ((hskp31 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite(((hskp31 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) | hskp28) <=> (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.07/1.60 inference(bind,[status(th)],[])).
% 2.07/1.60 tff(591,plain,
% 2.07/1.60 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) | hskp28) <=> ![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.60 inference(quant_intro,[status(thm)],[590])).
% 2.07/1.60 tff(592,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp31) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 2.07/1.60 tff(593,plain,
% 2.07/1.60 (![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[592, 591])).
% 2.07/1.60 tff(594,plain,
% 2.07/1.60 (![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[593, 589])).
% 2.07/1.60 tff(595,plain,(
% 2.07/1.60 ![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.60 inference(skolemize,[status(sab)],[594])).
% 2.07/1.60 tff(596,plain,
% 2.07/1.60 (![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[595, 588])).
% 2.07/1.60 tff(597,assumption,(~c1_1(a117)), introduced(assumption)).
% 2.07/1.60 tff(598,plain,
% 2.07/1.60 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(599,plain,
% 2.07/1.60 ((hskp31 | hskp28 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117))) <=> (hskp31 | hskp28 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(600,plain,
% 2.07/1.60 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117))))),
% 2.07/1.60 inference(monotonicity,[status(thm)],[599])).
% 2.07/1.60 tff(601,plain,
% 2.07/1.60 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))),
% 2.07/1.60 inference(transitivity,[status(thm)],[600, 598])).
% 2.07/1.60 tff(602,plain,
% 2.07/1.60 ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117)))),
% 2.07/1.60 inference(quant_inst,[status(thm)],[])).
% 2.07/1.60 tff(603,plain,
% 2.07/1.60 ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[602, 601])).
% 2.07/1.60 tff(604,plain,
% 2.07/1.60 (hskp28 | (~c0_1(a117)) | (~c3_1(a117))),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[603, 23, 160, 597, 596])).
% 2.07/1.60 tff(605,plain,
% 2.07/1.60 ($false),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[604, 586, 575, 557])).
% 2.07/1.60 tff(606,plain,((~hskp15) | hskp28 | hskp31 | c1_1(a117)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.60 tff(607,plain,
% 2.07/1.60 ($false),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[606, 564, 558, 23, 557])).
% 2.07/1.60 tff(608,plain,((~hskp15) | hskp31 | hskp28), inference(lemma,lemma(discharge,[]))).
% 2.07/1.60 tff(609,plain,
% 2.07/1.60 (~hskp15),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[608, 556, 23])).
% 2.07/1.60 tff(610,plain,
% 2.07/1.60 ((hskp15 | hskp13 | hskp5) <=> (hskp15 | hskp13 | hskp5)),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(611,plain,
% 2.07/1.60 (((hskp15 | hskp5) | hskp13) <=> (hskp15 | hskp13 | hskp5)),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(612,plain,
% 2.07/1.60 ((hskp5 | hskp15) <=> (hskp15 | hskp5)),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(613,plain,
% 2.07/1.60 (((hskp5 | hskp15) | hskp13) <=> ((hskp15 | hskp5) | hskp13)),
% 2.07/1.60 inference(monotonicity,[status(thm)],[612])).
% 2.07/1.60 tff(614,plain,
% 2.07/1.60 (((hskp5 | hskp15) | hskp13) <=> (hskp15 | hskp13 | hskp5)),
% 2.07/1.60 inference(transitivity,[status(thm)],[613, 611])).
% 2.07/1.60 tff(615,axiom,((hskp5 | hskp15) | hskp13), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 2.07/1.60 tff(616,plain,
% 2.07/1.60 (hskp15 | hskp13 | hskp5),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[615, 614])).
% 2.07/1.60 tff(617,plain,
% 2.07/1.60 (hskp15 | hskp13 | hskp5),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[616, 610])).
% 2.07/1.60 tff(618,plain,
% 2.07/1.60 (hskp15 | hskp13 | hskp5),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[617, 610])).
% 2.07/1.60 tff(619,plain,
% 2.07/1.60 (hskp15 | hskp13 | hskp5),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[618, 610])).
% 2.07/1.60 tff(620,plain,
% 2.07/1.60 (hskp15 | hskp13 | hskp5),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[619, 610])).
% 2.07/1.60 tff(621,plain,
% 2.07/1.60 (hskp15 | hskp13 | hskp5),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[620, 610])).
% 2.07/1.60 tff(622,plain,
% 2.07/1.60 (hskp15 | hskp13 | hskp5),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[621, 610])).
% 2.07/1.60 tff(623,plain,
% 2.07/1.60 (hskp15 | hskp13 | hskp5),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[622, 610])).
% 2.07/1.60 tff(624,plain,
% 2.07/1.60 (hskp13),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[623, 609, 507])).
% 2.07/1.60 tff(625,plain,
% 2.07/1.60 (((~hskp13) | (~c3_1(a114))) <=> ((~hskp13) | (~c3_1(a114)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(626,plain,
% 2.07/1.60 (((~c3_1(a114)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a114)))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(627,axiom,((~c3_1(a114)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 2.07/1.60 tff(628,plain,
% 2.07/1.60 ((~hskp13) | (~c3_1(a114))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[627, 626])).
% 2.07/1.60 tff(629,plain,
% 2.07/1.60 ((~hskp13) | (~c3_1(a114))),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[628, 625])).
% 2.07/1.60 tff(630,plain,
% 2.07/1.60 (~c3_1(a114)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[629, 624])).
% 2.07/1.60 tff(631,plain,
% 2.07/1.60 (((~hskp13) | c2_1(a114)) <=> ((~hskp13) | c2_1(a114))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(632,axiom,((~hskp13) | c2_1(a114)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 2.07/1.60 tff(633,plain,
% 2.07/1.60 ((~hskp13) | c2_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[632, 631])).
% 2.07/1.60 tff(634,plain,
% 2.07/1.60 ((~hskp13) | c2_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[633, 631])).
% 2.07/1.60 tff(635,plain,
% 2.07/1.60 ((~hskp13) | c2_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[634, 631])).
% 2.07/1.60 tff(636,plain,
% 2.07/1.60 ((~hskp13) | c2_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[635, 631])).
% 2.07/1.60 tff(637,plain,
% 2.07/1.60 ((~hskp13) | c2_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[636, 631])).
% 2.07/1.60 tff(638,plain,
% 2.07/1.60 ((~hskp13) | c2_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[637, 631])).
% 2.07/1.60 tff(639,plain,
% 2.07/1.60 ((~hskp13) | c2_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[638, 631])).
% 2.07/1.60 tff(640,plain,
% 2.07/1.60 ((~hskp13) | c2_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[639, 631])).
% 2.07/1.60 tff(641,plain,
% 2.07/1.60 (c2_1(a114)),
% 2.07/1.60 inference(unit_resolution,[status(thm)],[640, 624])).
% 2.07/1.60 tff(642,plain,
% 2.07/1.60 (((~hskp13) | c1_1(a114)) <=> ((~hskp13) | c1_1(a114))),
% 2.07/1.60 inference(rewrite,[status(thm)],[])).
% 2.07/1.60 tff(643,axiom,((~hskp13) | c1_1(a114)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 2.07/1.60 tff(644,plain,
% 2.07/1.60 ((~hskp13) | c1_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[643, 642])).
% 2.07/1.60 tff(645,plain,
% 2.07/1.60 ((~hskp13) | c1_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[644, 642])).
% 2.07/1.60 tff(646,plain,
% 2.07/1.60 ((~hskp13) | c1_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[645, 642])).
% 2.07/1.60 tff(647,plain,
% 2.07/1.60 ((~hskp13) | c1_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[646, 642])).
% 2.07/1.60 tff(648,plain,
% 2.07/1.60 ((~hskp13) | c1_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[647, 642])).
% 2.07/1.60 tff(649,plain,
% 2.07/1.60 ((~hskp13) | c1_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[648, 642])).
% 2.07/1.60 tff(650,plain,
% 2.07/1.60 ((~hskp13) | c1_1(a114)),
% 2.07/1.60 inference(modus_ponens,[status(thm)],[649, 642])).
% 2.07/1.60 tff(651,plain,
% 2.07/1.61 ((~hskp13) | c1_1(a114)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[650, 642])).
% 2.07/1.61 tff(652,plain,
% 2.07/1.61 (c1_1(a114)),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[651, 624])).
% 2.07/1.61 tff(653,plain,
% 2.07/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a135)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(654,plain,
% 2.07/1.61 (((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114))) <=> (c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a135)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(655,plain,
% 2.07/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a135))))),
% 2.07/1.61 inference(monotonicity,[status(thm)],[654])).
% 2.07/1.61 tff(656,plain,
% 2.07/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a135)))),
% 2.07/1.61 inference(transitivity,[status(thm)],[655, 653])).
% 2.07/1.61 tff(657,plain,
% 2.07/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))),
% 2.07/1.61 inference(quant_inst,[status(thm)],[])).
% 2.07/1.61 tff(658,plain,
% 2.07/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a135))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[657, 656])).
% 2.07/1.61 tff(659,plain,
% 2.07/1.61 (c0_1(a114)),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[658, 160, 512, 652, 641, 513, 511, 630, 202])).
% 2.07/1.61 tff(660,plain,
% 2.07/1.61 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 2.07/1.61 inference(bind,[status(th)],[])).
% 2.07/1.61 tff(661,plain,
% 2.07/1.61 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.61 inference(quant_intro,[status(thm)],[660])).
% 2.07/1.61 tff(662,plain,
% 2.07/1.61 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(663,plain,
% 2.07/1.61 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp7) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 2.07/1.61 inference(bind,[status(th)],[])).
% 2.07/1.61 tff(664,plain,
% 2.07/1.61 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.61 inference(quant_intro,[status(thm)],[663])).
% 2.07/1.61 tff(665,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 2.07/1.61 tff(666,plain,
% 2.07/1.61 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[665, 664])).
% 2.07/1.61 tff(667,plain,
% 2.07/1.61 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[666, 662])).
% 2.07/1.61 tff(668,plain,(
% 2.07/1.61 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.61 inference(skolemize,[status(sab)],[667])).
% 2.07/1.61 tff(669,plain,
% 2.07/1.61 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[668, 661])).
% 2.07/1.61 tff(670,plain,
% 2.07/1.61 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | (~c0_1(a163)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(671,plain,
% 2.07/1.61 ((hskp7 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163))) <=> (hskp7 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | (~c0_1(a163)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(672,plain,
% 2.07/1.61 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | (~c0_1(a163))))),
% 2.07/1.61 inference(monotonicity,[status(thm)],[671])).
% 2.07/1.61 tff(673,plain,
% 2.07/1.61 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | (~c0_1(a163)))),
% 2.07/1.61 inference(transitivity,[status(thm)],[672, 670])).
% 2.07/1.61 tff(674,plain,
% 2.07/1.61 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))),
% 2.07/1.61 inference(quant_inst,[status(thm)],[])).
% 2.07/1.61 tff(675,plain,
% 2.07/1.61 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | (~c0_1(a163))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[674, 673])).
% 2.07/1.61 tff(676,plain,
% 2.07/1.61 (hskp7),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[675, 160, 652, 641, 52, 98, 669, 509, 659])).
% 2.07/1.61 tff(677,plain,
% 2.07/1.61 (((~hskp7) | (~c0_1(a108))) <=> ((~hskp7) | (~c0_1(a108)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(678,plain,
% 2.07/1.61 (((~c0_1(a108)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a108)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(679,axiom,((~c0_1(a108)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 2.07/1.61 tff(680,plain,
% 2.07/1.61 ((~hskp7) | (~c0_1(a108))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[679, 678])).
% 2.07/1.61 tff(681,plain,
% 2.07/1.61 ((~hskp7) | (~c0_1(a108))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[680, 677])).
% 2.07/1.61 tff(682,plain,
% 2.07/1.61 (~c0_1(a108)),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[681, 676])).
% 2.07/1.61 tff(683,assumption,(~hskp15), introduced(assumption)).
% 2.07/1.61 tff(684,plain,
% 2.07/1.61 (~hskp28),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[555, 486, 52, 98, 97, 463, 462])).
% 2.07/1.61 tff(685,assumption,(hskp7), introduced(assumption)).
% 2.07/1.61 tff(686,plain,
% 2.07/1.61 (((~hskp7) | c3_1(a108)) <=> ((~hskp7) | c3_1(a108))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(687,axiom,((~hskp7) | c3_1(a108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 2.07/1.61 tff(688,plain,
% 2.07/1.61 ((~hskp7) | c3_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[687, 686])).
% 2.07/1.61 tff(689,plain,
% 2.07/1.61 ((~hskp7) | c3_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[688, 686])).
% 2.07/1.61 tff(690,plain,
% 2.07/1.61 ((~hskp7) | c3_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[689, 686])).
% 2.07/1.61 tff(691,plain,
% 2.07/1.61 ((~hskp7) | c3_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[690, 686])).
% 2.07/1.61 tff(692,plain,
% 2.07/1.61 ((~hskp7) | c3_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[691, 686])).
% 2.07/1.61 tff(693,plain,
% 2.07/1.61 ((~hskp7) | c3_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[692, 686])).
% 2.07/1.61 tff(694,plain,
% 2.07/1.61 ((~hskp7) | c3_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[693, 686])).
% 2.07/1.61 tff(695,plain,
% 2.07/1.61 ((~hskp7) | c3_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[694, 686])).
% 2.07/1.61 tff(696,plain,
% 2.07/1.61 (c3_1(a108)),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[695, 685])).
% 2.07/1.61 tff(697,plain,
% 2.07/1.61 (^[U: $i] : refl((hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))),
% 2.07/1.61 inference(bind,[status(th)],[])).
% 2.07/1.61 tff(698,plain,
% 2.07/1.61 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.07/1.61 inference(quant_intro,[status(thm)],[697])).
% 2.07/1.61 tff(699,plain,
% 2.07/1.61 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(700,plain,
% 2.07/1.61 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) | hskp28) <=> ((hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp28))), rewrite(((hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp28) <=> (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) | hskp28) <=> (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))))),
% 2.07/1.61 inference(bind,[status(th)],[])).
% 2.07/1.61 tff(701,plain,
% 2.07/1.61 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) | hskp28) <=> ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.07/1.61 inference(quant_intro,[status(thm)],[700])).
% 2.07/1.61 tff(702,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp15) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 2.07/1.61 tff(703,plain,
% 2.07/1.61 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[702, 701])).
% 2.07/1.61 tff(704,plain,
% 2.07/1.61 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[703, 699])).
% 2.07/1.61 tff(705,plain,(
% 2.07/1.61 ![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.07/1.61 inference(skolemize,[status(sab)],[704])).
% 2.07/1.61 tff(706,plain,
% 2.07/1.61 (![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[705, 698])).
% 2.07/1.61 tff(707,assumption,(~c0_1(a108)), introduced(assumption)).
% 2.07/1.61 tff(708,plain,
% 2.07/1.61 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c3_1(a108)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp15 | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c3_1(a108)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(709,plain,
% 2.07/1.61 ((hskp28 | hskp15 | (~ndr1_0) | c0_1(a108) | c2_1(a108) | (~c3_1(a108))) <=> (hskp28 | hskp15 | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c3_1(a108)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(710,plain,
% 2.07/1.61 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c0_1(a108) | c2_1(a108) | (~c3_1(a108)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c3_1(a108))))),
% 2.07/1.61 inference(monotonicity,[status(thm)],[709])).
% 2.07/1.61 tff(711,plain,
% 2.07/1.61 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c0_1(a108) | c2_1(a108) | (~c3_1(a108)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp15 | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c3_1(a108)))),
% 2.07/1.61 inference(transitivity,[status(thm)],[710, 708])).
% 2.07/1.61 tff(712,plain,
% 2.07/1.61 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c0_1(a108) | c2_1(a108) | (~c3_1(a108)))),
% 2.07/1.61 inference(quant_inst,[status(thm)],[])).
% 2.07/1.61 tff(713,plain,
% 2.07/1.61 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp15 | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c3_1(a108))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[712, 711])).
% 2.07/1.61 tff(714,plain,
% 2.07/1.61 (hskp28 | hskp15 | c2_1(a108) | (~c3_1(a108))),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[713, 160, 707, 706])).
% 2.07/1.61 tff(715,plain,
% 2.07/1.61 (c2_1(a108)),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[714, 696, 684, 683])).
% 2.07/1.61 tff(716,plain,
% 2.07/1.61 (((~hskp7) | c1_1(a108)) <=> ((~hskp7) | c1_1(a108))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(717,axiom,((~hskp7) | c1_1(a108)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 2.07/1.61 tff(718,plain,
% 2.07/1.61 ((~hskp7) | c1_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[717, 716])).
% 2.07/1.61 tff(719,plain,
% 2.07/1.61 ((~hskp7) | c1_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[718, 716])).
% 2.07/1.61 tff(720,plain,
% 2.07/1.61 ((~hskp7) | c1_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[719, 716])).
% 2.07/1.61 tff(721,plain,
% 2.07/1.61 ((~hskp7) | c1_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[720, 716])).
% 2.07/1.61 tff(722,plain,
% 2.07/1.61 ((~hskp7) | c1_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[721, 716])).
% 2.07/1.61 tff(723,plain,
% 2.07/1.61 ((~hskp7) | c1_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[722, 716])).
% 2.07/1.61 tff(724,plain,
% 2.07/1.61 ((~hskp7) | c1_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[723, 716])).
% 2.07/1.61 tff(725,plain,
% 2.07/1.61 ((~hskp7) | c1_1(a108)),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[724, 716])).
% 2.07/1.61 tff(726,plain,
% 2.07/1.61 (c1_1(a108)),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[725, 685])).
% 2.07/1.61 tff(727,plain,
% 2.07/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | (~c0_1(a135)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(728,plain,
% 2.07/1.61 (((~ndr1_0) | (~c1_1(a108)) | (~c3_1(a108)) | (~c2_1(a108)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163)) <=> (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | (~c0_1(a135)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(729,plain,
% 2.07/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a108)) | (~c3_1(a108)) | (~c2_1(a108)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | (~c0_1(a135))))),
% 2.07/1.61 inference(monotonicity,[status(thm)],[728])).
% 2.07/1.61 tff(730,plain,
% 2.07/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a108)) | (~c3_1(a108)) | (~c2_1(a108)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | (~c0_1(a135)))),
% 2.07/1.61 inference(transitivity,[status(thm)],[729, 727])).
% 2.07/1.61 tff(731,plain,
% 2.07/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a108)) | (~c3_1(a108)) | (~c2_1(a108)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))),
% 2.07/1.61 inference(quant_inst,[status(thm)],[])).
% 2.07/1.61 tff(732,plain,
% 2.07/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a108)) | (~c3_1(a108)) | (~c1_1(a108)) | (~c0_1(a135))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[731, 730])).
% 2.07/1.61 tff(733,plain,
% 2.07/1.61 ($false),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[732, 160, 486, 726, 696, 52, 98, 97, 463, 462, 108, 715])).
% 2.07/1.61 tff(734,plain,((~hskp7) | (~c0_1(a135)) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | hskp15 | c0_1(a108)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.61 tff(735,plain,
% 2.07/1.61 ($false),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[734, 682, 676, 52, 98, 97, 513, 511, 512, 609])).
% 2.07/1.61 tff(736,plain,(hskp5 | c1_1(a163) | c2_1(a163) | c3_1(a163) | hskp31), inference(lemma,lemma(discharge,[]))).
% 2.07/1.61 tff(737,plain,
% 2.07/1.61 (hskp31),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[736, 507, 52, 98, 97])).
% 2.07/1.61 tff(738,plain,
% 2.07/1.61 (c3_1(a141)),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[63, 737])).
% 2.07/1.61 tff(739,plain,
% 2.07/1.61 (c1_1(a141)),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[74, 737])).
% 2.07/1.61 tff(740,plain,
% 2.07/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a163)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(741,plain,
% 2.07/1.61 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a163) | c1_1(a163) | c2_1(a163)) <=> (c1_1(a163) | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a163)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(742,plain,
% 2.07/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a163))))),
% 2.07/1.61 inference(monotonicity,[status(thm)],[741])).
% 2.07/1.61 tff(743,plain,
% 2.07/1.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a163)))),
% 2.07/1.61 inference(transitivity,[status(thm)],[742, 740])).
% 2.07/1.61 tff(744,plain,
% 2.07/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a163) | c1_1(a163) | c2_1(a163))),
% 2.07/1.61 inference(quant_inst,[status(thm)],[])).
% 2.07/1.61 tff(745,plain,
% 2.07/1.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a163))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[744, 743])).
% 2.07/1.61 tff(746,plain,
% 2.07/1.61 (~c2_1(a141)),
% 2.07/1.61 inference(unit_resolution,[status(thm)],[745, 160, 739, 738, 52, 98, 97, 108, 508])).
% 2.07/1.61 tff(747,plain,
% 2.07/1.61 (^[U: $i] : refl((hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.07/1.61 inference(bind,[status(th)],[])).
% 2.07/1.61 tff(748,plain,
% 2.07/1.61 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.61 inference(quant_intro,[status(thm)],[747])).
% 2.07/1.61 tff(749,plain,
% 2.07/1.61 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.61 inference(rewrite,[status(thm)],[])).
% 2.07/1.61 tff(750,plain,
% 2.07/1.61 (^[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)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp16) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp16) <=> (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.07/1.61 inference(bind,[status(th)],[])).
% 2.07/1.61 tff(751,plain,
% 2.07/1.61 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp16) <=> ![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.61 inference(quant_intro,[status(thm)],[750])).
% 2.07/1.61 tff(752,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 2.07/1.61 tff(753,plain,
% 2.07/1.61 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[752, 751])).
% 2.07/1.61 tff(754,plain,
% 2.07/1.61 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.61 inference(modus_ponens,[status(thm)],[753, 749])).
% 2.07/1.61 tff(755,plain,(
% 2.07/1.61 ![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.61 inference(skolemize,[status(sab)],[754])).
% 2.07/1.61 tff(756,plain,
% 2.07/1.61 (![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[755, 748])).
% 2.07/1.62 tff(757,plain,
% 2.07/1.62 (c0_1(a141)),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[85, 737])).
% 2.07/1.62 tff(758,assumption,(~hskp6), introduced(assumption)).
% 2.07/1.62 tff(759,plain,
% 2.07/1.62 (((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141))) <=> ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp6 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(760,plain,
% 2.07/1.62 ((hskp16 | hskp6 | (~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141))) <=> (hskp16 | hskp6 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(761,plain,
% 2.07/1.62 (((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)))) <=> ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141)))),
% 2.07/1.62 inference(monotonicity,[status(thm)],[760])).
% 2.07/1.62 tff(762,plain,
% 2.07/1.62 (((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)))) <=> ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp6 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141))),
% 2.07/1.62 inference(transitivity,[status(thm)],[761, 759])).
% 2.07/1.62 tff(763,plain,
% 2.07/1.62 ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp16 | hskp6 | (~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)))),
% 2.07/1.62 inference(quant_inst,[status(thm)],[])).
% 2.07/1.62 tff(764,plain,
% 2.07/1.62 ((~![U: $i] : (hskp16 | hskp6 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp16 | hskp6 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[763, 762])).
% 2.07/1.62 tff(765,plain,
% 2.07/1.62 (hskp16 | c2_1(a141)),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[764, 160, 758, 757, 738, 756])).
% 2.07/1.62 tff(766,plain,
% 2.07/1.62 (hskp16),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[765, 746])).
% 2.07/1.62 tff(767,plain,
% 2.07/1.62 (((~hskp16) | c1_1(a126)) <=> ((~hskp16) | c1_1(a126))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(768,axiom,((~hskp16) | c1_1(a126)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 2.07/1.62 tff(769,plain,
% 2.07/1.62 ((~hskp16) | c1_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[768, 767])).
% 2.07/1.62 tff(770,plain,
% 2.07/1.62 ((~hskp16) | c1_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[769, 767])).
% 2.07/1.62 tff(771,plain,
% 2.07/1.62 ((~hskp16) | c1_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[770, 767])).
% 2.07/1.62 tff(772,plain,
% 2.07/1.62 ((~hskp16) | c1_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[771, 767])).
% 2.07/1.62 tff(773,plain,
% 2.07/1.62 ((~hskp16) | c1_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[772, 767])).
% 2.07/1.62 tff(774,plain,
% 2.07/1.62 ((~hskp16) | c1_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[773, 767])).
% 2.07/1.62 tff(775,plain,
% 2.07/1.62 ((~hskp16) | c1_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[774, 767])).
% 2.07/1.62 tff(776,plain,
% 2.07/1.62 ((~hskp16) | c1_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[775, 767])).
% 2.07/1.62 tff(777,plain,
% 2.07/1.62 (c1_1(a126)),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[776, 766])).
% 2.07/1.62 tff(778,plain,
% 2.07/1.62 (((~hskp16) | c3_1(a126)) <=> ((~hskp16) | c3_1(a126))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(779,axiom,((~hskp16) | c3_1(a126)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 2.07/1.62 tff(780,plain,
% 2.07/1.62 ((~hskp16) | c3_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[779, 778])).
% 2.07/1.62 tff(781,plain,
% 2.07/1.62 ((~hskp16) | c3_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[780, 778])).
% 2.07/1.62 tff(782,plain,
% 2.07/1.62 ((~hskp16) | c3_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[781, 778])).
% 2.07/1.62 tff(783,plain,
% 2.07/1.62 ((~hskp16) | c3_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[782, 778])).
% 2.07/1.62 tff(784,plain,
% 2.07/1.62 ((~hskp16) | c3_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[783, 778])).
% 2.07/1.62 tff(785,plain,
% 2.07/1.62 ((~hskp16) | c3_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[784, 778])).
% 2.07/1.62 tff(786,plain,
% 2.07/1.62 ((~hskp16) | c3_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[785, 778])).
% 2.07/1.62 tff(787,plain,
% 2.07/1.62 ((~hskp16) | c3_1(a126)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[786, 778])).
% 2.07/1.62 tff(788,plain,
% 2.07/1.62 (c3_1(a126)),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[787, 766])).
% 2.07/1.62 tff(789,plain,
% 2.07/1.62 (((~hskp16) | (~c2_1(a126))) <=> ((~hskp16) | (~c2_1(a126)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(790,plain,
% 2.07/1.62 (((~c2_1(a126)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a126)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(791,axiom,((~c2_1(a126)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 2.07/1.62 tff(792,plain,
% 2.07/1.62 ((~hskp16) | (~c2_1(a126))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[791, 790])).
% 2.07/1.62 tff(793,plain,
% 2.07/1.62 ((~hskp16) | (~c2_1(a126))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[792, 789])).
% 2.07/1.62 tff(794,plain,
% 2.07/1.62 (~c2_1(a126)),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[793, 766])).
% 2.07/1.62 tff(795,plain,
% 2.07/1.62 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 2.07/1.62 inference(bind,[status(th)],[])).
% 2.07/1.62 tff(796,plain,
% 2.07/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(quant_intro,[status(thm)],[795])).
% 2.07/1.62 tff(797,plain,
% 2.07/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(798,plain,
% 2.07/1.62 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~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)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~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))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c2_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(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 2.07/1.62 inference(bind,[status(th)],[])).
% 2.07/1.62 tff(799,plain,
% 2.07/1.62 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(quant_intro,[status(thm)],[798])).
% 2.07/1.62 tff(800,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c3_1(W))) | c0_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 2.07/1.62 tff(801,plain,
% 2.07/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[800, 799])).
% 2.07/1.62 tff(802,plain,
% 2.07/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[801, 797])).
% 2.07/1.62 tff(803,plain,(
% 2.07/1.62 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(skolemize,[status(sab)],[802])).
% 2.07/1.62 tff(804,plain,
% 2.07/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[803, 796])).
% 2.07/1.62 tff(805,assumption,(~c2_1(a126)), introduced(assumption)).
% 2.07/1.62 tff(806,assumption,(~c2_1(a141)), introduced(assumption)).
% 2.07/1.62 tff(807,plain,
% 2.07/1.62 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 2.07/1.62 inference(bind,[status(th)],[])).
% 2.07/1.62 tff(808,plain,
% 2.07/1.62 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.62 inference(quant_intro,[status(thm)],[807])).
% 2.07/1.62 tff(809,plain,
% 2.07/1.62 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(810,plain,
% 2.07/1.62 (^[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)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 2.07/1.62 inference(bind,[status(th)],[])).
% 2.07/1.62 tff(811,plain,
% 2.07/1.62 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.62 inference(quant_intro,[status(thm)],[810])).
% 2.07/1.62 tff(812,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 2.07/1.62 tff(813,plain,
% 2.07/1.62 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[812, 811])).
% 2.07/1.62 tff(814,plain,
% 2.07/1.62 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[813, 809])).
% 2.07/1.62 tff(815,plain,(
% 2.07/1.62 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.62 inference(skolemize,[status(sab)],[814])).
% 2.07/1.62 tff(816,plain,
% 2.07/1.62 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[815, 808])).
% 2.07/1.62 tff(817,assumption,(c1_1(a141)), introduced(assumption)).
% 2.07/1.62 tff(818,assumption,(c0_1(a141)), introduced(assumption)).
% 2.07/1.62 tff(819,plain,
% 2.07/1.62 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(820,plain,
% 2.07/1.62 ((hskp17 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163))) <=> (hskp17 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(821,plain,
% 2.07/1.62 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163))))),
% 2.07/1.62 inference(monotonicity,[status(thm)],[820])).
% 2.07/1.62 tff(822,plain,
% 2.07/1.62 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))),
% 2.07/1.62 inference(transitivity,[status(thm)],[821, 819])).
% 2.07/1.62 tff(823,plain,
% 2.07/1.62 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))),
% 2.07/1.62 inference(quant_inst,[status(thm)],[])).
% 2.07/1.62 tff(824,plain,
% 2.07/1.62 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[823, 822])).
% 2.07/1.62 tff(825,plain,
% 2.07/1.62 (hskp17 | (~c0_1(a163))),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[824, 160, 818, 817, 52, 98, 816, 806])).
% 2.07/1.62 tff(826,plain,
% 2.07/1.62 (hskp17),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[825, 110])).
% 2.07/1.62 tff(827,plain,
% 2.07/1.62 (((~hskp17) | (~c1_1(a132))) <=> ((~hskp17) | (~c1_1(a132)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(828,plain,
% 2.07/1.62 (((~c1_1(a132)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a132)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(829,axiom,((~c1_1(a132)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 2.07/1.62 tff(830,plain,
% 2.07/1.62 ((~hskp17) | (~c1_1(a132))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[829, 828])).
% 2.07/1.62 tff(831,plain,
% 2.07/1.62 ((~hskp17) | (~c1_1(a132))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[830, 827])).
% 2.07/1.62 tff(832,plain,
% 2.07/1.62 (~c1_1(a132)),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[831, 826])).
% 2.07/1.62 tff(833,plain,
% 2.07/1.62 (((~hskp17) | (~c0_1(a132))) <=> ((~hskp17) | (~c0_1(a132)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(834,plain,
% 2.07/1.62 (((~c0_1(a132)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a132)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(835,axiom,((~c0_1(a132)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 2.07/1.62 tff(836,plain,
% 2.07/1.62 ((~hskp17) | (~c0_1(a132))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[835, 834])).
% 2.07/1.62 tff(837,plain,
% 2.07/1.62 ((~hskp17) | (~c0_1(a132))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[836, 833])).
% 2.07/1.62 tff(838,plain,
% 2.07/1.62 (~c0_1(a132)),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[837, 826])).
% 2.07/1.62 tff(839,assumption,(c3_1(a126)), introduced(assumption)).
% 2.07/1.62 tff(840,plain,
% 2.07/1.62 (((~hskp17) | c3_1(a132)) <=> ((~hskp17) | c3_1(a132))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(841,axiom,((~hskp17) | c3_1(a132)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 2.07/1.62 tff(842,plain,
% 2.07/1.62 ((~hskp17) | c3_1(a132)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[841, 840])).
% 2.07/1.62 tff(843,plain,
% 2.07/1.62 ((~hskp17) | c3_1(a132)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[842, 840])).
% 2.07/1.62 tff(844,plain,
% 2.07/1.62 ((~hskp17) | c3_1(a132)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[843, 840])).
% 2.07/1.62 tff(845,plain,
% 2.07/1.62 ((~hskp17) | c3_1(a132)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[844, 840])).
% 2.07/1.62 tff(846,plain,
% 2.07/1.62 ((~hskp17) | c3_1(a132)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[845, 840])).
% 2.07/1.62 tff(847,plain,
% 2.07/1.62 ((~hskp17) | c3_1(a132)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[846, 840])).
% 2.07/1.62 tff(848,plain,
% 2.07/1.62 ((~hskp17) | c3_1(a132)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[847, 840])).
% 2.07/1.62 tff(849,plain,
% 2.07/1.62 ((~hskp17) | c3_1(a132)),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[848, 840])).
% 2.07/1.62 tff(850,plain,
% 2.07/1.62 (c3_1(a132)),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[849, 826])).
% 2.07/1.62 tff(851,assumption,(c3_1(a141)), introduced(assumption)).
% 2.07/1.62 tff(852,plain,
% 2.07/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a126)) | c0_1(a126) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a126)) | c0_1(a126) | (~c3_1(a132)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(853,plain,
% 2.07/1.62 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a126)) | c0_1(a126) | (~c3_1(a132)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(854,plain,
% 2.07/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a126)) | c0_1(a126) | (~c3_1(a132))))),
% 2.07/1.62 inference(monotonicity,[status(thm)],[853])).
% 2.07/1.62 tff(855,plain,
% 2.07/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a126)) | c0_1(a126) | (~c3_1(a132)))),
% 2.07/1.62 inference(transitivity,[status(thm)],[854, 852])).
% 2.07/1.62 tff(856,plain,
% 2.07/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 2.07/1.62 inference(quant_inst,[status(thm)],[])).
% 2.07/1.62 tff(857,plain,
% 2.07/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a126)) | c0_1(a126) | (~c3_1(a132))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[856, 855])).
% 2.07/1.62 tff(858,plain,
% 2.07/1.62 (c0_1(a126)),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[857, 160, 818, 817, 851, 850, 839, 838, 832, 805, 804])).
% 2.07/1.62 tff(859,plain,
% 2.07/1.62 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 2.07/1.62 inference(bind,[status(th)],[])).
% 2.07/1.62 tff(860,plain,
% 2.07/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(quant_intro,[status(thm)],[859])).
% 2.07/1.62 tff(861,plain,
% 2.07/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(862,plain,
% 2.07/1.62 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 2.07/1.62 inference(bind,[status(th)],[])).
% 2.07/1.62 tff(863,plain,
% 2.07/1.62 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(quant_intro,[status(thm)],[862])).
% 2.07/1.62 tff(864,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 2.07/1.62 tff(865,plain,
% 2.07/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[864, 863])).
% 2.07/1.62 tff(866,plain,
% 2.07/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[865, 861])).
% 2.07/1.62 tff(867,plain,(
% 2.07/1.62 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(skolemize,[status(sab)],[866])).
% 2.07/1.62 tff(868,plain,
% 2.07/1.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[867, 860])).
% 2.07/1.62 tff(869,assumption,(c1_1(a126)), introduced(assumption)).
% 2.07/1.62 tff(870,plain,
% 2.07/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a126)) | (~c1_1(a126)) | (~c3_1(a132)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a126)) | (~c1_1(a126)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(871,plain,
% 2.07/1.62 (((~ndr1_0) | c2_1(a126) | (~c1_1(a126)) | (~c0_1(a126)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a126)) | (~c1_1(a126)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(872,plain,
% 2.07/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a126) | (~c1_1(a126)) | (~c0_1(a126)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a126)) | (~c1_1(a126)) | (~c3_1(a132)) | (~c0_1(a163))))),
% 2.07/1.62 inference(monotonicity,[status(thm)],[871])).
% 2.07/1.62 tff(873,plain,
% 2.07/1.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a126) | (~c1_1(a126)) | (~c0_1(a126)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a126)) | (~c1_1(a126)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 2.07/1.62 inference(transitivity,[status(thm)],[872, 870])).
% 2.07/1.62 tff(874,plain,
% 2.07/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a126) | (~c1_1(a126)) | (~c0_1(a126)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 2.07/1.62 inference(quant_inst,[status(thm)],[])).
% 2.07/1.62 tff(875,plain,
% 2.07/1.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a126) | (~ndr1_0) | (~c0_1(a126)) | (~c1_1(a126)) | (~c3_1(a132)) | (~c0_1(a163))),
% 2.07/1.62 inference(modus_ponens,[status(thm)],[874, 873])).
% 2.07/1.62 tff(876,plain,
% 2.07/1.62 ($false),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[875, 160, 850, 869, 52, 98, 838, 832, 805, 868, 110, 858])).
% 2.07/1.62 tff(877,plain,((~c0_1(a163)) | (~c1_1(a126)) | c1_1(a163) | c2_1(a163) | c2_1(a126) | (~c0_1(a141)) | (~c1_1(a141)) | (~c3_1(a141)) | (~c3_1(a126)) | c2_1(a141)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.62 tff(878,plain,
% 2.07/1.62 ($false),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[877, 794, 788, 52, 98, 508, 757, 739, 738, 746, 777])).
% 2.07/1.62 tff(879,plain,(hskp5 | c1_1(a163) | c2_1(a163) | hskp6 | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.62 tff(880,plain,
% 2.07/1.62 (hskp5),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[879, 506, 98, 52, 97])).
% 2.07/1.62 tff(881,assumption,(hskp5), introduced(assumption)).
% 2.07/1.62 tff(882,plain,
% 2.07/1.62 (c0_1(a106)),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[337, 881])).
% 2.07/1.62 tff(883,plain,
% 2.07/1.62 (c1_1(a106)),
% 2.07/1.62 inference(unit_resolution,[status(thm)],[257, 881])).
% 2.07/1.62 tff(884,assumption,(c0_1(a106)), introduced(assumption)).
% 2.07/1.62 tff(885,plain,
% 2.07/1.62 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.62 tff(886,plain,
% 2.07/1.62 ((hskp17 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163))) <=> (hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163)))),
% 2.07/1.62 inference(rewrite,[status(thm)],[])).
% 2.07/1.63 tff(887,plain,
% 2.07/1.63 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163))))),
% 2.07/1.63 inference(monotonicity,[status(thm)],[886])).
% 2.07/1.63 tff(888,plain,
% 2.07/1.63 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163)))),
% 2.07/1.63 inference(transitivity,[status(thm)],[887, 885])).
% 2.07/1.63 tff(889,plain,
% 2.07/1.63 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))),
% 2.07/1.63 inference(quant_inst,[status(thm)],[])).
% 2.07/1.63 tff(890,plain,
% 2.07/1.63 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163))),
% 2.07/1.63 inference(modus_ponens,[status(thm)],[889, 888])).
% 2.07/1.63 tff(891,plain,
% 2.07/1.63 (hskp17 | (~c0_1(a106)) | (~c1_1(a106)) | (~c0_1(a163))),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[890, 160, 52, 98, 109, 816])).
% 2.07/1.63 tff(892,plain,
% 2.07/1.63 (hskp17),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[891, 110, 884, 236])).
% 2.07/1.63 tff(893,plain,
% 2.07/1.63 (~c1_1(a132)),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[831, 892])).
% 2.07/1.63 tff(894,plain,
% 2.07/1.63 (~c0_1(a132)),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[837, 892])).
% 2.07/1.63 tff(895,plain,
% 2.07/1.63 (c3_1(a132)),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[849, 892])).
% 2.07/1.63 tff(896,plain,
% 2.07/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a132)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 2.07/1.63 inference(rewrite,[status(thm)],[])).
% 2.07/1.63 tff(897,plain,
% 2.07/1.63 (((~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 2.07/1.63 inference(rewrite,[status(thm)],[])).
% 2.07/1.63 tff(898,plain,
% 2.07/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a132)) | (~c0_1(a163))))),
% 2.07/1.63 inference(monotonicity,[status(thm)],[897])).
% 2.07/1.63 tff(899,plain,
% 2.07/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 2.07/1.63 inference(transitivity,[status(thm)],[898, 896])).
% 2.07/1.63 tff(900,plain,
% 2.07/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 2.07/1.63 inference(quant_inst,[status(thm)],[])).
% 2.07/1.63 tff(901,plain,
% 2.07/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | c0_1(a132) | c1_1(a132) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a132)) | (~c0_1(a163))),
% 2.07/1.63 inference(modus_ponens,[status(thm)],[900, 899])).
% 2.07/1.63 tff(902,plain,
% 2.07/1.63 ($false),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[901, 160, 895, 884, 236, 52, 98, 894, 893, 109, 868, 110])).
% 2.07/1.63 tff(903,plain,((~c0_1(a163)) | (~c0_1(a106)) | (~c1_1(a106)) | c1_1(a163) | c2_1(a163) | c2_1(a106)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.63 tff(904,plain,
% 2.07/1.63 ($false),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[903, 883, 882, 110, 52, 98, 109])).
% 2.07/1.63 tff(905,plain,((~hskp5) | (~c0_1(a163)) | c1_1(a163) | c2_1(a163) | c2_1(a106)), inference(lemma,lemma(discharge,[]))).
% 2.07/1.63 tff(906,plain,
% 2.07/1.63 (~c0_1(a163)),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[905, 880, 52, 98, 109])).
% 2.07/1.63 tff(907,plain,
% 2.07/1.63 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 2.07/1.63 inference(bind,[status(th)],[])).
% 2.07/1.63 tff(908,plain,
% 2.07/1.63 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.63 inference(quant_intro,[status(thm)],[907])).
% 2.07/1.63 tff(909,plain,
% 2.07/1.63 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.63 inference(rewrite,[status(thm)],[])).
% 2.07/1.63 tff(910,plain,
% 2.07/1.63 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp7) <=> ((hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 2.07/1.63 inference(bind,[status(th)],[])).
% 2.07/1.63 tff(911,plain,
% 2.07/1.63 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.63 inference(quant_intro,[status(thm)],[910])).
% 2.07/1.63 tff(912,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 2.07/1.63 tff(913,plain,
% 2.07/1.63 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.63 inference(modus_ponens,[status(thm)],[912, 911])).
% 2.07/1.63 tff(914,plain,
% 2.07/1.63 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.63 inference(modus_ponens,[status(thm)],[913, 909])).
% 2.07/1.63 tff(915,plain,(
% 2.07/1.63 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.63 inference(skolemize,[status(sab)],[914])).
% 2.07/1.63 tff(916,plain,
% 2.07/1.63 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 2.07/1.63 inference(modus_ponens,[status(thm)],[915, 908])).
% 2.07/1.63 tff(917,plain,
% 2.07/1.63 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp7 | hskp6 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp7 | hskp6 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 2.07/1.63 inference(rewrite,[status(thm)],[])).
% 2.07/1.63 tff(918,plain,
% 2.07/1.63 ((hskp7 | hskp6 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (hskp7 | hskp6 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 2.07/1.63 inference(rewrite,[status(thm)],[])).
% 2.07/1.63 tff(919,plain,
% 2.07/1.63 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp7 | hskp6 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163)))),
% 2.07/1.63 inference(monotonicity,[status(thm)],[918])).
% 2.07/1.63 tff(920,plain,
% 2.07/1.63 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp7 | hskp6 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 2.07/1.63 inference(transitivity,[status(thm)],[919, 917])).
% 2.07/1.63 tff(921,plain,
% 2.07/1.63 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp7 | hskp6 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 2.07/1.63 inference(quant_inst,[status(thm)],[])).
% 2.07/1.63 tff(922,plain,
% 2.07/1.63 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp7 | hskp6 | c1_1(a163) | c3_1(a163) | (~ndr1_0) | c0_1(a163)),
% 2.07/1.63 inference(modus_ponens,[status(thm)],[921, 920])).
% 2.07/1.63 tff(923,plain,
% 2.07/1.63 (hskp7 | hskp6 | c3_1(a163) | c0_1(a163)),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[922, 160, 52, 916])).
% 2.07/1.63 tff(924,plain,
% 2.07/1.63 (hskp7),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[923, 906, 97, 506])).
% 2.07/1.63 tff(925,plain,
% 2.07/1.63 (c3_1(a108)),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[695, 924])).
% 2.07/1.63 tff(926,plain,
% 2.07/1.63 (c1_1(a108)),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[725, 924])).
% 2.07/1.63 tff(927,plain,
% 2.07/1.63 (c0_1(a135)),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[459, 427])).
% 2.07/1.63 tff(928,plain,
% 2.07/1.63 (~c2_1(a108)),
% 2.07/1.63 inference(unit_resolution,[status(thm)],[732, 160, 927, 926, 925, 52, 98, 97, 439, 433, 108])).
% 2.07/1.63 tff(929,plain,
% 2.07/1.63 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 2.07/1.63 inference(bind,[status(th)],[])).
% 2.07/1.63 tff(930,plain,
% 2.07/1.63 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.07/1.63 inference(quant_intro,[status(thm)],[929])).
% 2.07/1.63 tff(931,plain,
% 2.07/1.63 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.07/1.63 inference(rewrite,[status(thm)],[])).
% 2.07/1.63 tff(932,plain,
% 2.07/1.63 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 2.17/1.63 inference(bind,[status(th)],[])).
% 2.17/1.63 tff(933,plain,
% 2.17/1.63 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.17/1.63 inference(quant_intro,[status(thm)],[932])).
% 2.17/1.63 tff(934,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 2.17/1.63 tff(935,plain,
% 2.17/1.63 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.17/1.63 inference(modus_ponens,[status(thm)],[934, 933])).
% 2.17/1.63 tff(936,plain,
% 2.17/1.63 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.17/1.63 inference(modus_ponens,[status(thm)],[935, 931])).
% 2.17/1.63 tff(937,plain,(
% 2.17/1.63 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.17/1.63 inference(skolemize,[status(sab)],[936])).
% 2.17/1.63 tff(938,plain,
% 2.17/1.63 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 2.17/1.63 inference(modus_ponens,[status(thm)],[937, 930])).
% 2.17/1.63 tff(939,plain,
% 2.17/1.63 (~c0_1(a108)),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[681, 924])).
% 2.17/1.63 tff(940,plain,
% 2.17/1.63 (hskp15),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[734, 939, 52, 98, 97, 439, 433, 927, 924])).
% 2.17/1.63 tff(941,plain,
% 2.17/1.63 (~c1_1(a117)),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[563, 940])).
% 2.17/1.63 tff(942,plain,
% 2.17/1.63 (c3_1(a117)),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[585, 940])).
% 2.17/1.63 tff(943,plain,
% 2.17/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c1_1(a117) | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c1_1(a108)) | c2_1(a117) | (~c3_1(a117)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c1_1(a117) | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c1_1(a108)) | c2_1(a117) | (~c3_1(a117)))),
% 2.17/1.63 inference(rewrite,[status(thm)],[])).
% 2.17/1.63 tff(944,plain,
% 2.17/1.63 ((hskp6 | (~ndr1_0) | c1_1(a117) | c2_1(a117) | (~c3_1(a117)) | c2_1(a108) | c0_1(a108) | (~c1_1(a108))) <=> (hskp6 | c1_1(a117) | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c1_1(a108)) | c2_1(a117) | (~c3_1(a117)))),
% 2.17/1.63 inference(rewrite,[status(thm)],[])).
% 2.17/1.63 tff(945,plain,
% 2.17/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a117) | c2_1(a117) | (~c3_1(a117)) | c2_1(a108) | c0_1(a108) | (~c1_1(a108)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c1_1(a117) | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c1_1(a108)) | c2_1(a117) | (~c3_1(a117))))),
% 2.17/1.63 inference(monotonicity,[status(thm)],[944])).
% 2.17/1.63 tff(946,plain,
% 2.17/1.63 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a117) | c2_1(a117) | (~c3_1(a117)) | c2_1(a108) | c0_1(a108) | (~c1_1(a108)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c1_1(a117) | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c1_1(a108)) | c2_1(a117) | (~c3_1(a117)))),
% 2.17/1.63 inference(transitivity,[status(thm)],[945, 943])).
% 2.17/1.63 tff(947,plain,
% 2.17/1.63 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a117) | c2_1(a117) | (~c3_1(a117)) | c2_1(a108) | c0_1(a108) | (~c1_1(a108)))),
% 2.17/1.63 inference(quant_inst,[status(thm)],[])).
% 2.17/1.63 tff(948,plain,
% 2.17/1.63 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c1_1(a117) | c0_1(a108) | (~ndr1_0) | c2_1(a108) | (~c1_1(a108)) | c2_1(a117) | (~c3_1(a117))),
% 2.17/1.63 inference(modus_ponens,[status(thm)],[947, 946])).
% 2.17/1.63 tff(949,plain,
% 2.17/1.63 (c2_1(a117)),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[948, 160, 506, 942, 926, 941, 939, 938, 928])).
% 2.17/1.63 tff(950,plain,
% 2.17/1.63 (~hskp28),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[555, 439, 52, 98, 97, 927, 433])).
% 2.17/1.63 tff(951,plain,
% 2.17/1.63 (hskp31),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[608, 940, 950])).
% 2.17/1.63 tff(952,plain,
% 2.17/1.63 (c3_1(a141)),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[63, 951])).
% 2.17/1.63 tff(953,plain,
% 2.17/1.63 (c1_1(a141)),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[74, 951])).
% 2.17/1.63 tff(954,plain,
% 2.17/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a135)))),
% 2.17/1.63 inference(rewrite,[status(thm)],[])).
% 2.17/1.63 tff(955,plain,
% 2.17/1.63 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163)) <=> (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a135)))),
% 2.17/1.63 inference(rewrite,[status(thm)],[])).
% 2.17/1.63 tff(956,plain,
% 2.17/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a135))))),
% 2.17/1.63 inference(monotonicity,[status(thm)],[955])).
% 2.17/1.63 tff(957,plain,
% 2.17/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a135)))),
% 2.17/1.63 inference(transitivity,[status(thm)],[956, 954])).
% 2.17/1.63 tff(958,plain,
% 2.17/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c1_1(a163) | c2_1(a163))),
% 2.17/1.63 inference(quant_inst,[status(thm)],[])).
% 2.17/1.63 tff(959,plain,
% 2.17/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c1_1(a163) | c2_1(a163) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c0_1(a135))),
% 2.17/1.63 inference(modus_ponens,[status(thm)],[958, 957])).
% 2.17/1.63 tff(960,plain,
% 2.17/1.63 (~c2_1(a141)),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[959, 160, 953, 952, 927, 52, 98, 97, 439, 433, 108])).
% 2.17/1.63 tff(961,plain,
% 2.17/1.63 (c0_1(a117)),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[574, 940])).
% 2.17/1.63 tff(962,plain,
% 2.17/1.63 (c0_1(a141)),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[85, 951])).
% 2.17/1.63 tff(963,plain,
% 2.17/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a117) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a117)) | (~c2_1(a117)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a117) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a117)) | (~c2_1(a117)))),
% 2.17/1.63 inference(rewrite,[status(thm)],[])).
% 2.17/1.63 tff(964,plain,
% 2.17/1.63 (((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a117) | (~c0_1(a117)) | (~c2_1(a117))) <=> (c1_1(a117) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a117)) | (~c2_1(a117)))),
% 2.17/1.63 inference(rewrite,[status(thm)],[])).
% 2.17/1.63 tff(965,plain,
% 2.17/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a117) | (~c0_1(a117)) | (~c2_1(a117)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a117) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a117)) | (~c2_1(a117))))),
% 2.17/1.63 inference(monotonicity,[status(thm)],[964])).
% 2.17/1.63 tff(966,plain,
% 2.17/1.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a117) | (~c0_1(a117)) | (~c2_1(a117)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a117) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a117)) | (~c2_1(a117)))),
% 2.17/1.63 inference(transitivity,[status(thm)],[965, 963])).
% 2.17/1.63 tff(967,plain,
% 2.17/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a117) | (~c0_1(a117)) | (~c2_1(a117)))),
% 2.17/1.63 inference(quant_inst,[status(thm)],[])).
% 2.17/1.63 tff(968,plain,
% 2.17/1.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a117) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a117)) | (~c2_1(a117))),
% 2.17/1.63 inference(modus_ponens,[status(thm)],[967, 966])).
% 2.17/1.63 tff(969,plain,
% 2.17/1.63 ($false),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[968, 160, 962, 953, 952, 961, 941, 320, 960, 949])).
% 2.17/1.63 tff(970,plain,(c2_1(a106) | c1_1(a163) | c2_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.63 tff(971,plain,
% 2.17/1.63 (c2_1(a106)),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[970, 97, 98, 52])).
% 2.17/1.63 tff(972,plain,
% 2.17/1.63 (((~hskp5) | (~c2_1(a106))) <=> ((~hskp5) | (~c2_1(a106)))),
% 2.17/1.63 inference(rewrite,[status(thm)],[])).
% 2.17/1.63 tff(973,plain,
% 2.17/1.63 (((~c2_1(a106)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a106)))),
% 2.17/1.63 inference(rewrite,[status(thm)],[])).
% 2.17/1.63 tff(974,axiom,((~c2_1(a106)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 2.17/1.63 tff(975,plain,
% 2.17/1.63 ((~hskp5) | (~c2_1(a106))),
% 2.17/1.63 inference(modus_ponens,[status(thm)],[974, 973])).
% 2.17/1.63 tff(976,plain,
% 2.17/1.63 ((~hskp5) | (~c2_1(a106))),
% 2.17/1.63 inference(modus_ponens,[status(thm)],[975, 972])).
% 2.17/1.63 tff(977,plain,
% 2.17/1.63 (~hskp5),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[976, 971])).
% 2.17/1.63 tff(978,plain,
% 2.17/1.63 (c0_1(a163)),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[234, 977, 97])).
% 2.17/1.63 tff(979,plain,
% 2.17/1.63 (hskp19),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[216, 978, 97, 98])).
% 2.17/1.63 tff(980,plain,
% 2.17/1.63 (hskp6),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[879, 977, 98, 52, 97])).
% 2.17/1.63 tff(981,plain,
% 2.17/1.63 (~c0_1(a107)),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[446, 980])).
% 2.17/1.63 tff(982,plain,
% 2.17/1.63 ($false),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[503, 981, 980, 979, 52, 98, 97])).
% 2.17/1.63 tff(983,plain,(c3_1(a163) | c1_1(a163) | c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.63 tff(984,plain,
% 2.17/1.63 (c3_1(a163)),
% 2.17/1.63 inference(unit_resolution,[status(thm)],[983, 98, 52])).
% 2.17/1.63 tff(985,plain,
% 2.17/1.63 (((~hskp24) | (~c3_1(a163))) <=> ((~hskp24) | (~c3_1(a163)))),
% 2.17/1.63 inference(rewrite,[status(thm)],[])).
% 2.17/1.63 tff(986,plain,
% 2.17/1.63 (((~c3_1(a163)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a163)))),
% 2.17/1.63 inference(rewrite,[status(thm)],[])).
% 2.17/1.63 tff(987,axiom,((~c3_1(a163)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 2.17/1.63 tff(988,plain,
% 2.17/1.63 ((~hskp24) | (~c3_1(a163))),
% 2.17/1.63 inference(modus_ponens,[status(thm)],[987, 986])).
% 2.17/1.64 tff(989,plain,
% 2.17/1.64 ((~hskp24) | (~c3_1(a163))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[988, 985])).
% 2.17/1.64 tff(990,plain,
% 2.17/1.64 (~hskp24),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[989, 984])).
% 2.17/1.64 tff(991,plain,
% 2.17/1.64 (hskp30),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[158, 23, 990])).
% 2.17/1.64 tff(992,plain,
% 2.17/1.64 (((~hskp30) | c3_1(a131)) <=> ((~hskp30) | c3_1(a131))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(993,axiom,((~hskp30) | c3_1(a131)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 2.17/1.64 tff(994,plain,
% 2.17/1.64 ((~hskp30) | c3_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[993, 992])).
% 2.17/1.64 tff(995,plain,
% 2.17/1.64 ((~hskp30) | c3_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[994, 992])).
% 2.17/1.64 tff(996,plain,
% 2.17/1.64 ((~hskp30) | c3_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[995, 992])).
% 2.17/1.64 tff(997,plain,
% 2.17/1.64 ((~hskp30) | c3_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[996, 992])).
% 2.17/1.64 tff(998,plain,
% 2.17/1.64 ((~hskp30) | c3_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[997, 992])).
% 2.17/1.64 tff(999,plain,
% 2.17/1.64 ((~hskp30) | c3_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[998, 992])).
% 2.17/1.64 tff(1000,plain,
% 2.17/1.64 ((~hskp30) | c3_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[999, 992])).
% 2.17/1.64 tff(1001,plain,
% 2.17/1.64 ((~hskp30) | c3_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1000, 992])).
% 2.17/1.64 tff(1002,plain,
% 2.17/1.64 (c3_1(a131)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1001, 991])).
% 2.17/1.64 tff(1003,plain,
% 2.17/1.64 (((~hskp30) | c2_1(a131)) <=> ((~hskp30) | c2_1(a131))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1004,axiom,((~hskp30) | c2_1(a131)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 2.17/1.64 tff(1005,plain,
% 2.17/1.64 ((~hskp30) | c2_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 2.17/1.64 tff(1006,plain,
% 2.17/1.64 ((~hskp30) | c2_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1005, 1003])).
% 2.17/1.64 tff(1007,plain,
% 2.17/1.64 ((~hskp30) | c2_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1006, 1003])).
% 2.17/1.64 tff(1008,plain,
% 2.17/1.64 ((~hskp30) | c2_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1007, 1003])).
% 2.17/1.64 tff(1009,plain,
% 2.17/1.64 ((~hskp30) | c2_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1008, 1003])).
% 2.17/1.64 tff(1010,plain,
% 2.17/1.64 ((~hskp30) | c2_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1009, 1003])).
% 2.17/1.64 tff(1011,plain,
% 2.17/1.64 ((~hskp30) | c2_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1010, 1003])).
% 2.17/1.64 tff(1012,plain,
% 2.17/1.64 ((~hskp30) | c2_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1011, 1003])).
% 2.17/1.64 tff(1013,plain,
% 2.17/1.64 (c2_1(a131)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1012, 991])).
% 2.17/1.64 tff(1014,plain,
% 2.17/1.64 (((~hskp30) | c0_1(a131)) <=> ((~hskp30) | c0_1(a131))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1015,axiom,((~hskp30) | c0_1(a131)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 2.17/1.64 tff(1016,plain,
% 2.17/1.64 ((~hskp30) | c0_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 2.17/1.64 tff(1017,plain,
% 2.17/1.64 ((~hskp30) | c0_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1016, 1014])).
% 2.17/1.64 tff(1018,plain,
% 2.17/1.64 ((~hskp30) | c0_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1017, 1014])).
% 2.17/1.64 tff(1019,plain,
% 2.17/1.64 ((~hskp30) | c0_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1018, 1014])).
% 2.17/1.64 tff(1020,plain,
% 2.17/1.64 ((~hskp30) | c0_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1019, 1014])).
% 2.17/1.64 tff(1021,plain,
% 2.17/1.64 ((~hskp30) | c0_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1020, 1014])).
% 2.17/1.64 tff(1022,plain,
% 2.17/1.64 ((~hskp30) | c0_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1021, 1014])).
% 2.17/1.64 tff(1023,plain,
% 2.17/1.64 ((~hskp30) | c0_1(a131)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1022, 1014])).
% 2.17/1.64 tff(1024,plain,
% 2.17/1.64 (c0_1(a131)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1023, 991])).
% 2.17/1.64 tff(1025,plain,
% 2.17/1.64 (^[U: $i] : refl((hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 2.17/1.64 inference(bind,[status(th)],[])).
% 2.17/1.64 tff(1026,plain,
% 2.17/1.64 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.17/1.64 inference(quant_intro,[status(thm)],[1025])).
% 2.17/1.64 tff(1027,plain,
% 2.17/1.64 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1028,plain,
% 2.17/1.64 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp11) <=> ((hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp11))), rewrite(((hskp19 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp11) <=> (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 2.17/1.64 inference(bind,[status(th)],[])).
% 2.17/1.64 tff(1029,plain,
% 2.17/1.64 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp11) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.17/1.64 inference(quant_intro,[status(thm)],[1028])).
% 2.17/1.64 tff(1030,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp19) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 2.17/1.64 tff(1031,plain,
% 2.17/1.64 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 2.17/1.64 tff(1032,plain,
% 2.17/1.64 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1031, 1027])).
% 2.17/1.64 tff(1033,plain,(
% 2.17/1.64 ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.17/1.64 inference(skolemize,[status(sab)],[1032])).
% 2.17/1.64 tff(1034,plain,
% 2.17/1.64 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1033, 1026])).
% 2.17/1.64 tff(1035,assumption,(hskp30), introduced(assumption)).
% 2.17/1.64 tff(1036,plain,
% 2.17/1.64 (c3_1(a131)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1001, 1035])).
% 2.17/1.64 tff(1037,plain,
% 2.17/1.64 (c2_1(a131)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1012, 1035])).
% 2.17/1.64 tff(1038,plain,
% 2.17/1.64 (c0_1(a131)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1023, 1035])).
% 2.17/1.64 tff(1039,assumption,(hskp11), introduced(assumption)).
% 2.17/1.64 tff(1040,plain,
% 2.17/1.64 (((~hskp11) | (~c3_1(a112))) <=> ((~hskp11) | (~c3_1(a112)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1041,plain,
% 2.17/1.64 (((~c3_1(a112)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a112)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1042,axiom,((~c3_1(a112)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 2.17/1.64 tff(1043,plain,
% 2.17/1.64 ((~hskp11) | (~c3_1(a112))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 2.17/1.64 tff(1044,plain,
% 2.17/1.64 ((~hskp11) | (~c3_1(a112))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1043, 1040])).
% 2.17/1.64 tff(1045,plain,
% 2.17/1.64 (~c3_1(a112)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1044, 1039])).
% 2.17/1.64 tff(1046,plain,
% 2.17/1.64 (((~hskp11) | (~c2_1(a112))) <=> ((~hskp11) | (~c2_1(a112)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1047,plain,
% 2.17/1.64 (((~c2_1(a112)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a112)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1048,axiom,((~c2_1(a112)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 2.17/1.64 tff(1049,plain,
% 2.17/1.64 ((~hskp11) | (~c2_1(a112))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 2.17/1.64 tff(1050,plain,
% 2.17/1.64 ((~hskp11) | (~c2_1(a112))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1049, 1046])).
% 2.17/1.64 tff(1051,plain,
% 2.17/1.64 (~c2_1(a112)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1050, 1039])).
% 2.17/1.64 tff(1052,plain,
% 2.17/1.64 (((~hskp11) | c1_1(a112)) <=> ((~hskp11) | c1_1(a112))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1053,axiom,((~hskp11) | c1_1(a112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 2.17/1.64 tff(1054,plain,
% 2.17/1.64 ((~hskp11) | c1_1(a112)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 2.17/1.64 tff(1055,plain,
% 2.17/1.64 ((~hskp11) | c1_1(a112)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1054, 1052])).
% 2.17/1.64 tff(1056,plain,
% 2.17/1.64 ((~hskp11) | c1_1(a112)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1055, 1052])).
% 2.17/1.64 tff(1057,plain,
% 2.17/1.64 ((~hskp11) | c1_1(a112)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1056, 1052])).
% 2.17/1.64 tff(1058,plain,
% 2.17/1.64 ((~hskp11) | c1_1(a112)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1057, 1052])).
% 2.17/1.64 tff(1059,plain,
% 2.17/1.64 ((~hskp11) | c1_1(a112)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1058, 1052])).
% 2.17/1.64 tff(1060,plain,
% 2.17/1.64 ((~hskp11) | c1_1(a112)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1059, 1052])).
% 2.17/1.64 tff(1061,plain,
% 2.17/1.64 ((~hskp11) | c1_1(a112)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1060, 1052])).
% 2.17/1.64 tff(1062,plain,
% 2.17/1.64 (c1_1(a112)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1061, 1039])).
% 2.17/1.64 tff(1063,plain,
% 2.17/1.64 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a112) | c3_1(a112) | (~ndr1_0) | (~c1_1(a112)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a112) | c3_1(a112) | (~ndr1_0) | (~c1_1(a112)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1064,plain,
% 2.17/1.64 ((hskp19 | (~ndr1_0) | c3_1(a112) | c2_1(a112) | (~c1_1(a112))) <=> (hskp19 | c2_1(a112) | c3_1(a112) | (~ndr1_0) | (~c1_1(a112)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1065,plain,
% 2.17/1.64 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a112) | c2_1(a112) | (~c1_1(a112)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a112) | c3_1(a112) | (~ndr1_0) | (~c1_1(a112))))),
% 2.17/1.64 inference(monotonicity,[status(thm)],[1064])).
% 2.17/1.64 tff(1066,plain,
% 2.17/1.64 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a112) | c2_1(a112) | (~c1_1(a112)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a112) | c3_1(a112) | (~ndr1_0) | (~c1_1(a112)))),
% 2.17/1.64 inference(transitivity,[status(thm)],[1065, 1063])).
% 2.17/1.64 tff(1067,plain,
% 2.17/1.64 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a112) | c2_1(a112) | (~c1_1(a112)))),
% 2.17/1.64 inference(quant_inst,[status(thm)],[])).
% 2.17/1.64 tff(1068,plain,
% 2.17/1.64 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a112) | c3_1(a112) | (~ndr1_0) | (~c1_1(a112))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 2.17/1.64 tff(1069,plain,
% 2.17/1.64 ($false),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1068, 160, 1, 1062, 1051, 1045, 11])).
% 2.17/1.64 tff(1070,plain,((~hskp11) | hskp19), inference(lemma,lemma(discharge,[]))).
% 2.17/1.64 tff(1071,plain,
% 2.17/1.64 (~hskp11),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1070, 1])).
% 2.17/1.64 tff(1072,plain,
% 2.17/1.64 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1073,plain,
% 2.17/1.64 ((hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131))) <=> (hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1074,plain,
% 2.17/1.64 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131))))),
% 2.17/1.64 inference(monotonicity,[status(thm)],[1073])).
% 2.17/1.64 tff(1075,plain,
% 2.17/1.64 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))),
% 2.17/1.64 inference(transitivity,[status(thm)],[1074, 1072])).
% 2.17/1.64 tff(1076,plain,
% 2.17/1.64 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)))),
% 2.17/1.64 inference(quant_inst,[status(thm)],[])).
% 2.17/1.64 tff(1077,plain,
% 2.17/1.64 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 2.17/1.64 tff(1078,plain,
% 2.17/1.64 ($false),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1077, 160, 1, 1071, 1038, 1037, 1036, 1034])).
% 2.17/1.64 tff(1079,plain,((~hskp30) | hskp19), inference(lemma,lemma(discharge,[]))).
% 2.17/1.64 tff(1080,plain,
% 2.17/1.64 (~hskp30),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1079, 1])).
% 2.17/1.64 tff(1081,assumption,(~hskp30), introduced(assumption)).
% 2.17/1.64 tff(1082,plain,
% 2.17/1.64 (hskp24),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[158, 23, 1081])).
% 2.17/1.64 tff(1083,plain,
% 2.17/1.64 (~c3_1(a163)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[989, 1082])).
% 2.17/1.64 tff(1084,plain,
% 2.17/1.64 (((~hskp24) | (~c2_1(a163))) <=> ((~hskp24) | (~c2_1(a163)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1085,plain,
% 2.17/1.64 (((~c2_1(a163)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a163)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1086,axiom,((~c2_1(a163)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 2.17/1.64 tff(1087,plain,
% 2.17/1.64 ((~hskp24) | (~c2_1(a163))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 2.17/1.64 tff(1088,plain,
% 2.17/1.64 ((~hskp24) | (~c2_1(a163))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1087, 1084])).
% 2.17/1.64 tff(1089,plain,
% 2.17/1.64 (~c2_1(a163)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1088, 1082])).
% 2.17/1.64 tff(1090,plain,
% 2.17/1.64 (((~hskp24) | (~c1_1(a163))) <=> ((~hskp24) | (~c1_1(a163)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1091,plain,
% 2.17/1.64 (((~c1_1(a163)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a163)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1092,axiom,((~c1_1(a163)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 2.17/1.64 tff(1093,plain,
% 2.17/1.64 ((~hskp24) | (~c1_1(a163))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 2.17/1.64 tff(1094,plain,
% 2.17/1.64 ((~hskp24) | (~c1_1(a163))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1093, 1090])).
% 2.17/1.64 tff(1095,plain,
% 2.17/1.64 (~c1_1(a163)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1094, 1082])).
% 2.17/1.64 tff(1096,plain,
% 2.17/1.64 (hskp5),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[736, 1095, 1089, 1083, 23])).
% 2.17/1.64 tff(1097,plain,
% 2.17/1.64 (~c2_1(a106)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[976, 1096])).
% 2.17/1.64 tff(1098,plain,
% 2.17/1.64 (~c0_1(a163)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[905, 1096, 1095, 1089, 1097])).
% 2.17/1.64 tff(1099,plain,
% 2.17/1.64 (c1_1(a106)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[257, 1096])).
% 2.17/1.64 tff(1100,plain,
% 2.17/1.64 (hskp19),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[423, 1099, 1095, 1089, 1097, 1098, 1083])).
% 2.17/1.64 tff(1101,plain,
% 2.17/1.64 (~c3_1(a135)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[432, 1100])).
% 2.17/1.64 tff(1102,plain,
% 2.17/1.64 (c0_1(a135)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[459, 1100])).
% 2.17/1.64 tff(1103,plain,
% 2.17/1.64 (~c2_1(a135)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[438, 1100])).
% 2.17/1.64 tff(1104,plain,
% 2.17/1.64 (~hskp28),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[555, 1103, 1095, 1089, 1083, 1102, 1101])).
% 2.17/1.64 tff(1105,plain,
% 2.17/1.64 (~hskp15),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[608, 1104, 23])).
% 2.17/1.64 tff(1106,plain,
% 2.17/1.64 (~hskp6),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[505, 1100, 1095, 1089, 1083])).
% 2.17/1.64 tff(1107,plain,
% 2.17/1.64 (hskp7 | hskp6 | c0_1(a163)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[922, 160, 1095, 1083, 916])).
% 2.17/1.64 tff(1108,plain,
% 2.17/1.64 (hskp7),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1107, 1106, 1098])).
% 2.17/1.64 tff(1109,plain,
% 2.17/1.64 (~c0_1(a108)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[681, 1108])).
% 2.17/1.64 tff(1110,plain,
% 2.17/1.64 ($false),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[734, 1109, 1108, 1095, 1089, 1083, 1103, 1101, 1102, 1105])).
% 2.17/1.64 tff(1111,plain,(hskp31 | hskp30), inference(lemma,lemma(discharge,[]))).
% 2.17/1.64 tff(1112,plain,
% 2.17/1.64 (hskp31),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1111, 1080])).
% 2.17/1.64 tff(1113,plain,
% 2.17/1.64 (c3_1(a141)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[63, 1112])).
% 2.17/1.64 tff(1114,plain,
% 2.17/1.64 (c1_1(a141)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[74, 1112])).
% 2.17/1.64 tff(1115,plain,
% 2.17/1.64 (c0_1(a141)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[85, 1112])).
% 2.17/1.64 tff(1116,plain,
% 2.17/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1117,plain,
% 2.17/1.64 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1118,plain,
% 2.17/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)))),
% 2.17/1.64 inference(monotonicity,[status(thm)],[1117])).
% 2.17/1.64 tff(1119,plain,
% 2.17/1.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.17/1.64 inference(transitivity,[status(thm)],[1118, 1116])).
% 2.17/1.64 tff(1120,plain,
% 2.17/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 2.17/1.64 inference(quant_inst,[status(thm)],[])).
% 2.17/1.64 tff(1121,plain,
% 2.17/1.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1120, 1119])).
% 2.17/1.64 tff(1122,plain,
% 2.17/1.64 (c0_1(a163)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1121, 160, 1115, 1114, 1113, 52, 98, 984, 804])).
% 2.17/1.64 tff(1123,plain,
% 2.17/1.64 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 2.17/1.64 inference(bind,[status(th)],[])).
% 2.17/1.64 tff(1124,plain,
% 2.17/1.64 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.17/1.64 inference(quant_intro,[status(thm)],[1123])).
% 2.17/1.64 tff(1125,plain,
% 2.17/1.64 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1126,plain,
% 2.17/1.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 2.17/1.64 inference(bind,[status(th)],[])).
% 2.17/1.64 tff(1127,plain,
% 2.17/1.64 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.17/1.64 inference(quant_intro,[status(thm)],[1126])).
% 2.17/1.64 tff(1128,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 2.17/1.64 tff(1129,plain,
% 2.17/1.64 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 2.17/1.64 tff(1130,plain,
% 2.17/1.64 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1129, 1125])).
% 2.17/1.64 tff(1131,plain,(
% 2.17/1.64 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.17/1.64 inference(skolemize,[status(sab)],[1130])).
% 2.17/1.64 tff(1132,plain,
% 2.17/1.64 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1131, 1124])).
% 2.17/1.64 tff(1133,plain,
% 2.17/1.64 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1134,plain,
% 2.17/1.64 ((hskp16 | (~ndr1_0) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163))) <=> (hskp16 | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1135,plain,
% 2.17/1.64 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))))),
% 2.17/1.64 inference(monotonicity,[status(thm)],[1134])).
% 2.17/1.64 tff(1136,plain,
% 2.17/1.64 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.17/1.64 inference(transitivity,[status(thm)],[1135, 1133])).
% 2.17/1.64 tff(1137,plain,
% 2.17/1.64 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))),
% 2.17/1.64 inference(quant_inst,[status(thm)],[])).
% 2.17/1.64 tff(1138,plain,
% 2.17/1.64 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a163) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))),
% 2.17/1.64 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 2.17/1.64 tff(1139,plain,
% 2.17/1.64 (hskp16 | (~c3_1(a163)) | (~c0_1(a163))),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1138, 160, 52, 98, 1132])).
% 2.17/1.64 tff(1140,plain,
% 2.17/1.64 (hskp16),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[1139, 1122, 984])).
% 2.17/1.64 tff(1141,plain,
% 2.17/1.64 (c1_1(a126)),
% 2.17/1.64 inference(unit_resolution,[status(thm)],[776, 1140])).
% 2.17/1.64 tff(1142,plain,
% 2.17/1.64 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1143,plain,
% 2.17/1.64 ((hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141))) <=> (hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))),
% 2.17/1.64 inference(rewrite,[status(thm)],[])).
% 2.17/1.64 tff(1144,plain,
% 2.17/1.64 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141))))),
% 2.17/1.64 inference(monotonicity,[status(thm)],[1143])).
% 2.17/1.64 tff(1145,plain,
% 2.17/1.64 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))),
% 2.17/1.64 inference(transitivity,[status(thm)],[1144, 1142])).
% 2.17/1.64 tff(1146,plain,
% 2.17/1.64 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)))),
% 2.17/1.64 inference(quant_inst,[status(thm)],[])).
% 2.17/1.64 tff(1147,plain,
% 2.17/1.64 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141))),
% 2.17/1.65 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 2.17/1.65 tff(1148,plain,
% 2.17/1.65 (~c2_1(a141)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1147, 160, 1, 1071, 1115, 1113, 1034])).
% 2.17/1.65 tff(1149,plain,
% 2.17/1.65 (c3_1(a126)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[787, 1140])).
% 2.17/1.65 tff(1150,plain,
% 2.17/1.65 (~c2_1(a126)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[793, 1140])).
% 2.17/1.65 tff(1151,plain,
% 2.17/1.65 ($false),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[877, 1150, 1149, 52, 98, 1122, 1115, 1114, 1113, 1148, 1141])).
% 2.17/1.65 tff(1152,plain,(hskp19 | c1_1(a163) | c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.65 tff(1153,plain,
% 2.17/1.65 (hskp19),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1152, 98, 52])).
% 2.17/1.65 tff(1154,plain,
% 2.17/1.65 (~c3_1(a135)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[432, 1153])).
% 2.17/1.65 tff(1155,plain,
% 2.17/1.65 (~c2_1(a135)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[438, 1153])).
% 2.17/1.65 tff(1156,plain,
% 2.17/1.65 (c0_1(a135)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[459, 1153])).
% 2.17/1.65 tff(1157,plain,
% 2.17/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1158,plain,
% 2.17/1.65 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135)) <=> (c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1159,plain,
% 2.17/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 2.17/1.65 inference(monotonicity,[status(thm)],[1158])).
% 2.17/1.65 tff(1160,plain,
% 2.17/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.17/1.65 inference(transitivity,[status(thm)],[1159, 1157])).
% 2.17/1.65 tff(1161,plain,
% 2.17/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))),
% 2.17/1.65 inference(quant_inst,[status(thm)],[])).
% 2.17/1.65 tff(1162,plain,
% 2.17/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 2.17/1.65 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 2.17/1.65 tff(1163,plain,
% 2.17/1.65 (c1_1(a135)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1162, 160, 547, 536, 525, 1156, 1155, 1154, 108])).
% 2.17/1.65 tff(1164,assumption,(c3_1(a131)), introduced(assumption)).
% 2.17/1.65 tff(1165,assumption,(c2_1(a131)), introduced(assumption)).
% 2.17/1.65 tff(1166,assumption,(c0_1(a131)), introduced(assumption)).
% 2.17/1.65 tff(1167,plain,
% 2.17/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c0_1(a163) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c0_1(a163) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1168,plain,
% 2.17/1.65 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c0_1(a163) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1169,plain,
% 2.17/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c0_1(a163) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 2.17/1.65 inference(monotonicity,[status(thm)],[1168])).
% 2.17/1.65 tff(1170,plain,
% 2.17/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c0_1(a163) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.17/1.65 inference(transitivity,[status(thm)],[1169, 1167])).
% 2.17/1.65 tff(1171,plain,
% 2.17/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 2.17/1.65 inference(quant_inst,[status(thm)],[])).
% 2.17/1.65 tff(1172,plain,
% 2.17/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c0_1(a163) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 2.17/1.65 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 2.17/1.65 tff(1173,plain,
% 2.17/1.65 (c0_1(a163)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1172, 160, 1166, 1165, 1164, 547, 536, 525, 52, 984, 96])).
% 2.17/1.65 tff(1174,plain,
% 2.17/1.65 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1175,plain,
% 2.17/1.65 ((hskp17 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163))) <=> (hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1176,plain,
% 2.17/1.65 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163))))),
% 2.17/1.65 inference(monotonicity,[status(thm)],[1175])).
% 2.17/1.65 tff(1177,plain,
% 2.17/1.65 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))),
% 2.17/1.65 inference(transitivity,[status(thm)],[1176, 1174])).
% 2.17/1.65 tff(1178,plain,
% 2.17/1.65 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c2_1(a163) | c1_1(a163) | (~c0_1(a163)))),
% 2.17/1.65 inference(quant_inst,[status(thm)],[])).
% 2.17/1.65 tff(1179,plain,
% 2.17/1.65 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp17 | c1_1(a163) | c2_1(a163) | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163))),
% 2.17/1.65 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 2.17/1.65 tff(1180,plain,
% 2.17/1.65 (hskp17 | (~c1_1(a135)) | (~c0_1(a163))),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1179, 160, 1156, 52, 98, 1155, 816])).
% 2.17/1.65 tff(1181,plain,
% 2.17/1.65 (hskp17),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1180, 1173, 1163])).
% 2.17/1.65 tff(1182,plain,
% 2.17/1.65 (~c1_1(a132)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[831, 1181])).
% 2.17/1.65 tff(1183,plain,
% 2.17/1.65 (~c0_1(a132)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[837, 1181])).
% 2.17/1.65 tff(1184,plain,
% 2.17/1.65 (c3_1(a132)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[849, 1181])).
% 2.17/1.65 tff(1185,plain,
% 2.17/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1186,plain,
% 2.17/1.65 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1187,plain,
% 2.17/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 2.17/1.65 inference(monotonicity,[status(thm)],[1186])).
% 2.17/1.65 tff(1188,plain,
% 2.17/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.17/1.65 inference(transitivity,[status(thm)],[1187, 1185])).
% 2.17/1.65 tff(1189,plain,
% 2.17/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 2.17/1.65 inference(quant_inst,[status(thm)],[])).
% 2.17/1.65 tff(1190,plain,
% 2.17/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 2.17/1.65 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 2.17/1.65 tff(1191,plain,
% 2.17/1.65 ($false),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1190, 160, 1166, 1165, 1164, 547, 536, 525, 1184, 1183, 1182, 96])).
% 2.17/1.65 tff(1192,plain,((~hskp28) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a163) | c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.65 tff(1193,plain,
% 2.17/1.65 (~hskp28),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1192, 1024, 1013, 1002, 52, 98])).
% 2.17/1.65 tff(1194,plain,
% 2.17/1.65 (~hskp15),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[608, 1193, 23])).
% 2.17/1.65 tff(1195,plain,
% 2.17/1.65 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1196,plain,
% 2.17/1.65 ((hskp28 | hskp15 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163))) <=> (hskp28 | hskp15 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1197,plain,
% 2.17/1.65 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))))),
% 2.17/1.65 inference(monotonicity,[status(thm)],[1196])).
% 2.17/1.65 tff(1198,plain,
% 2.17/1.65 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.17/1.65 inference(transitivity,[status(thm)],[1197, 1195])).
% 2.17/1.65 tff(1199,plain,
% 2.17/1.65 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))),
% 2.17/1.65 inference(quant_inst,[status(thm)],[])).
% 2.17/1.65 tff(1200,plain,
% 2.17/1.65 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))),
% 2.17/1.65 inference(modus_ponens,[status(thm)],[1199, 1198])).
% 2.17/1.65 tff(1201,plain,
% 2.17/1.65 (hskp28 | hskp15 | (~c3_1(a163)) | (~c0_1(a163))),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1200, 160, 52, 33])).
% 2.17/1.65 tff(1202,plain,
% 2.17/1.65 (~c0_1(a163)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1201, 557, 984, 683])).
% 2.17/1.65 tff(1203,plain,
% 2.17/1.65 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | c0_1(a163))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp15 | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | c0_1(a163))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1204,plain,
% 2.17/1.65 ((hskp28 | hskp15 | (~ndr1_0) | c0_1(a163) | c2_1(a163) | (~c3_1(a163))) <=> (hskp28 | hskp15 | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | c0_1(a163))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1205,plain,
% 2.17/1.65 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c0_1(a163) | c2_1(a163) | (~c3_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | c0_1(a163)))),
% 2.17/1.65 inference(monotonicity,[status(thm)],[1204])).
% 2.17/1.65 tff(1206,plain,
% 2.17/1.65 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c0_1(a163) | c2_1(a163) | (~c3_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp15 | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | c0_1(a163))),
% 2.17/1.65 inference(transitivity,[status(thm)],[1205, 1203])).
% 2.17/1.65 tff(1207,plain,
% 2.17/1.65 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c0_1(a163) | c2_1(a163) | (~c3_1(a163)))),
% 2.17/1.65 inference(quant_inst,[status(thm)],[])).
% 2.17/1.65 tff(1208,plain,
% 2.17/1.65 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp15 | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | c0_1(a163)),
% 2.17/1.65 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 2.17/1.65 tff(1209,plain,
% 2.17/1.65 (hskp28 | hskp15 | (~c3_1(a163)) | c0_1(a163)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1208, 160, 98, 706])).
% 2.17/1.65 tff(1210,plain,
% 2.17/1.65 ($false),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1209, 1202, 557, 984, 683])).
% 2.17/1.65 tff(1211,plain,(hskp28 | hskp15 | c2_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.65 tff(1212,plain,
% 2.17/1.65 ($false),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1211, 1194, 1193, 98, 52])).
% 2.17/1.65 tff(1213,plain,(hskp31 | c2_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.65 tff(1214,plain,
% 2.17/1.65 (hskp31),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1213, 98, 52])).
% 2.17/1.65 tff(1215,plain,
% 2.17/1.65 (c3_1(a141)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[63, 1214])).
% 2.17/1.65 tff(1216,plain,
% 2.17/1.65 (c1_1(a141)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[74, 1214])).
% 2.17/1.65 tff(1217,plain,
% 2.17/1.65 (c0_1(a141)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[85, 1214])).
% 2.17/1.65 tff(1218,plain,
% 2.17/1.65 (c0_1(a163)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1121, 160, 1217, 1216, 1215, 52, 98, 984, 804])).
% 2.17/1.65 tff(1219,plain,
% 2.17/1.65 (hskp16),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[1139, 1218, 984])).
% 2.17/1.65 tff(1220,plain,
% 2.17/1.65 (c1_1(a126)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[776, 1219])).
% 2.17/1.65 tff(1221,plain,
% 2.17/1.65 (c3_1(a126)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[787, 1219])).
% 2.17/1.65 tff(1222,plain,
% 2.17/1.65 (~c2_1(a126)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[793, 1219])).
% 2.17/1.65 tff(1223,plain,
% 2.17/1.65 (c2_1(a141)),
% 2.17/1.65 inference(unit_resolution,[status(thm)],[877, 1222, 52, 98, 1217, 1216, 1218, 1215, 1221, 1220])).
% 2.17/1.65 tff(1224,plain,
% 2.17/1.65 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)))),
% 2.17/1.65 inference(bind,[status(th)],[])).
% 2.17/1.65 tff(1225,plain,
% 2.17/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 2.17/1.65 inference(quant_intro,[status(thm)],[1224])).
% 2.17/1.65 tff(1226,plain,
% 2.17/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1227,plain,
% 2.17/1.65 (^[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))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))))),
% 2.17/1.65 inference(bind,[status(th)],[])).
% 2.17/1.65 tff(1228,plain,
% 2.17/1.65 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 2.17/1.65 inference(quant_intro,[status(thm)],[1227])).
% 2.17/1.65 tff(1229,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 2.17/1.65 tff(1230,plain,
% 2.17/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 2.17/1.65 inference(modus_ponens,[status(thm)],[1229, 1228])).
% 2.17/1.65 tff(1231,plain,
% 2.17/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 2.17/1.65 inference(modus_ponens,[status(thm)],[1230, 1226])).
% 2.17/1.65 tff(1232,plain,(
% 2.17/1.65 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 2.17/1.65 inference(skolemize,[status(sab)],[1231])).
% 2.17/1.65 tff(1233,plain,
% 2.17/1.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))),
% 2.17/1.65 inference(modus_ponens,[status(thm)],[1232, 1225])).
% 2.17/1.65 tff(1234,plain,
% 2.17/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1235,plain,
% 2.17/1.65 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135)) <=> (c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)))),
% 2.17/1.65 inference(rewrite,[status(thm)],[])).
% 2.17/1.65 tff(1236,plain,
% 2.17/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135))))),
% 2.17/1.65 inference(monotonicity,[status(thm)],[1235])).
% 2.17/1.65 tff(1237,plain,
% 2.17/1.65 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)))),
% 2.17/1.65 inference(transitivity,[status(thm)],[1236, 1234])).
% 2.17/1.65 tff(1238,plain,
% 2.17/1.65 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))),
% 2.17/1.66 inference(quant_inst,[status(thm)],[])).
% 2.17/1.66 tff(1239,plain,
% 2.17/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1238, 1237])).
% 2.17/1.66 tff(1240,plain,
% 2.17/1.66 ((~c2_1(a141)) | c1_1(a135)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1239, 160, 1216, 1215, 1156, 1155, 1154, 108])).
% 2.17/1.66 tff(1241,plain,
% 2.17/1.66 (c1_1(a135)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1240, 1223])).
% 2.17/1.66 tff(1242,plain,
% 2.17/1.66 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1243,plain,
% 2.17/1.66 ((hskp24 | hskp1 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135))) <=> (hskp24 | hskp1 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1244,plain,
% 2.17/1.66 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135))))),
% 2.17/1.66 inference(monotonicity,[status(thm)],[1243])).
% 2.17/1.66 tff(1245,plain,
% 2.17/1.66 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))),
% 2.17/1.66 inference(transitivity,[status(thm)],[1244, 1242])).
% 2.17/1.66 tff(1246,plain,
% 2.17/1.66 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))),
% 2.17/1.66 inference(quant_inst,[status(thm)],[])).
% 2.17/1.66 tff(1247,plain,
% 2.17/1.66 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 2.17/1.66 tff(1248,plain,
% 2.17/1.66 (hskp1 | (~c1_1(a135))),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1247, 160, 990, 1156, 1155, 21])).
% 2.17/1.66 tff(1249,plain,
% 2.17/1.66 (hskp1),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1248, 1241])).
% 2.17/1.66 tff(1250,plain,
% 2.17/1.66 (((~hskp1) | (~c1_1(a102))) <=> ((~hskp1) | (~c1_1(a102)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1251,plain,
% 2.17/1.66 (((~c1_1(a102)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a102)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1252,axiom,((~c1_1(a102)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 2.17/1.66 tff(1253,plain,
% 2.17/1.66 ((~hskp1) | (~c1_1(a102))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 2.17/1.66 tff(1254,plain,
% 2.17/1.66 ((~hskp1) | (~c1_1(a102))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1253, 1250])).
% 2.17/1.66 tff(1255,plain,
% 2.17/1.66 (~c1_1(a102)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1254, 1249])).
% 2.17/1.66 tff(1256,plain,
% 2.17/1.66 (((~hskp1) | (~c0_1(a102))) <=> ((~hskp1) | (~c0_1(a102)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1257,plain,
% 2.17/1.66 (((~c0_1(a102)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a102)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1258,axiom,((~c0_1(a102)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 2.17/1.66 tff(1259,plain,
% 2.17/1.66 ((~hskp1) | (~c0_1(a102))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 2.17/1.66 tff(1260,plain,
% 2.17/1.66 ((~hskp1) | (~c0_1(a102))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1259, 1256])).
% 2.17/1.66 tff(1261,plain,
% 2.17/1.66 (~c0_1(a102)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1260, 1249])).
% 2.17/1.66 tff(1262,plain,
% 2.17/1.66 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(1263,plain,
% 2.17/1.66 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[1262])).
% 2.17/1.66 tff(1264,plain,
% 2.17/1.66 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1265,plain,
% 2.17/1.66 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(1266,plain,
% 2.17/1.66 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[1265])).
% 2.17/1.66 tff(1267,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 2.17/1.66 tff(1268,plain,
% 2.17/1.66 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1267, 1266])).
% 2.17/1.66 tff(1269,plain,
% 2.17/1.66 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1268, 1264])).
% 2.17/1.66 tff(1270,plain,(
% 2.17/1.66 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.17/1.66 inference(skolemize,[status(sab)],[1269])).
% 2.17/1.66 tff(1271,plain,
% 2.17/1.66 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1270, 1263])).
% 2.17/1.66 tff(1272,plain,
% 2.17/1.66 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c1_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c1_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1273,plain,
% 2.17/1.66 ((hskp22 | (~ndr1_0) | c3_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163))) <=> (hskp22 | c1_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1274,plain,
% 2.17/1.66 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c1_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163))))),
% 2.17/1.66 inference(monotonicity,[status(thm)],[1273])).
% 2.17/1.66 tff(1275,plain,
% 2.17/1.66 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c1_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163)))),
% 2.17/1.66 inference(transitivity,[status(thm)],[1274, 1272])).
% 2.17/1.66 tff(1276,plain,
% 2.17/1.66 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a135) | (~c1_1(a135)) | (~c0_1(a135)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))),
% 2.17/1.66 inference(quant_inst,[status(thm)],[])).
% 2.17/1.66 tff(1277,plain,
% 2.17/1.66 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c1_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)) | (~c0_1(a163))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 2.17/1.66 tff(1278,plain,
% 2.17/1.66 (hskp22 | (~c1_1(a135)) | (~c0_1(a163))),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1277, 160, 1156, 52, 984, 1154, 1271])).
% 2.17/1.66 tff(1279,plain,
% 2.17/1.66 (hskp22),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1278, 1241, 1218])).
% 2.17/1.66 tff(1280,plain,
% 2.17/1.66 (((~hskp22) | (~c2_1(a145))) <=> ((~hskp22) | (~c2_1(a145)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1281,plain,
% 2.17/1.66 (((~c2_1(a145)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a145)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1282,axiom,((~c2_1(a145)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 2.17/1.66 tff(1283,plain,
% 2.17/1.66 ((~hskp22) | (~c2_1(a145))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1282, 1281])).
% 2.17/1.66 tff(1284,plain,
% 2.17/1.66 ((~hskp22) | (~c2_1(a145))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1283, 1280])).
% 2.17/1.66 tff(1285,plain,
% 2.17/1.66 (~c2_1(a145)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1284, 1279])).
% 2.17/1.66 tff(1286,plain,
% 2.17/1.66 (((~hskp22) | (~c1_1(a145))) <=> ((~hskp22) | (~c1_1(a145)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1287,plain,
% 2.17/1.66 (((~c1_1(a145)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a145)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1288,axiom,((~c1_1(a145)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 2.17/1.66 tff(1289,plain,
% 2.17/1.66 ((~hskp22) | (~c1_1(a145))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1288, 1287])).
% 2.17/1.66 tff(1290,plain,
% 2.17/1.66 ((~hskp22) | (~c1_1(a145))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1289, 1286])).
% 2.17/1.66 tff(1291,plain,
% 2.17/1.66 (~c1_1(a145)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1290, 1279])).
% 2.17/1.66 tff(1292,plain,
% 2.17/1.66 (((~hskp22) | (~c0_1(a145))) <=> ((~hskp22) | (~c0_1(a145)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1293,plain,
% 2.17/1.66 (((~c0_1(a145)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a145)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1294,axiom,((~c0_1(a145)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 2.17/1.66 tff(1295,plain,
% 2.17/1.66 ((~hskp22) | (~c0_1(a145))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 2.17/1.66 tff(1296,plain,
% 2.17/1.66 ((~hskp22) | (~c0_1(a145))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1295, 1292])).
% 2.17/1.66 tff(1297,plain,
% 2.17/1.66 (~c0_1(a145)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1296, 1279])).
% 2.17/1.66 tff(1298,plain,
% 2.17/1.66 (((~hskp1) | c2_1(a102)) <=> ((~hskp1) | c2_1(a102))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1299,axiom,((~hskp1) | c2_1(a102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 2.17/1.66 tff(1300,plain,
% 2.17/1.66 ((~hskp1) | c2_1(a102)),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 2.17/1.66 tff(1301,plain,
% 2.17/1.66 ((~hskp1) | c2_1(a102)),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1300, 1298])).
% 2.17/1.66 tff(1302,plain,
% 2.17/1.66 ((~hskp1) | c2_1(a102)),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1301, 1298])).
% 2.17/1.66 tff(1303,plain,
% 2.17/1.66 ((~hskp1) | c2_1(a102)),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1302, 1298])).
% 2.17/1.66 tff(1304,plain,
% 2.17/1.66 ((~hskp1) | c2_1(a102)),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1303, 1298])).
% 2.17/1.66 tff(1305,plain,
% 2.17/1.66 ((~hskp1) | c2_1(a102)),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1304, 1298])).
% 2.17/1.66 tff(1306,plain,
% 2.17/1.66 ((~hskp1) | c2_1(a102)),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1305, 1298])).
% 2.17/1.66 tff(1307,plain,
% 2.17/1.66 ((~hskp1) | c2_1(a102)),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1306, 1298])).
% 2.17/1.66 tff(1308,plain,
% 2.17/1.66 (c2_1(a102)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1307, 1249])).
% 2.17/1.66 tff(1309,plain,
% 2.17/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a145) | c1_1(a145) | c2_1(a145) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a145) | c1_1(a145) | c2_1(a145) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1310,plain,
% 2.17/1.66 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a145) | c0_1(a145) | c2_1(a145)) <=> (c0_1(a145) | c1_1(a145) | c2_1(a145) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1311,plain,
% 2.17/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (c0_1(a145) | c1_1(a145) | c2_1(a145) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c2_1(a102))))),
% 2.17/1.66 inference(monotonicity,[status(thm)],[1310])).
% 2.17/1.66 tff(1312,plain,
% 2.17/1.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a145) | c1_1(a145) | c2_1(a145) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))),
% 2.17/1.66 inference(transitivity,[status(thm)],[1311, 1309])).
% 2.17/1.66 tff(1313,plain,
% 2.17/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a145) | c0_1(a145) | c2_1(a145))),
% 2.17/1.66 inference(quant_inst,[status(thm)],[])).
% 2.17/1.66 tff(1314,plain,
% 2.17/1.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | c0_1(a145) | c1_1(a145) | c2_1(a145) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c2_1(a102))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 2.17/1.66 tff(1315,plain,
% 2.17/1.66 ($false),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1314, 160, 1216, 1215, 1308, 1297, 1291, 1285, 1261, 1255, 1233, 1223])).
% 2.17/1.66 tff(1316,plain,(c2_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.66 tff(1317,plain,
% 2.17/1.66 (c2_1(a163)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1316, 52])).
% 2.17/1.66 tff(1318,plain,
% 2.17/1.66 (~hskp24),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1088, 1317])).
% 2.17/1.66 tff(1319,plain,
% 2.17/1.66 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(1320,plain,
% 2.17/1.66 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[1319])).
% 2.17/1.66 tff(1321,plain,
% 2.17/1.66 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1322,plain,
% 2.17/1.66 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp13))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(1323,plain,
% 2.17/1.66 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[1322])).
% 2.17/1.66 tff(1324,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 2.17/1.66 tff(1325,plain,
% 2.17/1.66 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 2.17/1.66 tff(1326,plain,
% 2.17/1.66 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1325, 1321])).
% 2.17/1.66 tff(1327,plain,(
% 2.17/1.66 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 2.17/1.66 inference(skolemize,[status(sab)],[1326])).
% 2.17/1.66 tff(1328,plain,
% 2.17/1.66 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1327, 1320])).
% 2.17/1.66 tff(1329,assumption,(hskp10), introduced(assumption)).
% 2.17/1.66 tff(1330,plain,
% 2.17/1.66 (((~hskp10) | (~c3_1(a111))) <=> ((~hskp10) | (~c3_1(a111)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1331,plain,
% 2.17/1.66 (((~c3_1(a111)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a111)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1332,axiom,((~c3_1(a111)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 2.17/1.66 tff(1333,plain,
% 2.17/1.66 ((~hskp10) | (~c3_1(a111))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 2.17/1.66 tff(1334,plain,
% 2.17/1.66 ((~hskp10) | (~c3_1(a111))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1333, 1330])).
% 2.17/1.66 tff(1335,plain,
% 2.17/1.66 (~c3_1(a111)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1334, 1329])).
% 2.17/1.66 tff(1336,plain,
% 2.17/1.66 (((~hskp10) | (~c2_1(a111))) <=> ((~hskp10) | (~c2_1(a111)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1337,plain,
% 2.17/1.66 (((~c2_1(a111)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a111)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1338,axiom,((~c2_1(a111)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 2.17/1.66 tff(1339,plain,
% 2.17/1.66 ((~hskp10) | (~c2_1(a111))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 2.17/1.66 tff(1340,plain,
% 2.17/1.66 ((~hskp10) | (~c2_1(a111))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1339, 1336])).
% 2.17/1.66 tff(1341,plain,
% 2.17/1.66 (~c2_1(a111)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1340, 1329])).
% 2.17/1.66 tff(1342,plain,
% 2.17/1.66 (((~hskp10) | (~c0_1(a111))) <=> ((~hskp10) | (~c0_1(a111)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1343,plain,
% 2.17/1.66 (((~c0_1(a111)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a111)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1344,axiom,((~c0_1(a111)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 2.17/1.66 tff(1345,plain,
% 2.17/1.66 ((~hskp10) | (~c0_1(a111))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 2.17/1.66 tff(1346,plain,
% 2.17/1.66 ((~hskp10) | (~c0_1(a111))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1345, 1342])).
% 2.17/1.66 tff(1347,plain,
% 2.17/1.66 (~c0_1(a111)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1346, 1329])).
% 2.17/1.66 tff(1348,plain,
% 2.17/1.66 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1349,plain,
% 2.17/1.66 ((hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a111) | c0_1(a111) | c3_1(a111)) <=> (hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1350,plain,
% 2.17/1.66 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a111) | c0_1(a111) | c3_1(a111))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141))))),
% 2.17/1.66 inference(monotonicity,[status(thm)],[1349])).
% 2.17/1.66 tff(1351,plain,
% 2.17/1.66 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a111) | c0_1(a111) | c3_1(a111))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))),
% 2.17/1.66 inference(transitivity,[status(thm)],[1350, 1348])).
% 2.17/1.66 tff(1352,plain,
% 2.17/1.66 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a111) | c0_1(a111) | c3_1(a111))),
% 2.17/1.66 inference(quant_inst,[status(thm)],[])).
% 2.17/1.66 tff(1353,plain,
% 2.17/1.66 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 2.17/1.66 tff(1354,plain,
% 2.17/1.66 (hskp13),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[1353, 160, 818, 817, 851, 1347, 1341, 1335, 1328])).
% 2.17/1.66 tff(1355,plain,
% 2.17/1.66 (~c3_1(a114)),
% 2.17/1.66 inference(unit_resolution,[status(thm)],[629, 1354])).
% 2.17/1.66 tff(1356,plain,
% 2.17/1.66 (^[U: $i] : refl((hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(1357,plain,
% 2.17/1.66 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[1356])).
% 2.17/1.66 tff(1358,plain,
% 2.17/1.66 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1359,plain,
% 2.17/1.66 (^[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) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp17) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp17))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp17) <=> (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp17) <=> (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 2.17/1.66 inference(bind,[status(th)],[])).
% 2.17/1.66 tff(1360,plain,
% 2.17/1.66 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp17) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.17/1.66 inference(quant_intro,[status(thm)],[1359])).
% 2.17/1.66 tff(1361,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp19) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 2.17/1.66 tff(1362,plain,
% 2.17/1.66 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 2.17/1.66 tff(1363,plain,
% 2.17/1.66 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1362, 1358])).
% 2.17/1.66 tff(1364,plain,(
% 2.17/1.66 ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.17/1.66 inference(skolemize,[status(sab)],[1363])).
% 2.17/1.66 tff(1365,plain,
% 2.17/1.66 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.17/1.66 inference(modus_ponens,[status(thm)],[1364, 1357])).
% 2.17/1.66 tff(1366,plain,
% 2.17/1.66 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1367,plain,
% 2.17/1.66 ((hskp19 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163))) <=> (hskp19 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 2.17/1.66 inference(rewrite,[status(thm)],[])).
% 2.17/1.66 tff(1368,plain,
% 2.17/1.66 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0)))),
% 2.17/1.66 inference(monotonicity,[status(thm)],[1367])).
% 2.17/1.66 tff(1369,plain,
% 2.17/1.66 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 2.17/1.66 inference(transitivity,[status(thm)],[1368, 1366])).
% 2.17/1.66 tff(1370,plain,
% 2.17/1.66 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163)))),
% 2.17/1.66 inference(quant_inst,[status(thm)],[])).
% 2.17/1.66 tff(1371,plain,
% 2.17/1.66 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0)),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[1370, 1369])).
% 2.17/1.67 tff(1372,plain,
% 2.17/1.67 (hskp19 | hskp17 | (~c2_1(a163)) | c3_1(a163)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1371, 160, 52, 1365])).
% 2.17/1.67 tff(1373,plain,
% 2.17/1.67 (hskp17),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1372, 1, 1317, 97])).
% 2.17/1.67 tff(1374,plain,
% 2.17/1.67 (~c1_1(a132)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[831, 1373])).
% 2.17/1.67 tff(1375,plain,
% 2.17/1.67 (~c0_1(a132)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[837, 1373])).
% 2.17/1.67 tff(1376,plain,
% 2.17/1.67 (c3_1(a132)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[849, 1373])).
% 2.17/1.67 tff(1377,plain,
% 2.17/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c3_1(a132)))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1378,plain,
% 2.17/1.67 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c3_1(a132)))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1379,plain,
% 2.17/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c3_1(a132))))),
% 2.17/1.67 inference(monotonicity,[status(thm)],[1378])).
% 2.17/1.67 tff(1380,plain,
% 2.17/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c3_1(a132)))),
% 2.17/1.67 inference(transitivity,[status(thm)],[1379, 1377])).
% 2.17/1.67 tff(1381,plain,
% 2.17/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 2.17/1.67 inference(quant_inst,[status(thm)],[])).
% 2.17/1.67 tff(1382,plain,
% 2.17/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | (~c3_1(a132))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 2.17/1.67 tff(1383,plain,
% 2.17/1.67 (~c2_1(a141)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1382, 160, 1115, 1114, 1113, 1376, 1375, 1374, 96])).
% 2.17/1.67 tff(1384,plain,
% 2.17/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1385,plain,
% 2.17/1.67 (((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163))) <=> (c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1386,plain,
% 2.17/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163))))),
% 2.17/1.67 inference(monotonicity,[status(thm)],[1385])).
% 2.17/1.67 tff(1387,plain,
% 2.17/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163)))),
% 2.17/1.67 inference(transitivity,[status(thm)],[1386, 1384])).
% 2.17/1.67 tff(1388,plain,
% 2.17/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163)))),
% 2.17/1.67 inference(quant_inst,[status(thm)],[])).
% 2.17/1.67 tff(1389,plain,
% 2.17/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a163))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[1388, 1387])).
% 2.17/1.67 tff(1390,plain,
% 2.17/1.67 (~c0_1(a163)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1389, 160, 1115, 1114, 1113, 52, 1317, 320, 1383])).
% 2.17/1.67 tff(1391,plain,
% 2.17/1.67 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 2.17/1.67 inference(bind,[status(th)],[])).
% 2.17/1.67 tff(1392,plain,
% 2.17/1.67 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.17/1.67 inference(quant_intro,[status(thm)],[1391])).
% 2.17/1.67 tff(1393,plain,
% 2.17/1.67 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1394,plain,
% 2.17/1.67 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_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) | (~c1_1(U)) | (~c3_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)) | hskp10) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_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)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 2.17/1.67 inference(bind,[status(th)],[])).
% 2.17/1.67 tff(1395,plain,
% 2.17/1.67 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c1_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.17/1.67 inference(quant_intro,[status(thm)],[1394])).
% 2.17/1.67 tff(1396,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)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 2.17/1.67 tff(1397,plain,
% 2.17/1.67 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 2.17/1.67 tff(1398,plain,
% 2.17/1.67 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[1397, 1393])).
% 2.17/1.67 tff(1399,plain,(
% 2.17/1.67 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.17/1.67 inference(skolemize,[status(sab)],[1398])).
% 2.17/1.67 tff(1400,plain,
% 2.17/1.67 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[1399, 1392])).
% 2.17/1.67 tff(1401,plain,
% 2.17/1.67 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1402,plain,
% 2.17/1.67 ((hskp24 | hskp1 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141))) <=> (hskp24 | hskp1 | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1403,plain,
% 2.17/1.67 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141))))),
% 2.17/1.67 inference(monotonicity,[status(thm)],[1402])).
% 2.17/1.67 tff(1404,plain,
% 2.17/1.67 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))),
% 2.17/1.67 inference(transitivity,[status(thm)],[1403, 1401])).
% 2.17/1.67 tff(1405,plain,
% 2.17/1.67 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))),
% 2.17/1.67 inference(quant_inst,[status(thm)],[])).
% 2.17/1.67 tff(1406,plain,
% 2.17/1.67 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 2.17/1.67 tff(1407,plain,
% 2.17/1.67 (hskp1),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1406, 160, 1318, 1115, 1114, 21, 1383])).
% 2.17/1.67 tff(1408,plain,
% 2.17/1.67 (~c1_1(a102)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1254, 1407])).
% 2.17/1.67 tff(1409,plain,
% 2.17/1.67 (~c0_1(a102)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1260, 1407])).
% 2.17/1.67 tff(1410,plain,
% 2.17/1.67 (c2_1(a102)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1307, 1407])).
% 2.17/1.67 tff(1411,plain,
% 2.17/1.67 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1412,plain,
% 2.17/1.67 ((hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102))) <=> (hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1413,plain,
% 2.17/1.67 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c2_1(a102))))),
% 2.17/1.67 inference(monotonicity,[status(thm)],[1412])).
% 2.17/1.67 tff(1414,plain,
% 2.17/1.67 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c2_1(a102)))),
% 2.17/1.67 inference(transitivity,[status(thm)],[1413, 1411])).
% 2.17/1.67 tff(1415,plain,
% 2.17/1.67 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)))),
% 2.17/1.67 inference(quant_inst,[status(thm)],[])).
% 2.17/1.67 tff(1416,plain,
% 2.17/1.67 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c2_1(a102))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 2.17/1.67 tff(1417,plain,
% 2.17/1.67 (hskp10),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1416, 160, 1115, 1114, 1113, 1410, 1409, 1408, 1400])).
% 2.17/1.67 tff(1418,plain,
% 2.17/1.67 (~c3_1(a111)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1334, 1417])).
% 2.17/1.67 tff(1419,plain,
% 2.17/1.67 (~c2_1(a111)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1340, 1417])).
% 2.17/1.67 tff(1420,plain,
% 2.17/1.67 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1421,plain,
% 2.17/1.67 ((hskp19 | (~ndr1_0) | c3_1(a111) | c2_1(a111) | (~c1_1(a111))) <=> (hskp19 | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1422,plain,
% 2.17/1.67 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a111) | c2_1(a111) | (~c1_1(a111)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111))))),
% 2.17/1.67 inference(monotonicity,[status(thm)],[1421])).
% 2.17/1.67 tff(1423,plain,
% 2.17/1.67 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a111) | c2_1(a111) | (~c1_1(a111)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)))),
% 2.17/1.67 inference(transitivity,[status(thm)],[1422, 1420])).
% 2.17/1.67 tff(1424,plain,
% 2.17/1.67 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a111) | c2_1(a111) | (~c1_1(a111)))),
% 2.17/1.67 inference(quant_inst,[status(thm)],[])).
% 2.17/1.67 tff(1425,plain,
% 2.17/1.67 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111))),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 2.17/1.67 tff(1426,plain,
% 2.17/1.67 (~c1_1(a111)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1425, 160, 1, 1419, 1418, 11])).
% 2.17/1.67 tff(1427,plain,
% 2.17/1.67 (hskp5),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[234, 1390, 97])).
% 2.17/1.67 tff(1428,plain,
% 2.17/1.67 (~c2_1(a106)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[976, 1427])).
% 2.17/1.67 tff(1429,plain,
% 2.17/1.67 (c1_1(a106)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[257, 1427])).
% 2.17/1.67 tff(1430,plain,
% 2.17/1.67 (c3_1(a106)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[242, 160, 1, 1429, 1428, 11])).
% 2.17/1.67 tff(1431,plain,
% 2.17/1.67 (~c0_1(a111)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1346, 1417])).
% 2.17/1.67 tff(1432,plain,
% 2.17/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a111) | c2_1(a111) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a111) | c2_1(a111) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1433,plain,
% 2.17/1.67 ((hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a111) | c1_1(a111) | c0_1(a111)) <=> (hskp2 | c0_1(a111) | c2_1(a111) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1434,plain,
% 2.17/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a111) | c2_1(a111) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111)))),
% 2.17/1.67 inference(monotonicity,[status(thm)],[1433])).
% 2.17/1.67 tff(1435,plain,
% 2.17/1.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a111) | c2_1(a111) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111))),
% 2.17/1.67 inference(transitivity,[status(thm)],[1434, 1432])).
% 2.17/1.67 tff(1436,plain,
% 2.17/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a111) | c1_1(a111) | c0_1(a111))),
% 2.17/1.67 inference(quant_inst,[status(thm)],[])).
% 2.17/1.67 tff(1437,plain,
% 2.17/1.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a111) | c2_1(a111) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111)),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[1436, 1435])).
% 2.17/1.67 tff(1438,plain,
% 2.17/1.67 (hskp2 | c1_1(a111)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1437, 160, 1429, 1431, 1419, 1428, 270, 1430])).
% 2.17/1.67 tff(1439,plain,
% 2.17/1.67 (hskp2),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1438, 1426])).
% 2.17/1.67 tff(1440,plain,
% 2.17/1.67 (~c3_1(a103)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[419, 1439])).
% 2.17/1.67 tff(1441,plain,
% 2.17/1.67 (c0_1(a103)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[308, 1439])).
% 2.17/1.67 tff(1442,plain,
% 2.17/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1443,plain,
% 2.17/1.67 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1444,plain,
% 2.17/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163)))),
% 2.17/1.67 inference(monotonicity,[status(thm)],[1443])).
% 2.17/1.67 tff(1445,plain,
% 2.17/1.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163))),
% 2.17/1.67 inference(transitivity,[status(thm)],[1444, 1442])).
% 2.17/1.67 tff(1446,plain,
% 2.17/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 2.17/1.67 inference(quant_inst,[status(thm)],[])).
% 2.17/1.67 tff(1447,plain,
% 2.17/1.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a163)),
% 2.17/1.67 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 2.17/1.67 tff(1448,plain,
% 2.17/1.67 (~c2_1(a103)),
% 2.17/1.67 inference(unit_resolution,[status(thm)],[1447, 160, 1441, 52, 1317, 97, 1440, 367, 1390])).
% 2.17/1.67 tff(1449,plain,
% 2.17/1.67 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 2.17/1.67 inference(bind,[status(th)],[])).
% 2.17/1.67 tff(1450,plain,
% 2.17/1.67 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.17/1.67 inference(quant_intro,[status(thm)],[1449])).
% 2.17/1.67 tff(1451,plain,
% 2.17/1.67 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.17/1.67 inference(rewrite,[status(thm)],[])).
% 2.17/1.67 tff(1452,plain,
% 2.17/1.67 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 2.17/1.67 inference(bind,[status(th)],[])).
% 2.17/1.67 tff(1453,plain,
% 2.17/1.67 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.17/1.67 inference(quant_intro,[status(thm)],[1452])).
% 2.17/1.67 tff(1454,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 2.17/1.68 tff(1455,plain,
% 2.17/1.68 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 2.17/1.68 tff(1456,plain,
% 2.17/1.68 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[1455, 1451])).
% 2.17/1.68 tff(1457,plain,(
% 2.17/1.68 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.17/1.68 inference(skolemize,[status(sab)],[1456])).
% 2.17/1.68 tff(1458,plain,
% 2.17/1.68 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[1457, 1450])).
% 2.17/1.68 tff(1459,plain,
% 2.17/1.68 (c1_1(a103)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[288, 1439])).
% 2.17/1.68 tff(1460,plain,
% 2.17/1.68 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a132) | c1_1(a132) | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a132) | c1_1(a132) | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)) | (~c3_1(a132)))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(1461,plain,
% 2.17/1.68 ((hskp11 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (hskp11 | c0_1(a132) | c1_1(a132) | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)) | (~c3_1(a132)))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(1462,plain,
% 2.17/1.68 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a132) | c1_1(a132) | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)) | (~c3_1(a132))))),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1461])).
% 2.17/1.68 tff(1463,plain,
% 2.17/1.68 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a132) | c1_1(a132) | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)) | (~c3_1(a132)))),
% 2.17/1.68 inference(transitivity,[status(thm)],[1462, 1460])).
% 2.17/1.68 tff(1464,plain,
% 2.17/1.68 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c3_1(a103) | c2_1(a103) | (~c1_1(a103)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 2.17/1.68 inference(quant_inst,[status(thm)],[])).
% 2.17/1.68 tff(1465,plain,
% 2.17/1.68 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a132) | c1_1(a132) | c3_1(a103) | (~ndr1_0) | c2_1(a103) | (~c1_1(a103)) | (~c3_1(a132))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 2.17/1.68 tff(1466,plain,
% 2.17/1.68 ($false),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1465, 160, 1071, 1376, 1459, 1375, 1374, 1440, 1458, 1448])).
% 2.17/1.68 tff(1467,plain,(hskp19 | c1_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.17/1.68 tff(1468,plain,
% 2.17/1.68 (hskp19),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1467, 97, 52])).
% 2.17/1.68 tff(1469,plain,
% 2.17/1.68 (~c3_1(a135)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[432, 1468])).
% 2.17/1.68 tff(1470,plain,
% 2.17/1.68 (~c2_1(a135)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[438, 1468])).
% 2.17/1.68 tff(1471,plain,
% 2.17/1.68 (c2_1(a114)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[640, 1354])).
% 2.17/1.68 tff(1472,plain,
% 2.17/1.68 (c1_1(a114)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[651, 1354])).
% 2.17/1.68 tff(1473,plain,
% 2.17/1.68 (c0_1(a135)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[459, 1468])).
% 2.17/1.68 tff(1474,plain,
% 2.17/1.68 (c0_1(a114)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[658, 160, 1473, 1472, 1471, 1470, 1469, 1355, 202])).
% 2.17/1.68 tff(1475,assumption,(c1_1(a111)), introduced(assumption)).
% 2.17/1.68 tff(1476,assumption,(~c3_1(a111)), introduced(assumption)).
% 2.17/1.68 tff(1477,assumption,(~c0_1(a111)), introduced(assumption)).
% 2.17/1.68 tff(1478,assumption,(hskp13), introduced(assumption)).
% 2.17/1.68 tff(1479,plain,
% 2.17/1.68 (~c3_1(a114)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[629, 1478])).
% 2.17/1.68 tff(1480,plain,
% 2.17/1.68 (c2_1(a114)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[640, 1478])).
% 2.17/1.68 tff(1481,plain,
% 2.17/1.68 (c1_1(a114)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[651, 1478])).
% 2.17/1.68 tff(1482,plain,
% 2.17/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(1483,plain,
% 2.17/1.68 (((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111))) <=> (c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(1484,plain,
% 2.17/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135))))),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1483])).
% 2.17/1.68 tff(1485,plain,
% 2.17/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))),
% 2.17/1.68 inference(transitivity,[status(thm)],[1484, 1482])).
% 2.17/1.68 tff(1486,plain,
% 2.17/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111)))),
% 2.17/1.68 inference(quant_inst,[status(thm)],[])).
% 2.17/1.68 tff(1487,plain,
% 2.17/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 2.17/1.68 tff(1488,plain,
% 2.17/1.68 ($false),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1487, 160, 486, 1481, 1480, 463, 462, 1479, 1477, 1476, 202, 1475])).
% 2.17/1.68 tff(1489,plain,((~hskp13) | (~c0_1(a135)) | c2_1(a135) | c3_1(a135) | c0_1(a111) | c3_1(a111) | (~c1_1(a111))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.68 tff(1490,plain,
% 2.17/1.68 (~c1_1(a111)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1489, 1354, 1470, 1469, 1347, 1335, 1473])).
% 2.17/1.68 tff(1491,plain,
% 2.17/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a135)))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(1492,plain,
% 2.17/1.68 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111)) <=> (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a135)))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(1493,plain,
% 2.17/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a135))))),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1492])).
% 2.17/1.68 tff(1494,plain,
% 2.17/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a135)))),
% 2.17/1.68 inference(transitivity,[status(thm)],[1493, 1491])).
% 2.17/1.68 tff(1495,plain,
% 2.17/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))),
% 2.17/1.68 inference(quant_inst,[status(thm)],[])).
% 2.17/1.68 tff(1496,plain,
% 2.17/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a135))),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 2.17/1.68 tff(1497,plain,
% 2.17/1.68 ((~c2_1(a141)) | c1_1(a111)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1496, 160, 817, 851, 1473, 1470, 1469, 1341, 1335, 108])).
% 2.17/1.68 tff(1498,plain,
% 2.17/1.68 (~c2_1(a141)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1497, 1490])).
% 2.17/1.68 tff(1499,plain,
% 2.17/1.68 (~c0_1(a163)),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1389, 160, 818, 817, 851, 52, 1317, 320, 1498])).
% 2.17/1.68 tff(1500,plain,
% 2.17/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(1501,plain,
% 2.17/1.68 (((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163)) <=> (c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(1502,plain,
% 2.17/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163)))),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1501])).
% 2.17/1.68 tff(1503,plain,
% 2.17/1.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163))),
% 2.17/1.68 inference(transitivity,[status(thm)],[1502, 1500])).
% 2.17/1.68 tff(1504,plain,
% 2.17/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163) | c3_1(a163) | (~c2_1(a163)) | c3_1(a163) | c1_1(a163) | c0_1(a163))),
% 2.17/1.68 inference(quant_inst,[status(thm)],[])).
% 2.17/1.68 tff(1505,plain,
% 2.17/1.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a163)),
% 2.17/1.68 inference(modus_ponens,[status(thm)],[1504, 1503])).
% 2.17/1.68 tff(1506,plain,
% 2.17/1.68 ($false),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1505, 160, 1471, 52, 1317, 97, 1355, 367, 1499, 1474])).
% 2.17/1.68 tff(1507,plain,((~hskp10) | c1_1(a163) | c3_1(a163) | (~c0_1(a141)) | (~c1_1(a141)) | (~c3_1(a141))), inference(lemma,lemma(discharge,[]))).
% 2.17/1.68 tff(1508,plain,
% 2.17/1.68 (~hskp10),
% 2.17/1.68 inference(unit_resolution,[status(thm)],[1507, 86, 97, 52, 75, 64])).
% 2.17/1.68 tff(1509,plain,
% 2.17/1.68 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(1510,plain,
% 2.17/1.68 ((hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163))) <=> (hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.17/1.68 inference(rewrite,[status(thm)],[])).
% 2.17/1.68 tff(1511,plain,
% 2.17/1.68 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)))),
% 2.17/1.68 inference(monotonicity,[status(thm)],[1510])).
% 2.17/1.68 tff(1512,plain,
% 2.17/1.68 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.22/1.68 inference(transitivity,[status(thm)],[1511, 1509])).
% 2.22/1.68 tff(1513,plain,
% 2.22/1.68 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163)))),
% 2.22/1.68 inference(quant_inst,[status(thm)],[])).
% 2.22/1.68 tff(1514,plain,
% 2.22/1.68 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 2.22/1.68 tff(1515,plain,
% 2.22/1.68 (hskp10 | c0_1(a163)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1514, 160, 86, 75, 64, 52, 1317, 1400])).
% 2.22/1.68 tff(1516,plain,
% 2.22/1.68 (c0_1(a163)),
% 2.22/1.68 inference(unit_resolution,[status(thm)],[1515, 1508])).
% 2.22/1.68 tff(1517,plain,
% 2.22/1.68 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 2.22/1.68 inference(bind,[status(th)],[])).
% 2.22/1.68 tff(1518,plain,
% 2.22/1.68 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(quant_intro,[status(thm)],[1517])).
% 2.22/1.68 tff(1519,plain,
% 2.22/1.68 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1520,plain,
% 2.22/1.68 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 2.22/1.68 inference(bind,[status(th)],[])).
% 2.22/1.68 tff(1521,plain,
% 2.22/1.68 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(quant_intro,[status(thm)],[1520])).
% 2.22/1.68 tff(1522,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 2.22/1.68 tff(1523,plain,
% 2.22/1.68 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 2.22/1.68 tff(1524,plain,
% 2.22/1.68 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1523, 1519])).
% 2.22/1.68 tff(1525,plain,(
% 2.22/1.68 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(skolemize,[status(sab)],[1524])).
% 2.22/1.68 tff(1526,plain,
% 2.22/1.68 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1525, 1518])).
% 2.22/1.68 tff(1527,plain,
% 2.22/1.68 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 2.22/1.68 inference(bind,[status(th)],[])).
% 2.22/1.68 tff(1528,plain,
% 2.22/1.68 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(quant_intro,[status(thm)],[1527])).
% 2.22/1.68 tff(1529,plain,
% 2.22/1.68 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1530,plain,
% 2.22/1.68 (^[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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp17) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp17))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 2.22/1.68 inference(bind,[status(th)],[])).
% 2.22/1.68 tff(1531,plain,
% 2.22/1.68 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(quant_intro,[status(thm)],[1530])).
% 2.22/1.68 tff(1532,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 2.22/1.68 tff(1533,plain,
% 2.22/1.68 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 2.22/1.68 tff(1534,plain,
% 2.22/1.68 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1533, 1529])).
% 2.22/1.68 tff(1535,plain,(
% 2.22/1.68 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(skolemize,[status(sab)],[1534])).
% 2.22/1.68 tff(1536,plain,
% 2.22/1.68 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.68 inference(modus_ponens,[status(thm)],[1535, 1528])).
% 2.22/1.68 tff(1537,plain,
% 2.22/1.68 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1538,plain,
% 2.22/1.68 ((hskp17 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163))) <=> (hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.68 inference(rewrite,[status(thm)],[])).
% 2.22/1.68 tff(1539,plain,
% 2.22/1.68 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163))))),
% 2.22/1.68 inference(monotonicity,[status(thm)],[1538])).
% 2.22/1.68 tff(1540,plain,
% 2.22/1.68 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.69 inference(transitivity,[status(thm)],[1539, 1537])).
% 2.22/1.69 tff(1541,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp17 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a163) | (~c0_1(a163)) | (~c2_1(a163)))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(1542,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a163))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 2.22/1.69 tff(1543,plain,
% 2.22/1.69 (hskp17 | (~c0_1(a163))),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1542, 160, 52, 1317, 97, 1536])).
% 2.22/1.69 tff(1544,plain,
% 2.22/1.69 (hskp17),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1543, 1516])).
% 2.22/1.69 tff(1545,plain,
% 2.22/1.69 (~c0_1(a132)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[837, 1544])).
% 2.22/1.69 tff(1546,plain,
% 2.22/1.69 (c3_1(a132)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[849, 1544])).
% 2.22/1.69 tff(1547,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | (~ndr1_0) | (~c2_1(a132)) | (~c3_1(a132)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | (~ndr1_0) | (~c2_1(a132)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1548,plain,
% 2.22/1.69 ((hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132))) <=> (hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | (~ndr1_0) | (~c2_1(a132)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1549,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | (~ndr1_0) | (~c2_1(a132)) | (~c3_1(a132)) | (~c0_1(a163))))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[1548])).
% 2.22/1.69 tff(1550,plain,
% 2.22/1.69 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | (~ndr1_0) | (~c2_1(a132)) | (~c3_1(a132)) | (~c0_1(a163)))),
% 2.22/1.69 inference(transitivity,[status(thm)],[1549, 1547])).
% 2.22/1.69 tff(1551,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a132) | (~c3_1(a132)) | (~c2_1(a132)))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(1552,plain,
% 2.22/1.69 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | (~ndr1_0) | (~c2_1(a132)) | (~c3_1(a132)) | (~c0_1(a163))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1551, 1550])).
% 2.22/1.69 tff(1553,plain,
% 2.22/1.69 (~c2_1(a132)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1552, 160, 1508, 1546, 1317, 97, 1545, 1526, 1516])).
% 2.22/1.69 tff(1554,plain,
% 2.22/1.69 (~c1_1(a132)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[831, 1544])).
% 2.22/1.69 tff(1555,plain,
% 2.22/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c2_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c2_1(a132) | (~c3_1(a132)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1556,plain,
% 2.22/1.69 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c2_1(a132) | (~c3_1(a132)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1557,plain,
% 2.22/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c2_1(a132) | (~c3_1(a132))))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[1556])).
% 2.22/1.69 tff(1558,plain,
% 2.22/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c2_1(a132) | (~c3_1(a132)))),
% 2.22/1.69 inference(transitivity,[status(thm)],[1557, 1555])).
% 2.22/1.69 tff(1559,plain,
% 2.22/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a132) | c0_1(a132) | (~c3_1(a132)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(1560,plain,
% 2.22/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c2_1(a132) | (~c3_1(a132))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1559, 1558])).
% 2.22/1.69 tff(1561,plain,
% 2.22/1.69 ($false),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1560, 160, 86, 75, 64, 1546, 1545, 1554, 804, 1553])).
% 2.22/1.69 tff(1562,plain,((~hskp31) | c3_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.69 tff(1563,plain,
% 2.22/1.69 (~hskp31),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1562, 97, 52])).
% 2.22/1.69 tff(1564,plain,
% 2.22/1.69 (hskp30),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[158, 1563, 1318])).
% 2.22/1.69 tff(1565,plain,
% 2.22/1.69 (c3_1(a131)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1001, 1564])).
% 2.22/1.69 tff(1566,plain,
% 2.22/1.69 (c2_1(a131)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1012, 1564])).
% 2.22/1.69 tff(1567,plain,
% 2.22/1.69 (c0_1(a131)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1023, 1564])).
% 2.22/1.69 tff(1568,plain,
% 2.22/1.69 (hskp30),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[158, 23, 1318])).
% 2.22/1.69 tff(1569,plain,
% 2.22/1.69 (c3_1(a131)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1001, 1568])).
% 2.22/1.69 tff(1570,plain,
% 2.22/1.69 (c0_1(a131)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1023, 1568])).
% 2.22/1.69 tff(1571,plain,
% 2.22/1.69 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1572,plain,
% 2.22/1.69 ((hskp31 | hskp28 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131))) <=> (hskp31 | hskp28 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1573,plain,
% 2.22/1.69 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131)))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[1572])).
% 2.22/1.69 tff(1574,plain,
% 2.22/1.69 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))),
% 2.22/1.69 inference(transitivity,[status(thm)],[1573, 1571])).
% 2.22/1.69 tff(1575,plain,
% 2.22/1.69 ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131)))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(1576,plain,
% 2.22/1.69 ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1575, 1574])).
% 2.22/1.69 tff(1577,plain,
% 2.22/1.69 (hskp28 | c1_1(a131)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1576, 23, 160, 1570, 1569, 596])).
% 2.22/1.69 tff(1578,plain,
% 2.22/1.69 (c1_1(a131)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1577, 557])).
% 2.22/1.69 tff(1579,plain,
% 2.22/1.69 (^[U: $i] : refl((hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 2.22/1.69 inference(bind,[status(th)],[])).
% 2.22/1.69 tff(1580,plain,
% 2.22/1.69 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.22/1.69 inference(quant_intro,[status(thm)],[1579])).
% 2.22/1.69 tff(1581,plain,
% 2.22/1.69 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1582,plain,
% 2.22/1.69 (^[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) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp28))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp28) | hskp17) <=> ((hskp28 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp17))), rewrite(((hskp28 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp17) <=> (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp28) | hskp17) <=> (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 2.22/1.69 inference(bind,[status(th)],[])).
% 2.22/1.69 tff(1583,plain,
% 2.22/1.69 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp28) | hskp17) <=> ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.22/1.69 inference(quant_intro,[status(thm)],[1582])).
% 2.22/1.69 tff(1584,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp28) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 2.22/1.69 tff(1585,plain,
% 2.22/1.69 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 2.22/1.69 tff(1586,plain,
% 2.22/1.69 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1585, 1581])).
% 2.22/1.69 tff(1587,plain,(
% 2.22/1.69 ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.22/1.69 inference(skolemize,[status(sab)],[1586])).
% 2.22/1.69 tff(1588,plain,
% 2.22/1.69 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1587, 1580])).
% 2.22/1.69 tff(1589,plain,
% 2.22/1.69 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp28 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp28 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1590,plain,
% 2.22/1.69 ((hskp28 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163))) <=> (hskp28 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1591,plain,
% 2.22/1.69 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp28 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0)))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[1590])).
% 2.22/1.69 tff(1592,plain,
% 2.22/1.69 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163)))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp28 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 2.22/1.69 inference(transitivity,[status(thm)],[1591, 1589])).
% 2.22/1.69 tff(1593,plain,
% 2.22/1.69 ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c3_1(a163) | c1_1(a163) | (~c2_1(a163)))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(1594,plain,
% 2.22/1.69 ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp28 | hskp17 | c1_1(a163) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1593, 1592])).
% 2.22/1.69 tff(1595,plain,
% 2.22/1.69 (hskp28 | hskp17 | (~c2_1(a163)) | c3_1(a163)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1594, 160, 52, 1588])).
% 2.22/1.69 tff(1596,plain,
% 2.22/1.69 (hskp17),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1595, 557, 1317, 97])).
% 2.22/1.69 tff(1597,plain,
% 2.22/1.69 (~c1_1(a132)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[831, 1596])).
% 2.22/1.69 tff(1598,plain,
% 2.22/1.69 (~c0_1(a132)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[837, 1596])).
% 2.22/1.69 tff(1599,plain,
% 2.22/1.69 (c3_1(a132)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[849, 1596])).
% 2.22/1.69 tff(1600,plain,
% 2.22/1.69 (c2_1(a131)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1012, 1568])).
% 2.22/1.69 tff(1601,plain,
% 2.22/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a132)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1602,plain,
% 2.22/1.69 (((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a132)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1603,plain,
% 2.22/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a132))))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[1602])).
% 2.22/1.69 tff(1604,plain,
% 2.22/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a132)))),
% 2.22/1.69 inference(transitivity,[status(thm)],[1603, 1601])).
% 2.22/1.69 tff(1605,plain,
% 2.22/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(1606,plain,
% 2.22/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a132))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1605, 1604])).
% 2.22/1.69 tff(1607,plain,
% 2.22/1.69 ($false),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1606, 160, 1570, 1600, 1569, 1599, 1598, 1597, 96, 1578])).
% 2.22/1.69 tff(1608,plain,(hskp28 | hskp31 | c3_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.69 tff(1609,plain,
% 2.22/1.69 (hskp28),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1608, 23, 97, 52])).
% 2.22/1.69 tff(1610,plain,
% 2.22/1.69 (c3_1(a118)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[524, 1609])).
% 2.22/1.69 tff(1611,plain,
% 2.22/1.69 (c2_1(a118)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[535, 1609])).
% 2.22/1.69 tff(1612,plain,
% 2.22/1.69 (c1_1(a118)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[546, 1609])).
% 2.22/1.69 tff(1613,assumption,(c3_1(a118)), introduced(assumption)).
% 2.22/1.69 tff(1614,assumption,(c2_1(a118)), introduced(assumption)).
% 2.22/1.69 tff(1615,assumption,(c1_1(a118)), introduced(assumption)).
% 2.22/1.69 tff(1616,plain,
% 2.22/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a105)) | c0_1(a105) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a105)) | c0_1(a105) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1617,plain,
% 2.22/1.69 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105))) <=> (c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a105)) | c0_1(a105) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1618,plain,
% 2.22/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a105)) | c0_1(a105) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 2.22/1.69 inference(monotonicity,[status(thm)],[1617])).
% 2.22/1.69 tff(1619,plain,
% 2.22/1.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a105)) | c0_1(a105) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.22/1.69 inference(transitivity,[status(thm)],[1618, 1616])).
% 2.22/1.69 tff(1620,plain,
% 2.22/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105)))),
% 2.22/1.69 inference(quant_inst,[status(thm)],[])).
% 2.22/1.69 tff(1621,plain,
% 2.22/1.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a105)) | c0_1(a105) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 2.22/1.69 tff(1622,plain,
% 2.22/1.69 (c0_1(a105)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1621, 160, 1166, 1165, 1164, 1615, 1614, 1613, 51, 40, 96])).
% 2.22/1.69 tff(1623,plain,
% 2.22/1.69 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 2.22/1.69 inference(bind,[status(th)],[])).
% 2.22/1.69 tff(1624,plain,
% 2.22/1.69 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.69 inference(quant_intro,[status(thm)],[1623])).
% 2.22/1.69 tff(1625,plain,
% 2.22/1.69 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1626,plain,
% 2.22/1.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp17) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 2.22/1.69 inference(bind,[status(th)],[])).
% 2.22/1.69 tff(1627,plain,
% 2.22/1.69 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.69 inference(quant_intro,[status(thm)],[1626])).
% 2.22/1.69 tff(1628,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 2.22/1.69 tff(1629,plain,
% 2.22/1.69 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 2.22/1.69 tff(1630,plain,
% 2.22/1.69 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1629, 1625])).
% 2.22/1.69 tff(1631,plain,(
% 2.22/1.69 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.69 inference(skolemize,[status(sab)],[1630])).
% 2.22/1.69 tff(1632,plain,
% 2.22/1.69 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1631, 1624])).
% 2.22/1.69 tff(1633,plain,
% 2.22/1.69 (((~hskp4) | c2_1(a105)) <=> ((~hskp4) | c2_1(a105))),
% 2.22/1.69 inference(rewrite,[status(thm)],[])).
% 2.22/1.69 tff(1634,axiom,((~hskp4) | c2_1(a105)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 2.22/1.69 tff(1635,plain,
% 2.22/1.69 ((~hskp4) | c2_1(a105)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 2.22/1.69 tff(1636,plain,
% 2.22/1.69 ((~hskp4) | c2_1(a105)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1635, 1633])).
% 2.22/1.69 tff(1637,plain,
% 2.22/1.69 ((~hskp4) | c2_1(a105)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1636, 1633])).
% 2.22/1.69 tff(1638,plain,
% 2.22/1.69 ((~hskp4) | c2_1(a105)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1637, 1633])).
% 2.22/1.69 tff(1639,plain,
% 2.22/1.69 ((~hskp4) | c2_1(a105)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1638, 1633])).
% 2.22/1.69 tff(1640,plain,
% 2.22/1.69 ((~hskp4) | c2_1(a105)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1639, 1633])).
% 2.22/1.69 tff(1641,plain,
% 2.22/1.69 ((~hskp4) | c2_1(a105)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1640, 1633])).
% 2.22/1.69 tff(1642,plain,
% 2.22/1.69 ((~hskp4) | c2_1(a105)),
% 2.22/1.69 inference(modus_ponens,[status(thm)],[1641, 1633])).
% 2.22/1.69 tff(1643,plain,
% 2.22/1.69 (c2_1(a105)),
% 2.22/1.69 inference(unit_resolution,[status(thm)],[1642, 34])).
% 2.22/1.70 tff(1644,assumption,(~hskp17), introduced(assumption)).
% 2.22/1.70 tff(1645,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1646,plain,
% 2.22/1.70 ((hskp17 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c2_1(a105)) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105))) <=> (hskp17 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1647,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c2_1(a105)) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105))))),
% 2.22/1.70 inference(monotonicity,[status(thm)],[1646])).
% 2.22/1.70 tff(1648,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c2_1(a105)) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)))),
% 2.22/1.70 inference(transitivity,[status(thm)],[1647, 1645])).
% 2.22/1.70 tff(1649,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c2_1(a105)) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105)))),
% 2.22/1.70 inference(quant_inst,[status(thm)],[])).
% 2.22/1.70 tff(1650,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 2.22/1.70 tff(1651,plain,
% 2.22/1.70 ($false),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1650, 160, 1644, 1643, 51, 40, 1632, 1622])).
% 2.22/1.70 tff(1652,plain,((~hskp4) | hskp17 | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a118)) | (~c2_1(a118)) | (~c3_1(a118))), inference(lemma,lemma(discharge,[]))).
% 2.22/1.70 tff(1653,plain,
% 2.22/1.70 (hskp17),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1652, 34, 1166, 1165, 1164, 1615, 1614, 1613])).
% 2.22/1.70 tff(1654,plain,
% 2.22/1.70 (~c1_1(a132)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[831, 1653])).
% 2.22/1.70 tff(1655,plain,
% 2.22/1.70 (~c0_1(a132)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[837, 1653])).
% 2.22/1.70 tff(1656,plain,
% 2.22/1.70 (c3_1(a132)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[849, 1653])).
% 2.22/1.70 tff(1657,plain,
% 2.22/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1658,plain,
% 2.22/1.70 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1659,plain,
% 2.22/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 2.22/1.70 inference(monotonicity,[status(thm)],[1658])).
% 2.22/1.70 tff(1660,plain,
% 2.22/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.22/1.70 inference(transitivity,[status(thm)],[1659, 1657])).
% 2.22/1.70 tff(1661,plain,
% 2.22/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 2.22/1.70 inference(quant_inst,[status(thm)],[])).
% 2.22/1.70 tff(1662,plain,
% 2.22/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)) | (~c2_1(a105)) | (~c3_1(a132)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 2.22/1.70 tff(1663,plain,
% 2.22/1.70 (~c0_1(a105)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1662, 160, 1615, 1614, 1613, 1656, 1643, 51, 1655, 1654, 96])).
% 2.22/1.70 tff(1664,plain,
% 2.22/1.70 ($false),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1621, 160, 1166, 1165, 1164, 1615, 1614, 1613, 51, 40, 96, 1663])).
% 2.22/1.70 tff(1665,plain,((~hskp4) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a118)) | (~c2_1(a118)) | (~c3_1(a118))), inference(lemma,lemma(discharge,[]))).
% 2.22/1.70 tff(1666,plain,
% 2.22/1.70 (~hskp4),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1665, 1570, 1600, 1569, 1612, 1611, 1610])).
% 2.22/1.70 tff(1667,plain,
% 2.22/1.70 (hskp17),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1543, 508])).
% 2.22/1.70 tff(1668,plain,
% 2.22/1.70 (~c1_1(a132)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[831, 1667])).
% 2.22/1.70 tff(1669,plain,
% 2.22/1.70 (~c0_1(a132)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[837, 1667])).
% 2.22/1.70 tff(1670,plain,
% 2.22/1.70 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))))),
% 2.22/1.70 inference(bind,[status(th)],[])).
% 2.22/1.70 tff(1671,plain,
% 2.22/1.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.22/1.70 inference(quant_intro,[status(thm)],[1670])).
% 2.22/1.70 tff(1672,plain,
% 2.22/1.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1673,plain,
% 2.22/1.70 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))))),
% 2.22/1.70 inference(bind,[status(th)],[])).
% 2.22/1.70 tff(1674,plain,
% 2.22/1.70 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.22/1.70 inference(quant_intro,[status(thm)],[1673])).
% 2.22/1.70 tff(1675,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 2.22/1.70 tff(1676,plain,
% 2.22/1.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1675, 1674])).
% 2.22/1.70 tff(1677,plain,
% 2.22/1.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1676, 1672])).
% 2.22/1.70 tff(1678,plain,(
% 2.22/1.70 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.22/1.70 inference(skolemize,[status(sab)],[1677])).
% 2.22/1.70 tff(1679,plain,
% 2.22/1.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1678, 1671])).
% 2.22/1.70 tff(1680,plain,
% 2.22/1.70 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 2.22/1.70 inference(bind,[status(th)],[])).
% 2.22/1.70 tff(1681,plain,
% 2.22/1.70 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.22/1.70 inference(quant_intro,[status(thm)],[1680])).
% 2.22/1.70 tff(1682,plain,
% 2.22/1.70 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1683,plain,
% 2.22/1.70 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 2.22/1.70 inference(bind,[status(th)],[])).
% 2.22/1.70 tff(1684,plain,
% 2.22/1.70 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.22/1.70 inference(quant_intro,[status(thm)],[1683])).
% 2.22/1.70 tff(1685,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 2.22/1.70 tff(1686,plain,
% 2.22/1.70 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1685, 1684])).
% 2.22/1.70 tff(1687,plain,
% 2.22/1.70 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1686, 1682])).
% 2.22/1.70 tff(1688,plain,(
% 2.22/1.70 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.22/1.70 inference(skolemize,[status(sab)],[1687])).
% 2.22/1.70 tff(1689,plain,
% 2.22/1.70 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1688, 1681])).
% 2.22/1.70 tff(1690,plain,
% 2.22/1.70 (c3_1(a132)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[849, 1667])).
% 2.22/1.70 tff(1691,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c0_1(a163)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1692,plain,
% 2.22/1.70 ((hskp12 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (hskp12 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c0_1(a163)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1693,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c0_1(a163))))),
% 2.22/1.70 inference(monotonicity,[status(thm)],[1692])).
% 2.22/1.70 tff(1694,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c0_1(a163)))),
% 2.22/1.70 inference(transitivity,[status(thm)],[1693, 1691])).
% 2.22/1.70 tff(1695,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 2.22/1.70 inference(quant_inst,[status(thm)],[])).
% 2.22/1.70 tff(1696,plain,
% 2.22/1.70 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | (~c2_1(a163)) | c3_1(a163) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c3_1(a132)) | (~c0_1(a163))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1695, 1694])).
% 2.22/1.70 tff(1697,plain,
% 2.22/1.70 (hskp12),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1696, 160, 1690, 1317, 97, 1669, 1668, 1689, 508])).
% 2.22/1.70 tff(1698,plain,
% 2.22/1.70 (((~hskp12) | (~c2_1(a113))) <=> ((~hskp12) | (~c2_1(a113)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1699,plain,
% 2.22/1.70 (((~c2_1(a113)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a113)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1700,axiom,((~c2_1(a113)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 2.22/1.70 tff(1701,plain,
% 2.22/1.70 ((~hskp12) | (~c2_1(a113))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1700, 1699])).
% 2.22/1.70 tff(1702,plain,
% 2.22/1.70 ((~hskp12) | (~c2_1(a113))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1701, 1698])).
% 2.22/1.70 tff(1703,plain,
% 2.22/1.70 (~c2_1(a113)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1702, 1697])).
% 2.22/1.70 tff(1704,plain,
% 2.22/1.70 (((~hskp12) | c3_1(a113)) <=> ((~hskp12) | c3_1(a113))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1705,axiom,((~hskp12) | c3_1(a113)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 2.22/1.70 tff(1706,plain,
% 2.22/1.70 ((~hskp12) | c3_1(a113)),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1705, 1704])).
% 2.22/1.70 tff(1707,plain,
% 2.22/1.70 ((~hskp12) | c3_1(a113)),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1706, 1704])).
% 2.22/1.70 tff(1708,plain,
% 2.22/1.70 ((~hskp12) | c3_1(a113)),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1707, 1704])).
% 2.22/1.70 tff(1709,plain,
% 2.22/1.70 ((~hskp12) | c3_1(a113)),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1708, 1704])).
% 2.22/1.70 tff(1710,plain,
% 2.22/1.70 ((~hskp12) | c3_1(a113)),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1709, 1704])).
% 2.22/1.70 tff(1711,plain,
% 2.22/1.70 ((~hskp12) | c3_1(a113)),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1710, 1704])).
% 2.22/1.70 tff(1712,plain,
% 2.22/1.70 ((~hskp12) | c3_1(a113)),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1711, 1704])).
% 2.22/1.70 tff(1713,plain,
% 2.22/1.70 ((~hskp12) | c3_1(a113)),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1712, 1704])).
% 2.22/1.70 tff(1714,plain,
% 2.22/1.70 (c3_1(a113)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1713, 1697])).
% 2.22/1.70 tff(1715,plain,
% 2.22/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a163) | c3_1(a163) | c2_1(a113) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a113)) | (~c1_1(a113)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a163) | c3_1(a163) | c2_1(a113) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a113)) | (~c1_1(a113)) | (~c0_1(a163)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1716,plain,
% 2.22/1.70 (((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a113) | (~c3_1(a113)) | (~c1_1(a113)) | c3_1(a163) | c1_1(a163) | (~c0_1(a163))) <=> (c1_1(a163) | c3_1(a163) | c2_1(a113) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a113)) | (~c1_1(a113)) | (~c0_1(a163)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1717,plain,
% 2.22/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a113) | (~c3_1(a113)) | (~c1_1(a113)) | c3_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a163) | c3_1(a163) | c2_1(a113) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a113)) | (~c1_1(a113)) | (~c0_1(a163))))),
% 2.22/1.70 inference(monotonicity,[status(thm)],[1716])).
% 2.22/1.70 tff(1718,plain,
% 2.22/1.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a113) | (~c3_1(a113)) | (~c1_1(a113)) | c3_1(a163) | c1_1(a163) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a163) | c3_1(a163) | c2_1(a113) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a113)) | (~c1_1(a113)) | (~c0_1(a163)))),
% 2.22/1.70 inference(transitivity,[status(thm)],[1717, 1715])).
% 2.22/1.70 tff(1719,plain,
% 2.22/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a113) | (~c3_1(a113)) | (~c1_1(a113)) | c3_1(a163) | c1_1(a163) | (~c0_1(a163)))),
% 2.22/1.70 inference(quant_inst,[status(thm)],[])).
% 2.22/1.70 tff(1720,plain,
% 2.22/1.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a163) | c3_1(a163) | c2_1(a113) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a113)) | (~c1_1(a113)) | (~c0_1(a163))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1719, 1718])).
% 2.22/1.70 tff(1721,plain,
% 2.22/1.70 (~c1_1(a113)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1720, 160, 1166, 1165, 1164, 1714, 52, 97, 1703, 1679, 508])).
% 2.22/1.70 tff(1722,plain,
% 2.22/1.70 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 2.22/1.70 inference(bind,[status(th)],[])).
% 2.22/1.70 tff(1723,plain,
% 2.22/1.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.22/1.70 inference(quant_intro,[status(thm)],[1722])).
% 2.22/1.70 tff(1724,plain,
% 2.22/1.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1725,plain,
% 2.22/1.70 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 2.22/1.70 inference(bind,[status(th)],[])).
% 2.22/1.70 tff(1726,plain,
% 2.22/1.70 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.22/1.70 inference(quant_intro,[status(thm)],[1725])).
% 2.22/1.70 tff(1727,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 2.22/1.70 tff(1728,plain,
% 2.22/1.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1727, 1726])).
% 2.22/1.70 tff(1729,plain,
% 2.22/1.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1728, 1724])).
% 2.22/1.70 tff(1730,plain,(
% 2.22/1.70 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.22/1.70 inference(skolemize,[status(sab)],[1729])).
% 2.22/1.70 tff(1731,plain,
% 2.22/1.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1730, 1723])).
% 2.22/1.70 tff(1732,plain,
% 2.22/1.70 (((~hskp12) | (~c0_1(a113))) <=> ((~hskp12) | (~c0_1(a113)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1733,plain,
% 2.22/1.70 (((~c0_1(a113)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a113)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1734,axiom,((~c0_1(a113)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 2.22/1.70 tff(1735,plain,
% 2.22/1.70 ((~hskp12) | (~c0_1(a113))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 2.22/1.70 tff(1736,plain,
% 2.22/1.70 ((~hskp12) | (~c0_1(a113))),
% 2.22/1.70 inference(modus_ponens,[status(thm)],[1735, 1732])).
% 2.22/1.70 tff(1737,plain,
% 2.22/1.70 (~c0_1(a113)),
% 2.22/1.70 inference(unit_resolution,[status(thm)],[1736, 1697])).
% 2.22/1.70 tff(1738,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a132) | c1_1(a132) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | c1_1(a113) | (~c3_1(a132)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a132) | c1_1(a132) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | c1_1(a113) | (~c3_1(a132)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1739,plain,
% 2.22/1.70 ((hskp0 | (~ndr1_0) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a113) | c1_1(a113) | c0_1(a113)) <=> (hskp0 | c0_1(a132) | c1_1(a132) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | c1_1(a113) | (~c3_1(a132)))),
% 2.22/1.70 inference(rewrite,[status(thm)],[])).
% 2.22/1.70 tff(1740,plain,
% 2.22/1.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a113) | c1_1(a113) | c0_1(a113))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a132) | c1_1(a132) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | c1_1(a113) | (~c3_1(a132))))),
% 2.22/1.71 inference(monotonicity,[status(thm)],[1739])).
% 2.22/1.71 tff(1741,plain,
% 2.22/1.71 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a113) | c1_1(a113) | c0_1(a113))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a132) | c1_1(a132) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | c1_1(a113) | (~c3_1(a132)))),
% 2.22/1.71 inference(transitivity,[status(thm)],[1740, 1738])).
% 2.22/1.71 tff(1742,plain,
% 2.22/1.71 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)) | c2_1(a113) | c1_1(a113) | c0_1(a113))),
% 2.22/1.71 inference(quant_inst,[status(thm)],[])).
% 2.22/1.71 tff(1743,plain,
% 2.22/1.71 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a132) | c1_1(a132) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | c1_1(a113) | (~c3_1(a132))),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 2.22/1.71 tff(1744,plain,
% 2.22/1.71 (hskp0),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1743, 160, 1690, 1669, 1668, 1737, 1703, 1731, 1721])).
% 2.22/1.71 tff(1745,plain,
% 2.22/1.71 (((~hskp0) | (~c0_1(a101))) <=> ((~hskp0) | (~c0_1(a101)))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1746,plain,
% 2.22/1.71 (((~c0_1(a101)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a101)))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1747,axiom,((~c0_1(a101)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 2.22/1.71 tff(1748,plain,
% 2.22/1.71 ((~hskp0) | (~c0_1(a101))),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1747, 1746])).
% 2.22/1.71 tff(1749,plain,
% 2.22/1.71 ((~hskp0) | (~c0_1(a101))),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1748, 1745])).
% 2.22/1.71 tff(1750,plain,
% 2.22/1.71 (~c0_1(a101)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1749, 1744])).
% 2.22/1.71 tff(1751,plain,
% 2.22/1.71 (((~hskp0) | c3_1(a101)) <=> ((~hskp0) | c3_1(a101))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1752,axiom,((~hskp0) | c3_1(a101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 2.22/1.71 tff(1753,plain,
% 2.22/1.71 ((~hskp0) | c3_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1752, 1751])).
% 2.22/1.71 tff(1754,plain,
% 2.22/1.71 ((~hskp0) | c3_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1753, 1751])).
% 2.22/1.71 tff(1755,plain,
% 2.22/1.71 ((~hskp0) | c3_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1754, 1751])).
% 2.22/1.71 tff(1756,plain,
% 2.22/1.71 ((~hskp0) | c3_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1755, 1751])).
% 2.22/1.71 tff(1757,plain,
% 2.22/1.71 ((~hskp0) | c3_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1756, 1751])).
% 2.22/1.71 tff(1758,plain,
% 2.22/1.71 ((~hskp0) | c3_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1757, 1751])).
% 2.22/1.71 tff(1759,plain,
% 2.22/1.71 ((~hskp0) | c3_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1758, 1751])).
% 2.22/1.71 tff(1760,plain,
% 2.22/1.71 ((~hskp0) | c3_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1759, 1751])).
% 2.22/1.71 tff(1761,plain,
% 2.22/1.71 (c3_1(a101)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1760, 1744])).
% 2.22/1.71 tff(1762,plain,
% 2.22/1.71 (((~hskp0) | c2_1(a101)) <=> ((~hskp0) | c2_1(a101))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1763,axiom,((~hskp0) | c2_1(a101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 2.22/1.71 tff(1764,plain,
% 2.22/1.71 ((~hskp0) | c2_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 2.22/1.71 tff(1765,plain,
% 2.22/1.71 ((~hskp0) | c2_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1764, 1762])).
% 2.22/1.71 tff(1766,plain,
% 2.22/1.71 ((~hskp0) | c2_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1765, 1762])).
% 2.22/1.71 tff(1767,plain,
% 2.22/1.71 ((~hskp0) | c2_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1766, 1762])).
% 2.22/1.71 tff(1768,plain,
% 2.22/1.71 ((~hskp0) | c2_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1767, 1762])).
% 2.22/1.71 tff(1769,plain,
% 2.22/1.71 ((~hskp0) | c2_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1768, 1762])).
% 2.22/1.71 tff(1770,plain,
% 2.22/1.71 ((~hskp0) | c2_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1769, 1762])).
% 2.22/1.71 tff(1771,plain,
% 2.22/1.71 ((~hskp0) | c2_1(a101)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1770, 1762])).
% 2.22/1.71 tff(1772,plain,
% 2.22/1.71 (c2_1(a101)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1771, 1744])).
% 2.22/1.71 tff(1773,plain,
% 2.22/1.71 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c2_1(a101)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c2_1(a101)) | (~c0_1(a163)))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1774,plain,
% 2.22/1.71 ((hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a101) | (~c3_1(a101)) | (~c2_1(a101))) <=> (hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c2_1(a101)) | (~c0_1(a163)))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1775,plain,
% 2.22/1.71 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a101) | (~c3_1(a101)) | (~c2_1(a101)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c2_1(a101)) | (~c0_1(a163))))),
% 2.22/1.71 inference(monotonicity,[status(thm)],[1774])).
% 2.22/1.71 tff(1776,plain,
% 2.22/1.71 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a101) | (~c3_1(a101)) | (~c2_1(a101)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c2_1(a101)) | (~c0_1(a163)))),
% 2.22/1.71 inference(transitivity,[status(thm)],[1775, 1773])).
% 2.22/1.71 tff(1777,plain,
% 2.22/1.71 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a101) | (~c3_1(a101)) | (~c2_1(a101)))),
% 2.22/1.71 inference(quant_inst,[status(thm)],[])).
% 2.22/1.71 tff(1778,plain,
% 2.22/1.71 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp10 | (~c2_1(a163)) | c3_1(a163) | c0_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c2_1(a101)) | (~c0_1(a163))),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 2.22/1.71 tff(1779,plain,
% 2.22/1.71 (hskp10),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1778, 160, 1772, 1761, 1317, 97, 1750, 1526, 508])).
% 2.22/1.71 tff(1780,plain,
% 2.22/1.71 (~c3_1(a111)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1334, 1779])).
% 2.22/1.71 tff(1781,plain,
% 2.22/1.71 (~c0_1(a111)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1346, 1779])).
% 2.22/1.71 tff(1782,plain,
% 2.22/1.71 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | c0_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c0_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1783,plain,
% 2.22/1.71 ((hskp5 | (~ndr1_0) | c3_1(a111) | c1_1(a111) | c0_1(a111)) <=> (hskp5 | c0_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1784,plain,
% 2.22/1.71 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | c0_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111)))),
% 2.22/1.71 inference(monotonicity,[status(thm)],[1783])).
% 2.22/1.71 tff(1785,plain,
% 2.22/1.71 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c0_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111))),
% 2.22/1.71 inference(transitivity,[status(thm)],[1784, 1782])).
% 2.22/1.71 tff(1786,plain,
% 2.22/1.71 ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a111) | c1_1(a111) | c0_1(a111))),
% 2.22/1.71 inference(quant_inst,[status(thm)],[])).
% 2.22/1.71 tff(1787,plain,
% 2.22/1.71 ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c0_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1786, 1785])).
% 2.22/1.71 tff(1788,plain,
% 2.22/1.71 (c1_1(a111)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1787, 160, 507, 1781, 1780, 227])).
% 2.22/1.71 tff(1789,plain,
% 2.22/1.71 (~c2_1(a111)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1340, 1779])).
% 2.22/1.71 tff(1790,plain,
% 2.22/1.71 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a113) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c3_1(a113)) | c1_1(a113))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a113) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c3_1(a113)) | c1_1(a113))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1791,plain,
% 2.22/1.71 ((hskp6 | (~ndr1_0) | c1_1(a113) | c2_1(a113) | (~c3_1(a113)) | c2_1(a111) | c0_1(a111) | (~c1_1(a111))) <=> (hskp6 | c2_1(a113) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c3_1(a113)) | c1_1(a113))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1792,plain,
% 2.22/1.71 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a113) | c2_1(a113) | (~c3_1(a113)) | c2_1(a111) | c0_1(a111) | (~c1_1(a111)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a113) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c3_1(a113)) | c1_1(a113)))),
% 2.22/1.71 inference(monotonicity,[status(thm)],[1791])).
% 2.22/1.71 tff(1793,plain,
% 2.22/1.71 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a113) | c2_1(a113) | (~c3_1(a113)) | c2_1(a111) | c0_1(a111) | (~c1_1(a111)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a113) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c3_1(a113)) | c1_1(a113))),
% 2.22/1.71 inference(transitivity,[status(thm)],[1792, 1790])).
% 2.22/1.71 tff(1794,plain,
% 2.22/1.71 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c1_1(a113) | c2_1(a113) | (~c3_1(a113)) | c2_1(a111) | c0_1(a111) | (~c1_1(a111)))),
% 2.22/1.71 inference(quant_inst,[status(thm)],[])).
% 2.22/1.71 tff(1795,plain,
% 2.22/1.71 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a113) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c3_1(a113)) | c1_1(a113)),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 2.22/1.71 tff(1796,plain,
% 2.22/1.71 (hskp6 | (~c1_1(a111))),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1795, 160, 1714, 1703, 1781, 1789, 938, 1721])).
% 2.22/1.71 tff(1797,plain,
% 2.22/1.71 (hskp6),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1796, 1788])).
% 2.22/1.71 tff(1798,plain,
% 2.22/1.71 (c2_1(a107)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[473, 1797])).
% 2.22/1.71 tff(1799,plain,
% 2.22/1.71 (c1_1(a107)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[484, 1797])).
% 2.22/1.71 tff(1800,plain,
% 2.22/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c3_1(a132)))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1801,plain,
% 2.22/1.71 (((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132))) <=> (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c3_1(a132)))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1802,plain,
% 2.22/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c3_1(a132))))),
% 2.22/1.71 inference(monotonicity,[status(thm)],[1801])).
% 2.22/1.71 tff(1803,plain,
% 2.22/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c3_1(a132)))),
% 2.22/1.71 inference(transitivity,[status(thm)],[1802, 1800])).
% 2.22/1.71 tff(1804,plain,
% 2.22/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a107)) | (~c3_1(a107)) | (~c2_1(a107)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a132) | c0_1(a132) | (~c3_1(a132)))),
% 2.22/1.71 inference(quant_inst,[status(thm)],[])).
% 2.22/1.71 tff(1805,plain,
% 2.22/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a132) | c1_1(a132) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c2_1(a107)) | (~c3_1(a107)) | (~c1_1(a107)) | (~c3_1(a132))),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1804, 1803])).
% 2.22/1.71 tff(1806,plain,
% 2.22/1.71 (~c3_1(a107)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1805, 160, 1166, 1165, 1164, 1690, 1799, 1798, 1669, 1668, 96])).
% 2.22/1.71 tff(1807,plain,
% 2.22/1.71 (~c0_1(a107)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[446, 1797])).
% 2.22/1.71 tff(1808,plain,
% 2.22/1.71 ($false),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[499, 160, 1473, 1799, 1798, 1470, 1469, 1807, 202, 1806])).
% 2.22/1.71 tff(1809,plain,(hskp5 | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c3_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.71 tff(1810,plain,
% 2.22/1.71 (hskp5),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1809, 1570, 1600, 1569, 97, 52])).
% 2.22/1.71 tff(1811,plain,
% 2.22/1.71 (c1_1(a106)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[257, 1810])).
% 2.22/1.71 tff(1812,plain,
% 2.22/1.71 (c0_1(a106)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[337, 1810])).
% 2.22/1.71 tff(1813,plain,
% 2.22/1.71 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1814,plain,
% 2.22/1.71 ((hskp24 | hskp1 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106))) <=> (hskp24 | hskp1 | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1815,plain,
% 2.22/1.71 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106))))),
% 2.22/1.71 inference(monotonicity,[status(thm)],[1814])).
% 2.22/1.71 tff(1816,plain,
% 2.22/1.71 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))),
% 2.22/1.71 inference(transitivity,[status(thm)],[1815, 1813])).
% 2.22/1.71 tff(1817,plain,
% 2.22/1.71 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))),
% 2.22/1.71 inference(quant_inst,[status(thm)],[])).
% 2.22/1.71 tff(1818,plain,
% 2.22/1.71 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106))),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 2.22/1.71 tff(1819,plain,
% 2.22/1.71 (hskp1 | (~c0_1(a106)) | (~c1_1(a106))),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1818, 160, 1318, 109, 21])).
% 2.22/1.71 tff(1820,plain,
% 2.22/1.71 (hskp1),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1819, 1812, 1811])).
% 2.22/1.71 tff(1821,plain,
% 2.22/1.71 (~c1_1(a102)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1254, 1820])).
% 2.22/1.71 tff(1822,plain,
% 2.22/1.71 (~c0_1(a102)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1260, 1820])).
% 2.22/1.71 tff(1823,plain,
% 2.22/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a102)) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a102)) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1824,plain,
% 2.22/1.71 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102))) <=> (c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a102)) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1825,plain,
% 2.22/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a102)) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 2.22/1.71 inference(monotonicity,[status(thm)],[1824])).
% 2.22/1.71 tff(1826,plain,
% 2.22/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a102)) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.22/1.71 inference(transitivity,[status(thm)],[1825, 1823])).
% 2.22/1.71 tff(1827,plain,
% 2.22/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))),
% 2.22/1.71 inference(quant_inst,[status(thm)],[])).
% 2.22/1.71 tff(1828,plain,
% 2.22/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c3_1(a102)) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1827, 1826])).
% 2.22/1.71 tff(1829,plain,
% 2.22/1.71 (~c3_1(a102)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1828, 160, 1570, 1600, 1569, 1612, 1611, 1610, 1822, 1821, 96])).
% 2.22/1.71 tff(1830,plain,
% 2.22/1.71 (c2_1(a102)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1307, 1820])).
% 2.22/1.71 tff(1831,plain,
% 2.22/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~c2_1(a163)) | c3_1(a163) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c2_1(a163)) | c3_1(a163) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c0_1(a163)))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1832,plain,
% 2.22/1.71 (((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102)) <=> ((~c2_1(a163)) | c3_1(a163) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c0_1(a163)))),
% 2.22/1.71 inference(rewrite,[status(thm)],[])).
% 2.22/1.71 tff(1833,plain,
% 2.22/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~c2_1(a163)) | c3_1(a163) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c0_1(a163))))),
% 2.22/1.71 inference(monotonicity,[status(thm)],[1832])).
% 2.22/1.71 tff(1834,plain,
% 2.22/1.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c2_1(a163)) | c3_1(a163) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c0_1(a163)))),
% 2.22/1.71 inference(transitivity,[status(thm)],[1833, 1831])).
% 2.22/1.71 tff(1835,plain,
% 2.22/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102))),
% 2.22/1.71 inference(quant_inst,[status(thm)],[])).
% 2.22/1.71 tff(1836,plain,
% 2.22/1.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c2_1(a163)) | c3_1(a163) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c0_1(a163))),
% 2.22/1.71 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 2.22/1.71 tff(1837,plain,
% 2.22/1.71 (~c0_1(a163)),
% 2.22/1.71 inference(unit_resolution,[status(thm)],[1836, 160, 1830, 1317, 97, 1822, 1821, 367, 1829])).
% 2.22/1.71 tff(1838,assumption,(~hskp4), introduced(assumption)).
% 2.22/1.72 tff(1839,plain,
% 2.22/1.72 (^[U: $i] : refl((hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.22/1.72 inference(bind,[status(th)],[])).
% 2.22/1.72 tff(1840,plain,
% 2.22/1.72 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(quant_intro,[status(thm)],[1839])).
% 2.22/1.72 tff(1841,plain,
% 2.22/1.72 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1842,plain,
% 2.22/1.72 (^[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)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp10) <=> ((hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp10) <=> (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.22/1.72 inference(bind,[status(th)],[])).
% 2.22/1.72 tff(1843,plain,
% 2.22/1.72 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp10) <=> ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(quant_intro,[status(thm)],[1842])).
% 2.22/1.72 tff(1844,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp4) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 2.22/1.72 tff(1845,plain,
% 2.22/1.72 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 2.22/1.72 tff(1846,plain,
% 2.22/1.72 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1845, 1841])).
% 2.22/1.72 tff(1847,plain,(
% 2.22/1.72 ![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(skolemize,[status(sab)],[1846])).
% 2.22/1.72 tff(1848,plain,
% 2.22/1.72 (![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1847, 1840])).
% 2.22/1.72 tff(1849,plain,
% 2.22/1.72 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1850,plain,
% 2.22/1.72 ((hskp10 | hskp4 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131))) <=> (hskp10 | hskp4 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1851,plain,
% 2.22/1.72 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131)))),
% 2.22/1.72 inference(monotonicity,[status(thm)],[1850])).
% 2.22/1.72 tff(1852,plain,
% 2.22/1.72 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131))),
% 2.22/1.72 inference(transitivity,[status(thm)],[1851, 1849])).
% 2.22/1.72 tff(1853,plain,
% 2.22/1.72 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a131) | (~c3_1(a131)) | (~c0_1(a131)))),
% 2.22/1.72 inference(quant_inst,[status(thm)],[])).
% 2.22/1.72 tff(1854,plain,
% 2.22/1.72 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a131)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1853, 1852])).
% 2.22/1.72 tff(1855,plain,
% 2.22/1.72 (hskp10 | hskp4 | c1_1(a131)),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1854, 160, 1166, 1164, 1848])).
% 2.22/1.72 tff(1856,plain,
% 2.22/1.72 (c1_1(a131)),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1855, 22, 1838])).
% 2.22/1.72 tff(1857,plain,
% 2.22/1.72 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1858,plain,
% 2.22/1.72 ((hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163))) <=> (hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1859,plain,
% 2.22/1.72 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163)))),
% 2.22/1.72 inference(monotonicity,[status(thm)],[1858])).
% 2.22/1.72 tff(1860,plain,
% 2.22/1.72 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 2.22/1.72 inference(transitivity,[status(thm)],[1859, 1857])).
% 2.22/1.72 tff(1861,plain,
% 2.22/1.72 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a163) | c0_1(a163) | (~c2_1(a163)))),
% 2.22/1.72 inference(quant_inst,[status(thm)],[])).
% 2.22/1.72 tff(1862,plain,
% 2.22/1.72 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a163) | (~c2_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1861, 1860])).
% 2.22/1.72 tff(1863,plain,
% 2.22/1.72 ($false),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1862, 160, 22, 1166, 1164, 52, 1317, 1400, 245, 1856])).
% 2.22/1.72 tff(1864,plain,(hskp10 | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a163) | c0_1(a163) | hskp4), inference(lemma,lemma(discharge,[]))).
% 2.22/1.72 tff(1865,plain,
% 2.22/1.72 (hskp10),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1864, 1570, 1569, 52, 1837, 1666])).
% 2.22/1.72 tff(1866,plain,
% 2.22/1.72 (~c0_1(a111)),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1346, 1865])).
% 2.22/1.72 tff(1867,plain,
% 2.22/1.72 (~c3_1(a111)),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1334, 1865])).
% 2.22/1.72 tff(1868,assumption,(~c2_1(a111)), introduced(assumption)).
% 2.22/1.72 tff(1869,plain,
% 2.22/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1870,plain,
% 2.22/1.72 (((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111)) <=> (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1871,plain,
% 2.22/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))))),
% 2.22/1.72 inference(monotonicity,[status(thm)],[1870])).
% 2.22/1.72 tff(1872,plain,
% 2.22/1.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118)))),
% 2.22/1.72 inference(transitivity,[status(thm)],[1871, 1869])).
% 2.22/1.72 tff(1873,plain,
% 2.22/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a118)) | (~c3_1(a118)) | (~c2_1(a118)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))),
% 2.22/1.72 inference(quant_inst,[status(thm)],[])).
% 2.22/1.72 tff(1874,plain,
% 2.22/1.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)) | (~c3_1(a118)) | (~c2_1(a118)) | (~c1_1(a118))),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1873, 1872])).
% 2.22/1.72 tff(1875,plain,
% 2.22/1.72 (c2_1(a111) | c1_1(a111)),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1874, 160, 1615, 1614, 1613, 486, 463, 462, 1476, 108])).
% 2.22/1.72 tff(1876,plain,
% 2.22/1.72 (c1_1(a111)),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1875, 1868])).
% 2.22/1.72 tff(1877,plain,
% 2.22/1.72 (c1_1(a135)),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1162, 160, 1615, 1614, 1613, 486, 463, 462, 108])).
% 2.22/1.72 tff(1878,assumption,(c1_1(a135)), introduced(assumption)).
% 2.22/1.72 tff(1879,plain,
% 2.22/1.72 (^[U: $i] : refl((hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 2.22/1.72 inference(bind,[status(th)],[])).
% 2.22/1.72 tff(1880,plain,
% 2.22/1.72 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(quant_intro,[status(thm)],[1879])).
% 2.22/1.72 tff(1881,plain,
% 2.22/1.72 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1882,plain,
% 2.22/1.72 (^[U: $i] : 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(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)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp4) <=> ((hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp4))), rewrite(((hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp4) <=> (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 2.22/1.72 inference(bind,[status(th)],[])).
% 2.22/1.72 tff(1883,plain,
% 2.22/1.72 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp4) <=> ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(quant_intro,[status(thm)],[1882])).
% 2.22/1.72 tff(1884,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 2.22/1.72 tff(1885,plain,
% 2.22/1.72 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1884, 1883])).
% 2.22/1.72 tff(1886,plain,
% 2.22/1.72 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1885, 1881])).
% 2.22/1.72 tff(1887,plain,(
% 2.22/1.72 ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(skolemize,[status(sab)],[1886])).
% 2.22/1.72 tff(1888,plain,
% 2.22/1.72 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1887, 1880])).
% 2.22/1.72 tff(1889,plain,
% 2.22/1.72 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1890,plain,
% 2.22/1.72 ((hskp29 | hskp4 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135))) <=> (hskp29 | hskp4 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1891,plain,
% 2.22/1.72 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135))))),
% 2.22/1.72 inference(monotonicity,[status(thm)],[1890])).
% 2.22/1.72 tff(1892,plain,
% 2.22/1.72 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135)))),
% 2.22/1.72 inference(transitivity,[status(thm)],[1891, 1889])).
% 2.22/1.72 tff(1893,plain,
% 2.22/1.72 ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))),
% 2.22/1.72 inference(quant_inst,[status(thm)],[])).
% 2.22/1.72 tff(1894,plain,
% 2.22/1.72 ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | c2_1(a135) | (~ndr1_0) | (~c1_1(a135)) | (~c0_1(a135))),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1893, 1892])).
% 2.22/1.72 tff(1895,plain,
% 2.22/1.72 (hskp29 | hskp4 | (~c1_1(a135))),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1894, 160, 486, 463, 1888])).
% 2.22/1.72 tff(1896,plain,
% 2.22/1.72 (hskp29),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1895, 1838, 1878])).
% 2.22/1.72 tff(1897,plain,
% 2.22/1.72 (((~hskp29) | c0_1(a128)) <=> ((~hskp29) | c0_1(a128))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1898,axiom,((~hskp29) | c0_1(a128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 2.22/1.72 tff(1899,plain,
% 2.22/1.72 ((~hskp29) | c0_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1898, 1897])).
% 2.22/1.72 tff(1900,plain,
% 2.22/1.72 ((~hskp29) | c0_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1899, 1897])).
% 2.22/1.72 tff(1901,plain,
% 2.22/1.72 ((~hskp29) | c0_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1900, 1897])).
% 2.22/1.72 tff(1902,plain,
% 2.22/1.72 ((~hskp29) | c0_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1901, 1897])).
% 2.22/1.72 tff(1903,plain,
% 2.22/1.72 ((~hskp29) | c0_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1902, 1897])).
% 2.22/1.72 tff(1904,plain,
% 2.22/1.72 ((~hskp29) | c0_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1903, 1897])).
% 2.22/1.72 tff(1905,plain,
% 2.22/1.72 ((~hskp29) | c0_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1904, 1897])).
% 2.22/1.72 tff(1906,plain,
% 2.22/1.72 ((~hskp29) | c0_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1905, 1897])).
% 2.22/1.72 tff(1907,plain,
% 2.22/1.72 (c0_1(a128)),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1906, 1896])).
% 2.22/1.72 tff(1908,assumption,(~hskp13), introduced(assumption)).
% 2.22/1.72 tff(1909,plain,
% 2.22/1.72 (((~hskp29) | c1_1(a128)) <=> ((~hskp29) | c1_1(a128))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1910,axiom,((~hskp29) | c1_1(a128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 2.22/1.72 tff(1911,plain,
% 2.22/1.72 ((~hskp29) | c1_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 2.22/1.72 tff(1912,plain,
% 2.22/1.72 ((~hskp29) | c1_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1911, 1909])).
% 2.22/1.72 tff(1913,plain,
% 2.22/1.72 ((~hskp29) | c1_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1912, 1909])).
% 2.22/1.72 tff(1914,plain,
% 2.22/1.72 ((~hskp29) | c1_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1913, 1909])).
% 2.22/1.72 tff(1915,plain,
% 2.22/1.72 ((~hskp29) | c1_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1914, 1909])).
% 2.22/1.72 tff(1916,plain,
% 2.22/1.72 ((~hskp29) | c1_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1915, 1909])).
% 2.22/1.72 tff(1917,plain,
% 2.22/1.72 ((~hskp29) | c1_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1916, 1909])).
% 2.22/1.72 tff(1918,plain,
% 2.22/1.72 ((~hskp29) | c1_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1917, 1909])).
% 2.22/1.72 tff(1919,plain,
% 2.22/1.72 (c1_1(a128)),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1918, 1896])).
% 2.22/1.72 tff(1920,plain,
% 2.22/1.72 (((~hskp29) | c2_1(a128)) <=> ((~hskp29) | c2_1(a128))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1921,axiom,((~hskp29) | c2_1(a128)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 2.22/1.72 tff(1922,plain,
% 2.22/1.72 ((~hskp29) | c2_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 2.22/1.72 tff(1923,plain,
% 2.22/1.72 ((~hskp29) | c2_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1922, 1920])).
% 2.22/1.72 tff(1924,plain,
% 2.22/1.72 ((~hskp29) | c2_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1923, 1920])).
% 2.22/1.72 tff(1925,plain,
% 2.22/1.72 ((~hskp29) | c2_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1924, 1920])).
% 2.22/1.72 tff(1926,plain,
% 2.22/1.72 ((~hskp29) | c2_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1925, 1920])).
% 2.22/1.72 tff(1927,plain,
% 2.22/1.72 ((~hskp29) | c2_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1926, 1920])).
% 2.22/1.72 tff(1928,plain,
% 2.22/1.72 ((~hskp29) | c2_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1927, 1920])).
% 2.22/1.72 tff(1929,plain,
% 2.22/1.72 ((~hskp29) | c2_1(a128)),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1928, 1920])).
% 2.22/1.72 tff(1930,plain,
% 2.22/1.72 (c2_1(a128)),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1929, 1896])).
% 2.22/1.72 tff(1931,assumption,(c1_1(a128)), introduced(assumption)).
% 2.22/1.72 tff(1932,assumption,(c0_1(a128)), introduced(assumption)).
% 2.22/1.72 tff(1933,plain,
% 2.22/1.72 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1934,plain,
% 2.22/1.72 ((hskp13 | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)) | c2_1(a111) | c0_1(a111) | c3_1(a111)) <=> (hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1935,plain,
% 2.22/1.72 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)) | c2_1(a111) | c0_1(a111) | c3_1(a111))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128))))),
% 2.22/1.72 inference(monotonicity,[status(thm)],[1934])).
% 2.22/1.72 tff(1936,plain,
% 2.22/1.72 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)) | c2_1(a111) | c0_1(a111) | c3_1(a111))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)))),
% 2.22/1.72 inference(transitivity,[status(thm)],[1935, 1933])).
% 2.22/1.72 tff(1937,plain,
% 2.22/1.72 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128)) | c2_1(a111) | c0_1(a111) | c3_1(a111))),
% 2.22/1.72 inference(quant_inst,[status(thm)],[])).
% 2.22/1.72 tff(1938,plain,
% 2.22/1.72 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a128)) | (~c0_1(a128))),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 2.22/1.72 tff(1939,plain,
% 2.22/1.72 (hskp13 | (~c3_1(a128))),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1938, 160, 1932, 1931, 1477, 1868, 1476, 1328])).
% 2.22/1.72 tff(1940,plain,
% 2.22/1.72 (~c3_1(a128)),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1939, 1908])).
% 2.22/1.72 tff(1941,plain,
% 2.22/1.72 (^[U: $i] : refl((hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))),
% 2.22/1.72 inference(bind,[status(th)],[])).
% 2.22/1.72 tff(1942,plain,
% 2.22/1.72 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.22/1.72 inference(quant_intro,[status(thm)],[1941])).
% 2.22/1.72 tff(1943,plain,
% 2.22/1.72 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1944,plain,
% 2.22/1.72 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp13) | hskp4) <=> ((hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp4))), rewrite(((hskp13 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U))) | hskp4) <=> (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp13) | hskp4) <=> (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))))),
% 2.22/1.72 inference(bind,[status(th)],[])).
% 2.22/1.72 tff(1945,plain,
% 2.22/1.72 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp13) | hskp4) <=> ![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.22/1.72 inference(quant_intro,[status(thm)],[1944])).
% 2.22/1.72 tff(1946,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp13) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 2.22/1.72 tff(1947,plain,
% 2.22/1.72 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 2.22/1.72 tff(1948,plain,
% 2.22/1.72 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1947, 1943])).
% 2.22/1.72 tff(1949,plain,(
% 2.22/1.72 ![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.22/1.72 inference(skolemize,[status(sab)],[1948])).
% 2.22/1.72 tff(1950,plain,
% 2.22/1.72 (![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1949, 1942])).
% 2.22/1.72 tff(1951,assumption,(c2_1(a128)), introduced(assumption)).
% 2.22/1.72 tff(1952,plain,
% 2.22/1.72 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp13 | hskp4 | (~ndr1_0) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a128)))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1953,plain,
% 2.22/1.72 ((hskp13 | hskp4 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c2_1(a128))) <=> (hskp13 | hskp4 | (~ndr1_0) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a128)))),
% 2.22/1.72 inference(rewrite,[status(thm)],[])).
% 2.22/1.72 tff(1954,plain,
% 2.22/1.72 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c2_1(a128)))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a128))))),
% 2.22/1.72 inference(monotonicity,[status(thm)],[1953])).
% 2.22/1.72 tff(1955,plain,
% 2.22/1.72 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c2_1(a128)))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp13 | hskp4 | (~ndr1_0) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a128)))),
% 2.22/1.72 inference(transitivity,[status(thm)],[1954, 1952])).
% 2.22/1.72 tff(1956,plain,
% 2.22/1.72 ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c2_1(a128)))),
% 2.22/1.72 inference(quant_inst,[status(thm)],[])).
% 2.22/1.72 tff(1957,plain,
% 2.22/1.72 ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp13 | hskp4 | (~ndr1_0) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a128))),
% 2.22/1.72 inference(modus_ponens,[status(thm)],[1956, 1955])).
% 2.22/1.72 tff(1958,plain,
% 2.22/1.72 (hskp13 | c3_1(a128)),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1957, 160, 1838, 1931, 1951, 1950])).
% 2.22/1.72 tff(1959,plain,
% 2.22/1.72 ($false),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1958, 1940, 1908])).
% 2.22/1.72 tff(1960,plain,(hskp13 | hskp4 | (~c1_1(a128)) | (~c2_1(a128)) | (~c0_1(a128)) | c0_1(a111) | c2_1(a111) | c3_1(a111)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.72 tff(1961,plain,
% 2.22/1.72 ($false),
% 2.22/1.72 inference(unit_resolution,[status(thm)],[1960, 1930, 1919, 1908, 1838, 1907, 1477, 1868, 1476])).
% 2.22/1.72 tff(1962,plain,(hskp4 | hskp13 | c0_1(a111) | c2_1(a111) | c3_1(a111) | (~c1_1(a135)) | (~c0_1(a135)) | c2_1(a135)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.73 tff(1963,plain,
% 2.22/1.73 (hskp13),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1962, 1868, 1477, 1838, 1476, 1877, 486, 463])).
% 2.22/1.73 tff(1964,plain,
% 2.22/1.73 ($false),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1489, 1963, 1876, 463, 462, 1477, 1476, 486])).
% 2.22/1.73 tff(1965,plain,(c2_1(a111) | c2_1(a135) | c3_1(a135) | c0_1(a111) | c3_1(a111) | (~c0_1(a135)) | hskp4 | (~c1_1(a118)) | (~c2_1(a118)) | (~c3_1(a118))), inference(lemma,lemma(discharge,[]))).
% 2.22/1.73 tff(1966,plain,
% 2.22/1.73 (c2_1(a111)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1965, 1838, 462, 1477, 1476, 486, 463, 1615, 1614, 1613])).
% 2.22/1.73 tff(1967,plain,
% 2.22/1.73 (~hskp10),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1340, 1966])).
% 2.22/1.73 tff(1968,plain,
% 2.22/1.73 (c1_1(a131)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1855, 1967, 1838])).
% 2.22/1.73 tff(1969,plain,
% 2.22/1.73 ($false),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1862, 160, 1967, 1166, 1164, 52, 1317, 1400, 245, 1968])).
% 2.22/1.73 tff(1970,plain,(hskp4 | (~c0_1(a131)) | (~c3_1(a131)) | c1_1(a163) | c0_1(a163) | c3_1(a135) | c0_1(a111) | c3_1(a111) | (~c0_1(a135)) | c2_1(a135) | (~c1_1(a118)) | (~c2_1(a118)) | (~c3_1(a118))), inference(lemma,lemma(discharge,[]))).
% 2.22/1.73 tff(1971,plain,
% 2.22/1.73 ($false),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1970, 1867, 1866, 1569, 52, 1837, 1469, 1666, 1570, 1473, 1470, 1612, 1611, 1610])).
% 2.22/1.73 tff(1972,plain,(hskp31 | c1_1(a163) | c3_1(a163) | c2_1(a106)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.73 tff(1973,plain,
% 2.22/1.73 (c2_1(a106)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1972, 1563, 97, 52])).
% 2.22/1.73 tff(1974,plain,
% 2.22/1.73 (~hskp5),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[976, 1973])).
% 2.22/1.73 tff(1975,plain,
% 2.22/1.73 ($false),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1809, 1974, 1567, 1566, 1565, 97, 52])).
% 2.22/1.73 tff(1976,plain,(c3_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.73 tff(1977,plain,
% 2.22/1.73 (c3_1(a163)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1976, 52])).
% 2.22/1.73 tff(1978,plain,
% 2.22/1.73 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a163) | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(1979,plain,
% 2.22/1.73 ((hskp17 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163))) <=> (hskp17 | c1_1(a163) | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(1980,plain,
% 2.22/1.73 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | c1_1(a163) | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))))),
% 2.22/1.73 inference(monotonicity,[status(thm)],[1979])).
% 2.22/1.73 tff(1981,plain,
% 2.22/1.73 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a163) | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.73 inference(transitivity,[status(thm)],[1980, 1978])).
% 2.22/1.73 tff(1982,plain,
% 2.22/1.73 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))),
% 2.22/1.73 inference(quant_inst,[status(thm)],[])).
% 2.22/1.73 tff(1983,plain,
% 2.22/1.73 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp17 | c1_1(a163) | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))),
% 2.22/1.73 inference(modus_ponens,[status(thm)],[1982, 1981])).
% 2.22/1.73 tff(1984,plain,
% 2.22/1.73 (hskp17 | (~c2_1(a163)) | (~c3_1(a163)) | (~c0_1(a163))),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1983, 160, 52, 1632])).
% 2.22/1.73 tff(1985,plain,
% 2.22/1.73 (hskp17),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1984, 110, 1317, 1977])).
% 2.22/1.73 tff(1986,plain,
% 2.22/1.73 (~c1_1(a132)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[831, 1985])).
% 2.22/1.73 tff(1987,plain,
% 2.22/1.73 (~c0_1(a132)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[837, 1985])).
% 2.22/1.73 tff(1988,plain,
% 2.22/1.73 (c3_1(a132)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[849, 1985])).
% 2.22/1.73 tff(1989,plain,
% 2.22/1.73 (~c2_1(a141)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1382, 160, 818, 817, 851, 1988, 1987, 1986, 96])).
% 2.22/1.73 tff(1990,plain,
% 2.22/1.73 ($false),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1389, 160, 818, 817, 851, 52, 1317, 320, 110, 1989])).
% 2.22/1.73 tff(1991,plain,((~c0_1(a163)) | (~c0_1(a141)) | (~c1_1(a141)) | (~c3_1(a141)) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.73 tff(1992,plain,
% 2.22/1.73 (~c0_1(a163)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1991, 86, 75, 64, 52])).
% 2.22/1.73 tff(1993,plain,
% 2.22/1.73 (hskp10),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1515, 1992])).
% 2.22/1.73 tff(1994,plain,
% 2.22/1.73 (~c3_1(a111)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1334, 1993])).
% 2.22/1.73 tff(1995,plain,
% 2.22/1.73 (~c0_1(a111)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1346, 1993])).
% 2.22/1.73 tff(1996,plain,
% 2.22/1.73 (~c2_1(a111)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1340, 1993])).
% 2.22/1.73 tff(1997,plain,
% 2.22/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(1998,plain,
% 2.22/1.73 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(1999,plain,
% 2.22/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c0_1(a163)))),
% 2.22/1.73 inference(monotonicity,[status(thm)],[1998])).
% 2.22/1.73 tff(2000,plain,
% 2.22/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.22/1.73 inference(transitivity,[status(thm)],[1999, 1997])).
% 2.22/1.73 tff(2001,plain,
% 2.22/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | (~c2_1(a141)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 2.22/1.73 inference(quant_inst,[status(thm)],[])).
% 2.22/1.73 tff(2002,plain,
% 2.22/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c0_1(a163)),
% 2.22/1.73 inference(modus_ponens,[status(thm)],[2001, 2000])).
% 2.22/1.73 tff(2003,plain,
% 2.22/1.73 ((~c2_1(a141)) | c0_1(a163)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[2002, 160, 818, 817, 851, 52, 1977, 96])).
% 2.22/1.73 tff(2004,plain,
% 2.22/1.73 (~c2_1(a141)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[2003, 245])).
% 2.22/1.73 tff(2005,assumption,(~c0_1(a135)), introduced(assumption)).
% 2.22/1.73 tff(2006,plain,
% 2.22/1.73 (~hskp19),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[459, 2005])).
% 2.22/1.73 tff(2007,plain,
% 2.22/1.73 (~hskp11),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1070, 2006])).
% 2.22/1.73 tff(2008,plain,
% 2.22/1.73 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(2009,plain,
% 2.22/1.73 ((hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a163)) | (~c2_1(a163)) | (~c0_1(a163))) <=> (hskp19 | hskp11 | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(2010,plain,
% 2.22/1.73 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a163)) | (~c2_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))))),
% 2.22/1.73 inference(monotonicity,[status(thm)],[2009])).
% 2.22/1.73 tff(2011,plain,
% 2.22/1.73 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a163)) | (~c2_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.73 inference(transitivity,[status(thm)],[2010, 2008])).
% 2.22/1.73 tff(2012,plain,
% 2.22/1.73 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(a163)) | (~c2_1(a163)) | (~c0_1(a163)))),
% 2.22/1.73 inference(quant_inst,[status(thm)],[])).
% 2.22/1.73 tff(2013,plain,
% 2.22/1.73 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp19 | hskp11 | (~c2_1(a163)) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))),
% 2.22/1.73 inference(modus_ponens,[status(thm)],[2012, 2011])).
% 2.22/1.73 tff(2014,plain,
% 2.22/1.73 (hskp19 | hskp11 | (~c3_1(a163)) | (~c0_1(a163))),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[2013, 160, 1317, 1034])).
% 2.22/1.73 tff(2015,plain,
% 2.22/1.73 (~c0_1(a163)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[2014, 2007, 1977, 2006])).
% 2.22/1.73 tff(2016,plain,
% 2.22/1.73 (hskp19 | hskp11 | (~c2_1(a141))),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1147, 160, 818, 851, 1034])).
% 2.22/1.73 tff(2017,plain,
% 2.22/1.73 (~c2_1(a141)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[2016, 2007, 2006])).
% 2.22/1.73 tff(2018,plain,
% 2.22/1.73 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 2.22/1.73 inference(bind,[status(th)],[])).
% 2.22/1.73 tff(2019,plain,
% 2.22/1.73 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.22/1.73 inference(quant_intro,[status(thm)],[2018])).
% 2.22/1.73 tff(2020,plain,
% 2.22/1.73 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(2021,plain,
% 2.22/1.73 (^[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) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 2.22/1.73 inference(bind,[status(th)],[])).
% 2.22/1.73 tff(2022,plain,
% 2.22/1.73 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.22/1.73 inference(quant_intro,[status(thm)],[2021])).
% 2.22/1.73 tff(2023,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 2.22/1.73 tff(2024,plain,
% 2.22/1.73 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.22/1.73 inference(modus_ponens,[status(thm)],[2023, 2022])).
% 2.22/1.73 tff(2025,plain,
% 2.22/1.73 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.22/1.73 inference(modus_ponens,[status(thm)],[2024, 2020])).
% 2.22/1.73 tff(2026,plain,(
% 2.22/1.73 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.22/1.73 inference(skolemize,[status(sab)],[2025])).
% 2.22/1.73 tff(2027,plain,
% 2.22/1.73 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.22/1.73 inference(modus_ponens,[status(thm)],[2026, 2019])).
% 2.22/1.73 tff(2028,plain,
% 2.22/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a135) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~c3_1(a135)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a135) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~c3_1(a135)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(2029,plain,
% 2.22/1.73 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | (~c3_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c0_1(a135) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~c3_1(a135)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(2030,plain,
% 2.22/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | (~c3_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a135) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~c3_1(a135)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)))),
% 2.22/1.73 inference(monotonicity,[status(thm)],[2029])).
% 2.22/1.73 tff(2031,plain,
% 2.22/1.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | (~c3_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a135) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~c3_1(a135)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.22/1.73 inference(transitivity,[status(thm)],[2030, 2028])).
% 2.22/1.73 tff(2032,plain,
% 2.22/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | (~c3_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 2.22/1.73 inference(quant_inst,[status(thm)],[])).
% 2.22/1.73 tff(2033,plain,
% 2.22/1.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a135) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~c3_1(a135)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)),
% 2.22/1.73 inference(modus_ponens,[status(thm)],[2032, 2031])).
% 2.22/1.73 tff(2034,plain,
% 2.22/1.73 (c0_1(a135) | (~c3_1(a135)) | c0_1(a163)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[2033, 160, 818, 817, 851, 52, 1977, 463, 804])).
% 2.22/1.73 tff(2035,plain,
% 2.22/1.73 (~c3_1(a135)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[2034, 2015, 2005])).
% 2.22/1.73 tff(2036,plain,
% 2.22/1.73 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a135) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a135) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(2037,plain,
% 2.22/1.73 ((hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | c3_1(a135)) <=> (hskp13 | c0_1(a135) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(2038,plain,
% 2.22/1.73 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | c3_1(a135))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c0_1(a135) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141))))),
% 2.22/1.73 inference(monotonicity,[status(thm)],[2037])).
% 2.22/1.73 tff(2039,plain,
% 2.22/1.73 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | c3_1(a135))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a135) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)))),
% 2.22/1.73 inference(transitivity,[status(thm)],[2038, 2036])).
% 2.22/1.73 tff(2040,plain,
% 2.22/1.73 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c0_1(a135) | c3_1(a135))),
% 2.22/1.73 inference(quant_inst,[status(thm)],[])).
% 2.22/1.73 tff(2041,plain,
% 2.22/1.73 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c0_1(a135) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141))),
% 2.22/1.73 inference(modus_ponens,[status(thm)],[2040, 2039])).
% 2.22/1.73 tff(2042,plain,
% 2.22/1.73 (hskp13 | c0_1(a135) | c3_1(a135)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[2041, 160, 818, 817, 851, 463, 1328])).
% 2.22/1.73 tff(2043,plain,
% 2.22/1.73 (hskp13),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[2042, 2035, 2005])).
% 2.22/1.73 tff(2044,plain,
% 2.22/1.73 (~c3_1(a114)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[629, 2043])).
% 2.22/1.73 tff(2045,plain,
% 2.22/1.73 (c2_1(a114)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[640, 2043])).
% 2.22/1.73 tff(2046,plain,
% 2.22/1.73 (c1_1(a114)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[651, 2043])).
% 2.22/1.73 tff(2047,plain,
% 2.22/1.73 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c1_1(a114)) | (~c2_1(a114)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c1_1(a114)) | (~c2_1(a114)))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(2048,plain,
% 2.22/1.73 ((hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141))) <=> (hskp12 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c1_1(a114)) | (~c2_1(a114)))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(2049,plain,
% 2.22/1.73 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c1_1(a114)) | (~c2_1(a114))))),
% 2.22/1.73 inference(monotonicity,[status(thm)],[2048])).
% 2.22/1.73 tff(2050,plain,
% 2.22/1.73 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c1_1(a114)) | (~c2_1(a114)))),
% 2.22/1.73 inference(transitivity,[status(thm)],[2049, 2047])).
% 2.22/1.73 tff(2051,plain,
% 2.22/1.73 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))),
% 2.22/1.73 inference(quant_inst,[status(thm)],[])).
% 2.22/1.73 tff(2052,plain,
% 2.22/1.73 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | (~c1_1(a114)) | (~c2_1(a114))),
% 2.22/1.73 inference(modus_ponens,[status(thm)],[2051, 2050])).
% 2.22/1.73 tff(2053,plain,
% 2.22/1.73 (hskp12),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[2052, 160, 818, 817, 2046, 2045, 2044, 2027, 2017])).
% 2.22/1.73 tff(2054,plain,
% 2.22/1.73 (~c2_1(a113)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1702, 2053])).
% 2.22/1.73 tff(2055,plain,
% 2.22/1.73 (~c0_1(a113)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[1736, 2053])).
% 2.22/1.73 tff(2056,plain,
% 2.22/1.73 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(2057,plain,
% 2.22/1.73 ((hskp19 | (~ndr1_0) | c3_1(a135) | c2_1(a135) | (~c1_1(a135))) <=> (hskp19 | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(2058,plain,
% 2.22/1.73 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a135) | c2_1(a135) | (~c1_1(a135)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135))))),
% 2.22/1.73 inference(monotonicity,[status(thm)],[2057])).
% 2.22/1.73 tff(2059,plain,
% 2.22/1.73 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a135) | c2_1(a135) | (~c1_1(a135)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135)))),
% 2.22/1.73 inference(transitivity,[status(thm)],[2058, 2056])).
% 2.22/1.73 tff(2060,plain,
% 2.22/1.73 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a135) | c2_1(a135) | (~c1_1(a135)))),
% 2.22/1.73 inference(quant_inst,[status(thm)],[])).
% 2.22/1.73 tff(2061,plain,
% 2.22/1.73 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c1_1(a135))),
% 2.22/1.73 inference(modus_ponens,[status(thm)],[2060, 2059])).
% 2.22/1.73 tff(2062,plain,
% 2.22/1.73 (hskp19 | c3_1(a135) | (~c1_1(a135))),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[2061, 160, 463, 11])).
% 2.22/1.73 tff(2063,plain,
% 2.22/1.73 (~c1_1(a135)),
% 2.22/1.73 inference(unit_resolution,[status(thm)],[2062, 2035, 2006])).
% 2.22/1.73 tff(2064,plain,
% 2.22/1.73 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | c0_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c0_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(2065,plain,
% 2.22/1.73 ((hskp5 | (~ndr1_0) | c3_1(a135) | c1_1(a135) | c0_1(a135)) <=> (hskp5 | c0_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135))),
% 2.22/1.73 inference(rewrite,[status(thm)],[])).
% 2.22/1.73 tff(2066,plain,
% 2.22/1.73 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a135) | c1_1(a135) | c0_1(a135))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | c0_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135)))),
% 2.22/1.73 inference(monotonicity,[status(thm)],[2065])).
% 2.22/1.73 tff(2067,plain,
% 2.22/1.73 (((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a135) | c1_1(a135) | c0_1(a135))) <=> ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c0_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135))),
% 2.22/1.73 inference(transitivity,[status(thm)],[2066, 2064])).
% 2.22/1.73 tff(2068,plain,
% 2.22/1.73 ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp5 | (~ndr1_0) | c3_1(a135) | c1_1(a135) | c0_1(a135))),
% 2.22/1.74 inference(quant_inst,[status(thm)],[])).
% 2.22/1.74 tff(2069,plain,
% 2.22/1.74 ((~![U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp5 | c0_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135)),
% 2.22/1.74 inference(modus_ponens,[status(thm)],[2068, 2067])).
% 2.22/1.74 tff(2070,plain,
% 2.22/1.74 (hskp5),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2069, 160, 2005, 2035, 227, 2063])).
% 2.22/1.74 tff(2071,plain,
% 2.22/1.74 (c1_1(a106)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[257, 2070])).
% 2.22/1.74 tff(2072,plain,
% 2.22/1.74 (c0_1(a106)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[337, 2070])).
% 2.22/1.74 tff(2073,plain,
% 2.22/1.74 (c3_1(a113)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1713, 2053])).
% 2.22/1.74 tff(2074,plain,
% 2.22/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a113)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a113)) | c0_1(a163))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2075,plain,
% 2.22/1.74 (((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a113)) | c0_1(a163))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2076,plain,
% 2.22/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a113)) | c0_1(a163)))),
% 2.22/1.74 inference(monotonicity,[status(thm)],[2075])).
% 2.22/1.74 tff(2077,plain,
% 2.22/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a113)) | c0_1(a163))),
% 2.22/1.74 inference(transitivity,[status(thm)],[2076, 2074])).
% 2.22/1.74 tff(2078,plain,
% 2.22/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 2.22/1.74 inference(quant_inst,[status(thm)],[])).
% 2.22/1.74 tff(2079,plain,
% 2.22/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a113)) | c0_1(a163)),
% 2.22/1.74 inference(modus_ponens,[status(thm)],[2078, 2077])).
% 2.22/1.74 tff(2080,plain,
% 2.22/1.74 (~c3_1(a106)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2079, 160, 2073, 2072, 2071, 52, 1977, 2055, 2054, 804, 2015])).
% 2.22/1.74 tff(2081,plain,
% 2.22/1.74 (~c2_1(a106)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[976, 2070])).
% 2.22/1.74 tff(2082,plain,
% 2.22/1.74 ($false),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[242, 160, 2006, 2071, 2081, 11, 2080])).
% 2.22/1.74 tff(2083,plain,(c0_1(a135) | c1_1(a163) | (~c0_1(a141)) | (~c1_1(a141)) | (~c3_1(a141)) | c2_1(a135)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.74 tff(2084,plain,
% 2.22/1.74 (c0_1(a135)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2083, 463, 818, 817, 851, 52])).
% 2.22/1.74 tff(2085,plain,
% 2.22/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)) | c0_1(a163))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2086,plain,
% 2.22/1.74 (((~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c1_1(a135) | (~c0_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)) | c0_1(a163))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2087,plain,
% 2.22/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c1_1(a135) | (~c0_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)) | c0_1(a163)))),
% 2.22/1.74 inference(monotonicity,[status(thm)],[2086])).
% 2.22/1.74 tff(2088,plain,
% 2.22/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c1_1(a135) | (~c0_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)) | c0_1(a163))),
% 2.22/1.74 inference(transitivity,[status(thm)],[2087, 2085])).
% 2.22/1.74 tff(2089,plain,
% 2.22/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)) | c2_1(a135) | c1_1(a135) | (~c0_1(a135)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 2.22/1.74 inference(quant_inst,[status(thm)],[])).
% 2.22/1.74 tff(2090,plain,
% 2.22/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c2_1(a135) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a135) | (~c0_1(a135)) | c0_1(a163)),
% 2.22/1.74 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 2.22/1.74 tff(2091,plain,
% 2.22/1.74 (c1_1(a135)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2090, 160, 818, 817, 2084, 52, 1977, 463, 868, 245, 2004])).
% 2.22/1.74 tff(2092,plain,
% 2.22/1.74 (hskp10 | c0_1(a163)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1514, 160, 818, 817, 851, 52, 1317, 1400])).
% 2.22/1.74 tff(2093,plain,
% 2.22/1.74 (hskp10),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2092, 245])).
% 2.22/1.74 tff(2094,plain,
% 2.22/1.74 (~c3_1(a111)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1334, 2093])).
% 2.22/1.74 tff(2095,plain,
% 2.22/1.74 (~c2_1(a111)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1340, 2093])).
% 2.22/1.74 tff(2096,plain,
% 2.22/1.74 (~c0_1(a111)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1346, 2093])).
% 2.22/1.74 tff(2097,plain,
% 2.22/1.74 (hskp13),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1353, 160, 818, 817, 851, 2096, 2095, 2094, 1328])).
% 2.22/1.74 tff(2098,plain,
% 2.22/1.74 (~c3_1(a114)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[629, 2097])).
% 2.22/1.74 tff(2099,plain,
% 2.22/1.74 (c2_1(a114)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[640, 2097])).
% 2.22/1.74 tff(2100,plain,
% 2.22/1.74 (c1_1(a114)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[651, 2097])).
% 2.22/1.74 tff(2101,plain,
% 2.22/1.74 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c1_1(a135)) | (~c0_1(a135)))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2102,plain,
% 2.22/1.74 ((hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135))) <=> (hskp12 | c2_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c1_1(a135)) | (~c0_1(a135)))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2103,plain,
% 2.22/1.74 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c1_1(a135)) | (~c0_1(a135))))),
% 2.22/1.74 inference(monotonicity,[status(thm)],[2102])).
% 2.22/1.74 tff(2104,plain,
% 2.22/1.74 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c1_1(a135)) | (~c0_1(a135)))),
% 2.22/1.74 inference(transitivity,[status(thm)],[2103, 2101])).
% 2.22/1.74 tff(2105,plain,
% 2.22/1.74 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | (~c1_1(a135)) | (~c0_1(a135)))),
% 2.22/1.74 inference(quant_inst,[status(thm)],[])).
% 2.22/1.74 tff(2106,plain,
% 2.22/1.74 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c1_1(a135)) | (~c0_1(a135))),
% 2.22/1.74 inference(modus_ponens,[status(thm)],[2105, 2104])).
% 2.22/1.74 tff(2107,plain,
% 2.22/1.74 (hskp12),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2106, 160, 2084, 2100, 2099, 463, 2098, 2027, 2091])).
% 2.22/1.74 tff(2108,plain,
% 2.22/1.74 (~c2_1(a113)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1702, 2107])).
% 2.22/1.74 tff(2109,plain,
% 2.22/1.74 (~c0_1(a113)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1736, 2107])).
% 2.22/1.74 tff(2110,plain,
% 2.22/1.74 (c3_1(a113)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1713, 2107])).
% 2.22/1.74 tff(2111,plain,
% 2.22/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a113)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a113)) | c0_1(a163))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2112,plain,
% 2.22/1.74 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a113)) | c0_1(a163))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2113,plain,
% 2.22/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a113)) | c0_1(a163)))),
% 2.22/1.74 inference(monotonicity,[status(thm)],[2112])).
% 2.22/1.74 tff(2114,plain,
% 2.22/1.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a113)) | c0_1(a163))),
% 2.22/1.74 inference(transitivity,[status(thm)],[2113, 2111])).
% 2.22/1.74 tff(2115,plain,
% 2.22/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 2.22/1.74 inference(quant_inst,[status(thm)],[])).
% 2.22/1.74 tff(2116,plain,
% 2.22/1.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a113)) | c0_1(a163)),
% 2.22/1.74 inference(modus_ponens,[status(thm)],[2115, 2114])).
% 2.22/1.74 tff(2117,plain,
% 2.22/1.74 ($false),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2116, 160, 818, 817, 851, 2110, 52, 1977, 2109, 2108, 804, 245])).
% 2.22/1.74 tff(2118,plain,(c0_1(a163) | (~c0_1(a141)) | (~c1_1(a141)) | (~c3_1(a141)) | c1_1(a163) | c2_1(a135)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.74 tff(2119,plain,
% 2.22/1.74 (c2_1(a135)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2118, 1992, 75, 64, 52, 86])).
% 2.22/1.74 tff(2120,plain,
% 2.22/1.74 (~hskp19),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[438, 2119])).
% 2.22/1.74 tff(2121,plain,
% 2.22/1.74 (~c1_1(a111)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1425, 160, 2120, 1996, 1994, 11])).
% 2.22/1.74 tff(2122,plain,
% 2.22/1.74 ((~c2_1(a141)) | c0_1(a163)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2002, 160, 86, 75, 64, 52, 1977, 96])).
% 2.22/1.74 tff(2123,plain,
% 2.22/1.74 (~c2_1(a141)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2122, 1992])).
% 2.22/1.74 tff(2124,plain,
% 2.22/1.74 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a111))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2125,plain,
% 2.22/1.74 ((hskp2 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c3_1(a141)) | c2_1(a111) | c1_1(a111) | c0_1(a111)) <=> (hskp2 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a111))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2126,plain,
% 2.22/1.74 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c3_1(a141)) | c2_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a111)))),
% 2.22/1.74 inference(monotonicity,[status(thm)],[2125])).
% 2.22/1.74 tff(2127,plain,
% 2.22/1.74 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c3_1(a141)) | c2_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a111))),
% 2.22/1.74 inference(transitivity,[status(thm)],[2126, 2124])).
% 2.22/1.74 tff(2128,plain,
% 2.22/1.74 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a141) | (~c1_1(a141)) | (~c3_1(a141)) | c2_1(a111) | c1_1(a111) | c0_1(a111))),
% 2.22/1.74 inference(quant_inst,[status(thm)],[])).
% 2.22/1.74 tff(2129,plain,
% 2.22/1.74 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | (~c3_1(a141)) | c2_1(a141) | (~c1_1(a141)) | c1_1(a111)),
% 2.22/1.74 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 2.22/1.74 tff(2130,plain,
% 2.22/1.74 (hskp2 | c1_1(a111)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2129, 160, 75, 64, 1995, 1996, 270, 2123])).
% 2.22/1.74 tff(2131,plain,
% 2.22/1.74 (hskp2),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2130, 2121])).
% 2.22/1.74 tff(2132,plain,
% 2.22/1.74 (~c3_1(a103)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[419, 2131])).
% 2.22/1.74 tff(2133,plain,
% 2.22/1.74 (hskp5 | c1_1(a111)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1787, 160, 1995, 1994, 227])).
% 2.22/1.74 tff(2134,plain,
% 2.22/1.74 (hskp5),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2133, 2121])).
% 2.22/1.74 tff(2135,plain,
% 2.22/1.74 (~c2_1(a106)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[976, 2134])).
% 2.22/1.74 tff(2136,plain,
% 2.22/1.74 (hskp19 | c2_1(a111) | (~c1_1(a111))),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1425, 160, 1476, 11])).
% 2.22/1.74 tff(2137,plain,
% 2.22/1.74 (~c1_1(a111)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2136, 1, 1868])).
% 2.22/1.74 tff(2138,plain,
% 2.22/1.74 (hskp5 | c0_1(a111) | c1_1(a111)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1787, 160, 1476, 227])).
% 2.22/1.74 tff(2139,plain,
% 2.22/1.74 (hskp5),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2138, 2137, 1477])).
% 2.22/1.74 tff(2140,plain,
% 2.22/1.74 (c1_1(a106)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[257, 2139])).
% 2.22/1.74 tff(2141,plain,
% 2.22/1.74 (c0_1(a106)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[337, 2139])).
% 2.22/1.74 tff(2142,assumption,(~hskp12), introduced(assumption)).
% 2.22/1.74 tff(2143,plain,
% 2.22/1.74 (c3_1(a106)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[259, 2140, 1])).
% 2.22/1.74 tff(2144,plain,
% 2.22/1.74 (hskp2 | c0_1(a111) | (~c3_1(a106)) | (~c1_1(a106)) | c1_1(a111)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1437, 160, 1868, 109, 270])).
% 2.22/1.74 tff(2145,plain,
% 2.22/1.74 (hskp2),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2144, 2143, 1477, 2140, 2137])).
% 2.22/1.74 tff(2146,plain,
% 2.22/1.74 (c1_1(a103)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[288, 2145])).
% 2.22/1.74 tff(2147,plain,
% 2.22/1.74 (c2_1(a103)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[297, 2146, 1])).
% 2.22/1.74 tff(2148,plain,
% 2.22/1.74 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a106) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a106) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106)))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2149,plain,
% 2.22/1.74 ((hskp12 | (~ndr1_0) | c3_1(a103) | (~c1_1(a103)) | (~c2_1(a103)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106))) <=> (hskp12 | c2_1(a106) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106)))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2150,plain,
% 2.22/1.74 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a103) | (~c1_1(a103)) | (~c2_1(a103)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c2_1(a106) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106))))),
% 2.22/1.74 inference(monotonicity,[status(thm)],[2149])).
% 2.22/1.74 tff(2151,plain,
% 2.22/1.74 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a103) | (~c1_1(a103)) | (~c2_1(a103)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a106) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106)))),
% 2.22/1.74 inference(transitivity,[status(thm)],[2150, 2148])).
% 2.22/1.74 tff(2152,plain,
% 2.22/1.74 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a103) | (~c1_1(a103)) | (~c2_1(a103)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))),
% 2.22/1.74 inference(quant_inst,[status(thm)],[])).
% 2.22/1.74 tff(2153,plain,
% 2.22/1.74 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c2_1(a106) | c3_1(a103) | (~ndr1_0) | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106))),
% 2.22/1.74 inference(modus_ponens,[status(thm)],[2152, 2151])).
% 2.22/1.74 tff(2154,plain,
% 2.22/1.74 (hskp12 | (~c2_1(a103)) | (~c1_1(a103)) | (~c0_1(a106)) | (~c1_1(a106))),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2153, 160, 109, 290, 2027])).
% 2.22/1.74 tff(2155,plain,
% 2.22/1.74 ($false),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2154, 2147, 2146, 2142, 2141, 2140])).
% 2.22/1.74 tff(2156,plain,(hskp19 | hskp12 | c2_1(a106) | c3_1(a103) | c0_1(a111) | c2_1(a111) | c3_1(a111)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.74 tff(2157,plain,
% 2.22/1.74 (hskp12),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[2156, 2135, 2120, 2132, 1996, 1995, 1994])).
% 2.22/1.74 tff(2158,plain,
% 2.22/1.74 (~c2_1(a113)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1702, 2157])).
% 2.22/1.74 tff(2159,plain,
% 2.22/1.74 (~c0_1(a113)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1736, 2157])).
% 2.22/1.74 tff(2160,plain,
% 2.22/1.74 (c3_1(a113)),
% 2.22/1.74 inference(unit_resolution,[status(thm)],[1713, 2157])).
% 2.22/1.74 tff(2161,plain,
% 2.22/1.74 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 2.22/1.74 inference(bind,[status(th)],[])).
% 2.22/1.74 tff(2162,plain,
% 2.22/1.74 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.22/1.74 inference(quant_intro,[status(thm)],[2161])).
% 2.22/1.74 tff(2163,plain,
% 2.22/1.74 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2164,plain,
% 2.22/1.74 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp16) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp16))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 2.22/1.74 inference(bind,[status(th)],[])).
% 2.22/1.74 tff(2165,plain,
% 2.22/1.74 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.22/1.74 inference(quant_intro,[status(thm)],[2164])).
% 2.22/1.74 tff(2166,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c2_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 2.22/1.74 tff(2167,plain,
% 2.22/1.74 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.22/1.74 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 2.22/1.74 tff(2168,plain,
% 2.22/1.74 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.22/1.74 inference(modus_ponens,[status(thm)],[2167, 2163])).
% 2.22/1.74 tff(2169,plain,(
% 2.22/1.74 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.22/1.74 inference(skolemize,[status(sab)],[2168])).
% 2.22/1.74 tff(2170,plain,
% 2.22/1.74 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 2.22/1.74 inference(modus_ponens,[status(thm)],[2169, 2162])).
% 2.22/1.74 tff(2171,plain,
% 2.22/1.74 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp16 | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp16 | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | c0_1(a163))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2172,plain,
% 2.22/1.74 ((hskp16 | (~ndr1_0) | c0_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a111) | c1_1(a111) | c3_1(a111)) <=> (hskp16 | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | c0_1(a163))),
% 2.22/1.74 inference(rewrite,[status(thm)],[])).
% 2.22/1.74 tff(2173,plain,
% 2.22/1.74 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp16 | (~ndr1_0) | c0_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a111) | c1_1(a111) | c3_1(a111))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp16 | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | c0_1(a163)))),
% 2.22/1.74 inference(monotonicity,[status(thm)],[2172])).
% 2.22/1.75 tff(2174,plain,
% 2.22/1.75 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp16 | (~ndr1_0) | c0_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a111) | c1_1(a111) | c3_1(a111))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp16 | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | c0_1(a163))),
% 2.22/1.75 inference(transitivity,[status(thm)],[2173, 2171])).
% 2.22/1.75 tff(2175,plain,
% 2.22/1.75 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp16 | (~ndr1_0) | c0_1(a163) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a111) | c1_1(a111) | c3_1(a111))),
% 2.22/1.75 inference(quant_inst,[status(thm)],[])).
% 2.22/1.75 tff(2176,plain,
% 2.22/1.75 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp16 | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | c0_1(a163)),
% 2.22/1.75 inference(modus_ponens,[status(thm)],[2175, 2174])).
% 2.22/1.75 tff(2177,plain,
% 2.22/1.75 (hskp16 | c1_1(a111)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2176, 160, 1317, 1977, 1996, 1994, 2170, 1992])).
% 2.22/1.75 tff(2178,plain,
% 2.22/1.75 (hskp16),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2177, 2121])).
% 2.22/1.75 tff(2179,plain,
% 2.22/1.75 (c3_1(a126)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[787, 2178])).
% 2.22/1.75 tff(2180,plain,
% 2.22/1.75 (c1_1(a126)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[776, 2178])).
% 2.22/1.75 tff(2181,plain,
% 2.22/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a113)) | (~c3_1(a126)) | (~c0_1(a126)) | (~c1_1(a126)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a113)) | (~c3_1(a126)) | (~c0_1(a126)) | (~c1_1(a126)) | c0_1(a163))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2182,plain,
% 2.22/1.75 (((~ndr1_0) | (~c1_1(a126)) | (~c3_1(a126)) | (~c0_1(a126)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a113)) | (~c3_1(a126)) | (~c0_1(a126)) | (~c1_1(a126)) | c0_1(a163))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2183,plain,
% 2.22/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a126)) | (~c3_1(a126)) | (~c0_1(a126)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a113)) | (~c3_1(a126)) | (~c0_1(a126)) | (~c1_1(a126)) | c0_1(a163)))),
% 2.22/1.75 inference(monotonicity,[status(thm)],[2182])).
% 2.22/1.75 tff(2184,plain,
% 2.22/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a126)) | (~c3_1(a126)) | (~c0_1(a126)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a113)) | (~c3_1(a126)) | (~c0_1(a126)) | (~c1_1(a126)) | c0_1(a163))),
% 2.22/1.75 inference(transitivity,[status(thm)],[2183, 2181])).
% 2.22/1.75 tff(2185,plain,
% 2.22/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a126)) | (~c3_1(a126)) | (~c0_1(a126)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 2.22/1.75 inference(quant_inst,[status(thm)],[])).
% 2.22/1.75 tff(2186,plain,
% 2.22/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c0_1(a113) | c2_1(a113) | (~ndr1_0) | (~c3_1(a113)) | (~c3_1(a126)) | (~c0_1(a126)) | (~c1_1(a126)) | c0_1(a163)),
% 2.22/1.75 inference(modus_ponens,[status(thm)],[2185, 2184])).
% 2.22/1.75 tff(2187,plain,
% 2.22/1.75 (~c0_1(a126)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2186, 160, 2180, 2179, 2160, 52, 1977, 2159, 2158, 804, 1992])).
% 2.22/1.75 tff(2188,plain,
% 2.22/1.75 (~c2_1(a126)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[793, 2178])).
% 2.22/1.75 tff(2189,plain,
% 2.22/1.75 (c1_1(a106)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[257, 2134])).
% 2.22/1.75 tff(2190,plain,
% 2.22/1.75 (c0_1(a106)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[337, 2134])).
% 2.22/1.75 tff(2191,plain,
% 2.22/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c2_1(a126) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a126)) | c0_1(a126) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c2_1(a126) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a126)) | c0_1(a126) | c0_1(a163))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2192,plain,
% 2.22/1.75 (((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | c2_1(a126) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a126)) | c0_1(a126) | c0_1(a163))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2193,plain,
% 2.22/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | c2_1(a126) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a126)) | c0_1(a126) | c0_1(a163)))),
% 2.22/1.75 inference(monotonicity,[status(thm)],[2192])).
% 2.22/1.75 tff(2194,plain,
% 2.22/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c2_1(a126) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a126)) | c0_1(a126) | c0_1(a163))),
% 2.22/1.75 inference(transitivity,[status(thm)],[2193, 2191])).
% 2.22/1.75 tff(2195,plain,
% 2.22/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a106)) | (~c3_1(a106)) | (~c0_1(a106)) | c2_1(a126) | c0_1(a126) | (~c3_1(a126)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 2.22/1.75 inference(quant_inst,[status(thm)],[])).
% 2.22/1.75 tff(2196,plain,
% 2.22/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | c2_1(a126) | (~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | (~c3_1(a126)) | c0_1(a126) | c0_1(a163)),
% 2.22/1.75 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 2.22/1.75 tff(2197,plain,
% 2.22/1.75 (~c3_1(a106)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2196, 160, 2179, 2190, 2189, 52, 1977, 2188, 804, 1992, 2187])).
% 2.22/1.75 tff(2198,plain,
% 2.22/1.75 ($false),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[242, 160, 2120, 2189, 2135, 11, 2197])).
% 2.22/1.75 tff(2199,plain,((~hskp31) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.75 tff(2200,plain,
% 2.22/1.75 (~hskp31),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2199, 52])).
% 2.22/1.75 tff(2201,assumption,(c1_1(a131)), introduced(assumption)).
% 2.22/1.75 tff(2202,plain,
% 2.22/1.75 (hskp30),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[158, 2200, 1318])).
% 2.22/1.75 tff(2203,plain,
% 2.22/1.75 (c3_1(a131)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1001, 2202])).
% 2.22/1.75 tff(2204,plain,
% 2.22/1.75 (c2_1(a131)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1012, 2202])).
% 2.22/1.75 tff(2205,plain,
% 2.22/1.75 (c0_1(a131)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1023, 2202])).
% 2.22/1.75 tff(2206,plain,
% 2.22/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2207,plain,
% 2.22/1.75 (((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163))) <=> (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2208,plain,
% 2.22/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163)))),
% 2.22/1.75 inference(monotonicity,[status(thm)],[2207])).
% 2.22/1.75 tff(2209,plain,
% 2.22/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 2.22/1.75 inference(transitivity,[status(thm)],[2208, 2206])).
% 2.22/1.75 tff(2210,plain,
% 2.22/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a163) | c0_1(a163) | (~c3_1(a163)))),
% 2.22/1.75 inference(quant_inst,[status(thm)],[])).
% 2.22/1.75 tff(2211,plain,
% 2.22/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163)),
% 2.22/1.75 inference(modus_ponens,[status(thm)],[2210, 2209])).
% 2.22/1.75 tff(2212,plain,
% 2.22/1.75 ($false),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2211, 160, 2205, 2204, 2203, 52, 1977, 96, 245, 2201])).
% 2.22/1.75 tff(2213,plain,((~c1_1(a131)) | c1_1(a163) | c0_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.75 tff(2214,plain,
% 2.22/1.75 (~c1_1(a131)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2213, 245, 52])).
% 2.22/1.75 tff(2215,plain,
% 2.22/1.75 (hskp28 | c1_1(a131)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1576, 2200, 160, 2205, 2203, 596])).
% 2.22/1.75 tff(2216,plain,
% 2.22/1.75 (hskp28),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2215, 2214])).
% 2.22/1.75 tff(2217,plain,
% 2.22/1.75 (c3_1(a118)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[524, 2216])).
% 2.22/1.75 tff(2218,plain,
% 2.22/1.75 (c2_1(a118)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[535, 2216])).
% 2.22/1.75 tff(2219,plain,
% 2.22/1.75 ($false),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1665, 536, 547, 1165, 1164, 1166, 34, 525])).
% 2.22/1.75 tff(2220,plain,((~hskp28) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~hskp4)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.75 tff(2221,plain,
% 2.22/1.75 (~hskp4),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2220, 2216, 2203, 2205, 2204])).
% 2.22/1.75 tff(2222,plain,
% 2.22/1.75 (hskp19),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1079, 2202])).
% 2.22/1.75 tff(2223,plain,
% 2.22/1.75 (~c2_1(a135)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[438, 2222])).
% 2.22/1.75 tff(2224,plain,
% 2.22/1.75 (c0_1(a135)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[459, 2222])).
% 2.22/1.75 tff(2225,plain,
% 2.22/1.75 (c1_1(a118)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[546, 2216])).
% 2.22/1.75 tff(2226,plain,
% 2.22/1.75 (~c3_1(a135)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[432, 2222])).
% 2.22/1.75 tff(2227,plain,
% 2.22/1.75 (hskp10 | hskp4 | c1_1(a131)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1854, 160, 2205, 2203, 1848])).
% 2.22/1.75 tff(2228,plain,
% 2.22/1.75 (hskp10),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2227, 2221, 2214])).
% 2.22/1.75 tff(2229,plain,
% 2.22/1.75 (~c0_1(a111)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1346, 2228])).
% 2.22/1.75 tff(2230,plain,
% 2.22/1.75 (~c3_1(a111)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1334, 2228])).
% 2.22/1.75 tff(2231,plain,
% 2.22/1.75 ($false),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1970, 2230, 2229, 2203, 52, 2226, 245, 2225, 2205, 2224, 2223, 2221, 2218, 2217])).
% 2.22/1.75 tff(2232,plain,(c0_1(a163) | c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.75 tff(2233,plain,
% 2.22/1.75 (c0_1(a163)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2232, 52])).
% 2.22/1.75 tff(2234,plain,
% 2.22/1.75 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2235,plain,
% 2.22/1.75 ((hskp31 | hskp28 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163))) <=> (hskp31 | hskp28 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2236,plain,
% 2.22/1.75 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))))),
% 2.22/1.75 inference(monotonicity,[status(thm)],[2235])).
% 2.22/1.75 tff(2237,plain,
% 2.22/1.75 (((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.75 inference(transitivity,[status(thm)],[2236, 2234])).
% 2.22/1.75 tff(2238,plain,
% 2.22/1.75 ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp31 | hskp28 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))),
% 2.22/1.75 inference(quant_inst,[status(thm)],[])).
% 2.22/1.75 tff(2239,plain,
% 2.22/1.75 ((~![U: $i] : (hskp31 | hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp31 | hskp28 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))),
% 2.22/1.75 inference(modus_ponens,[status(thm)],[2238, 2237])).
% 2.22/1.75 tff(2240,plain,
% 2.22/1.75 (hskp31 | hskp28 | (~c3_1(a163)) | (~c0_1(a163))),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2239, 160, 52, 596])).
% 2.22/1.75 tff(2241,plain,
% 2.22/1.75 (hskp28),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2240, 2233, 1977, 2200])).
% 2.22/1.75 tff(2242,plain,
% 2.22/1.75 (c3_1(a118)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[524, 2241])).
% 2.22/1.75 tff(2243,plain,
% 2.22/1.75 (c2_1(a118)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[535, 2241])).
% 2.22/1.75 tff(2244,plain,
% 2.22/1.75 (~hskp4),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2220, 2241, 2203, 2205, 2204])).
% 2.22/1.75 tff(2245,plain,
% 2.22/1.75 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2246,plain,
% 2.22/1.75 ((hskp10 | hskp4 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163))) <=> (hskp10 | hskp4 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2247,plain,
% 2.22/1.75 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))))),
% 2.22/1.75 inference(monotonicity,[status(thm)],[2246])).
% 2.22/1.75 tff(2248,plain,
% 2.22/1.75 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163)))),
% 2.22/1.75 inference(transitivity,[status(thm)],[2247, 2245])).
% 2.22/1.75 tff(2249,plain,
% 2.22/1.75 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a163) | (~c3_1(a163)) | (~c0_1(a163)))),
% 2.22/1.75 inference(quant_inst,[status(thm)],[])).
% 2.22/1.75 tff(2250,plain,
% 2.22/1.75 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | c1_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a163))),
% 2.22/1.75 inference(modus_ponens,[status(thm)],[2249, 2248])).
% 2.22/1.75 tff(2251,plain,
% 2.22/1.75 (hskp10 | hskp4 | (~c3_1(a163)) | (~c0_1(a163))),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2250, 160, 52, 1848])).
% 2.22/1.75 tff(2252,plain,
% 2.22/1.75 (hskp10),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2251, 2244, 1977, 2233])).
% 2.22/1.75 tff(2253,plain,
% 2.22/1.75 (~c3_1(a111)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1334, 2252])).
% 2.22/1.75 tff(2254,plain,
% 2.22/1.75 (c1_1(a118)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[546, 2241])).
% 2.22/1.75 tff(2255,plain,
% 2.22/1.75 (~c0_1(a111)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1346, 2252])).
% 2.22/1.75 tff(2256,plain,
% 2.22/1.75 (~c2_1(a111)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1340, 2252])).
% 2.22/1.75 tff(2257,plain,
% 2.22/1.75 ($false),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1965, 2256, 2255, 2226, 2254, 2244, 2224, 2223, 2253, 2243, 2242])).
% 2.22/1.75 tff(2258,plain,(c1_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.22/1.75 tff(2259,plain,
% 2.22/1.75 (~hskp24),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1094, 2258])).
% 2.22/1.75 tff(2260,plain,
% 2.22/1.75 (hskp30),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[158, 23, 2259])).
% 2.22/1.75 tff(2261,plain,
% 2.22/1.75 (c2_1(a131)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1012, 2260])).
% 2.22/1.75 tff(2262,plain,
% 2.22/1.75 (c0_1(a131)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1023, 2260])).
% 2.22/1.75 tff(2263,plain,
% 2.22/1.75 (c3_1(a131)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1001, 2260])).
% 2.22/1.75 tff(2264,plain,
% 2.22/1.75 (~hskp28),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2220, 34, 2263, 2262, 2261])).
% 2.22/1.75 tff(2265,plain,
% 2.22/1.75 (~hskp15),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[608, 2264, 23])).
% 2.22/1.75 tff(2266,plain,
% 2.22/1.75 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2267,plain,
% 2.22/1.75 ((hskp28 | hskp15 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105))) <=> (hskp28 | hskp15 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2268,plain,
% 2.22/1.75 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105))))),
% 2.22/1.75 inference(monotonicity,[status(thm)],[2267])).
% 2.22/1.75 tff(2269,plain,
% 2.22/1.75 (((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105)))) <=> ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105)))),
% 2.22/1.75 inference(transitivity,[status(thm)],[2268, 2266])).
% 2.22/1.75 tff(2270,plain,
% 2.22/1.75 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp15 | (~ndr1_0) | c1_1(a105) | (~c3_1(a105)) | (~c0_1(a105)))),
% 2.22/1.75 inference(quant_inst,[status(thm)],[])).
% 2.22/1.75 tff(2271,plain,
% 2.22/1.75 ((~![U: $i] : (hskp28 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp15 | c1_1(a105) | (~ndr1_0) | (~c3_1(a105)) | (~c0_1(a105))),
% 2.22/1.75 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 2.22/1.75 tff(2272,plain,
% 2.22/1.75 (~c0_1(a105)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2271, 160, 2264, 2265, 51, 40, 33])).
% 2.22/1.75 tff(2273,plain,
% 2.22/1.75 (hskp28 | c1_1(a131)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1576, 23, 160, 2262, 2263, 596])).
% 2.22/1.75 tff(2274,plain,
% 2.22/1.75 (c1_1(a131)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2273, 2264])).
% 2.22/1.75 tff(2275,plain,
% 2.22/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a105)) | c0_1(a105))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a105)) | c0_1(a105))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2276,plain,
% 2.22/1.75 (((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105))) <=> (c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a105)) | c0_1(a105))),
% 2.22/1.75 inference(rewrite,[status(thm)],[])).
% 2.22/1.75 tff(2277,plain,
% 2.22/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a105)) | c0_1(a105)))),
% 2.22/1.75 inference(monotonicity,[status(thm)],[2276])).
% 2.22/1.75 tff(2278,plain,
% 2.22/1.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a105)) | c0_1(a105))),
% 2.22/1.75 inference(transitivity,[status(thm)],[2277, 2275])).
% 2.22/1.75 tff(2279,plain,
% 2.22/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | (~c2_1(a131)) | c1_1(a105) | c0_1(a105) | (~c3_1(a105)))),
% 2.22/1.75 inference(quant_inst,[status(thm)],[])).
% 2.22/1.75 tff(2280,plain,
% 2.22/1.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a105) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | (~c3_1(a105)) | c0_1(a105)),
% 2.22/1.75 inference(modus_ponens,[status(thm)],[2279, 2278])).
% 2.22/1.75 tff(2281,plain,
% 2.22/1.75 ($false),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2280, 160, 2262, 2261, 2263, 51, 40, 96, 2274, 2272])).
% 2.22/1.75 tff(2282,plain,((~hskp4) | hskp31), inference(lemma,lemma(discharge,[]))).
% 2.22/1.75 tff(2283,plain,
% 2.22/1.75 (~hskp4),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[2282, 23])).
% 2.22/1.75 tff(2284,plain,
% 2.22/1.75 (c1_1(a131)),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1854, 160, 22, 2283, 2262, 2263, 1848])).
% 2.22/1.75 tff(2285,plain,
% 2.22/1.75 (hskp19),
% 2.22/1.75 inference(unit_resolution,[status(thm)],[1079, 2260])).
% 2.22/1.76 tff(2286,plain,
% 2.22/1.76 (~c3_1(a135)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[432, 2285])).
% 2.22/1.76 tff(2287,plain,
% 2.22/1.76 (~c2_1(a135)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[438, 2285])).
% 2.22/1.76 tff(2288,plain,
% 2.22/1.76 (c0_1(a135)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[459, 2285])).
% 2.22/1.76 tff(2289,plain,
% 2.22/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a135) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a135) | (~c0_1(a135)))),
% 2.22/1.76 inference(rewrite,[status(thm)],[])).
% 2.22/1.76 tff(2290,plain,
% 2.22/1.76 (((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135)) <=> (c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a135) | (~c0_1(a135)))),
% 2.22/1.76 inference(rewrite,[status(thm)],[])).
% 2.22/1.76 tff(2291,plain,
% 2.22/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a135) | (~c0_1(a135))))),
% 2.22/1.76 inference(monotonicity,[status(thm)],[2290])).
% 2.22/1.76 tff(2292,plain,
% 2.22/1.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a135) | (~c0_1(a135)))),
% 2.22/1.76 inference(transitivity,[status(thm)],[2291, 2289])).
% 2.22/1.76 tff(2293,plain,
% 2.22/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))),
% 2.22/1.76 inference(quant_inst,[status(thm)],[])).
% 2.22/1.76 tff(2294,plain,
% 2.22/1.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a135) | (~c0_1(a135))),
% 2.22/1.76 inference(modus_ponens,[status(thm)],[2293, 2292])).
% 2.22/1.76 tff(2295,plain,
% 2.22/1.76 (c1_1(a135)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[2294, 160, 2261, 2263, 2288, 2287, 2286, 108, 2284])).
% 2.22/1.76 tff(2296,plain,
% 2.22/1.76 (hskp1 | (~c1_1(a135))),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1247, 160, 2259, 2288, 2287, 21])).
% 2.22/1.76 tff(2297,plain,
% 2.22/1.76 (hskp1),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[2296, 2295])).
% 2.22/1.76 tff(2298,plain,
% 2.22/1.76 (~c1_1(a102)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1254, 2297])).
% 2.22/1.76 tff(2299,plain,
% 2.22/1.76 (c2_1(a102)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1307, 2297])).
% 2.22/1.76 tff(2300,plain,
% 2.22/1.76 (~c0_1(a102)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1260, 2297])).
% 2.22/1.76 tff(2301,assumption,(~c1_1(a102)), introduced(assumption)).
% 2.22/1.76 tff(2302,assumption,(~c0_1(a102)), introduced(assumption)).
% 2.22/1.76 tff(2303,assumption,(c2_1(a102)), introduced(assumption)).
% 2.22/1.76 tff(2304,plain,
% 2.22/1.76 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)))),
% 2.22/1.76 inference(rewrite,[status(thm)],[])).
% 2.22/1.76 tff(2305,plain,
% 2.22/1.76 ((hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102))) <=> (hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)))),
% 2.22/1.76 inference(rewrite,[status(thm)],[])).
% 2.22/1.76 tff(2306,plain,
% 2.22/1.76 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131))))),
% 2.22/1.76 inference(monotonicity,[status(thm)],[2305])).
% 2.22/1.76 tff(2307,plain,
% 2.22/1.76 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)))),
% 2.22/1.76 inference(transitivity,[status(thm)],[2306, 2304])).
% 2.22/1.76 tff(2308,plain,
% 2.22/1.76 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)))),
% 2.22/1.76 inference(quant_inst,[status(thm)],[])).
% 2.22/1.76 tff(2309,plain,
% 2.22/1.76 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131))),
% 2.22/1.76 inference(modus_ponens,[status(thm)],[2308, 2307])).
% 2.22/1.76 tff(2310,plain,
% 2.22/1.76 ($false),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[2309, 160, 22, 1166, 1164, 2303, 2302, 2301, 1400, 1856])).
% 2.22/1.76 tff(2311,plain,(hskp10 | (~c0_1(a131)) | (~c3_1(a131)) | (~c2_1(a102)) | c0_1(a102) | c1_1(a102) | hskp4), inference(lemma,lemma(discharge,[]))).
% 2.22/1.76 tff(2312,plain,
% 2.22/1.76 ($false),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[2311, 2300, 2299, 22, 2262, 2263, 2298, 2283])).
% 2.22/1.76 tff(2313,plain,(hskp31 | hskp10), inference(lemma,lemma(discharge,[]))).
% 2.22/1.76 tff(2314,plain,
% 2.22/1.76 (hskp31),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[2313, 22])).
% 2.22/1.76 tff(2315,plain,
% 2.22/1.76 (c1_1(a141)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[74, 2314])).
% 2.22/1.76 tff(2316,plain,
% 2.22/1.76 (c0_1(a141)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[85, 2314])).
% 2.22/1.76 tff(2317,plain,
% 2.22/1.76 (c3_1(a141)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[63, 2314])).
% 2.22/1.76 tff(2318,assumption,(hskp1), introduced(assumption)).
% 2.22/1.76 tff(2319,plain,
% 2.22/1.76 (~c1_1(a102)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1254, 2318])).
% 2.22/1.76 tff(2320,plain,
% 2.22/1.76 (~c0_1(a102)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1260, 2318])).
% 2.22/1.76 tff(2321,plain,
% 2.22/1.76 (c2_1(a102)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1307, 2318])).
% 2.22/1.76 tff(2322,plain,
% 2.22/1.76 ($false),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1416, 160, 22, 818, 817, 851, 2321, 2320, 2319, 1400])).
% 2.22/1.76 tff(2323,plain,((~hskp1) | hskp10 | (~c0_1(a141)) | (~c1_1(a141)) | (~c3_1(a141))), inference(lemma,lemma(discharge,[]))).
% 2.22/1.76 tff(2324,plain,
% 2.22/1.76 (~hskp1),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[2323, 2315, 22, 2316, 2317])).
% 2.22/1.76 tff(2325,plain,
% 2.22/1.76 (c2_1(a141)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1406, 160, 2259, 2324, 2316, 2315, 21])).
% 2.22/1.76 tff(2326,assumption,(c2_1(a141)), introduced(assumption)).
% 2.22/1.76 tff(2327,plain,
% 2.22/1.76 ($false),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[2016, 1071, 1, 2326])).
% 2.22/1.76 tff(2328,plain,(hskp19 | (~c2_1(a141)) | (~c0_1(a141)) | (~c3_1(a141))), inference(lemma,lemma(discharge,[]))).
% 2.22/1.76 tff(2329,plain,
% 2.22/1.76 (hskp19),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[2328, 2325, 2316, 2317])).
% 2.22/1.76 tff(2330,plain,
% 2.22/1.76 (~c2_1(a135)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[438, 2329])).
% 2.22/1.76 tff(2331,plain,
% 2.22/1.76 (c0_1(a135)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[459, 2329])).
% 2.22/1.76 tff(2332,plain,
% 2.22/1.76 (~c1_1(a135)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1247, 160, 2259, 2324, 2331, 2330, 21])).
% 2.22/1.76 tff(2333,plain,
% 2.22/1.76 (~c3_1(a135)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[432, 2329])).
% 2.22/1.76 tff(2334,plain,
% 2.22/1.76 ($false),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1239, 160, 2315, 2317, 2331, 2330, 2333, 108, 2332, 2325])).
% 2.22/1.76 tff(2335,plain,(hskp10), inference(lemma,lemma(discharge,[]))).
% 2.22/1.76 tff(2336,plain,
% 2.22/1.76 (~c3_1(a111)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1334, 2335])).
% 2.22/1.76 tff(2337,plain,
% 2.22/1.76 (~c2_1(a111)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1340, 2335])).
% 2.22/1.76 tff(2338,plain,
% 2.22/1.76 (hskp19 | (~c1_1(a111))),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1425, 160, 2337, 2336, 11])).
% 2.22/1.76 tff(2339,plain,
% 2.22/1.76 (~c1_1(a111)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[2338, 1])).
% 2.22/1.76 tff(2340,plain,
% 2.22/1.76 (~c0_1(a111)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[1346, 2335])).
% 2.22/1.76 tff(2341,plain,
% 2.22/1.76 (^[V: $i, U: $i] : refl((hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 2.22/1.76 inference(bind,[status(th)],[])).
% 2.22/1.76 tff(2342,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.76 inference(quant_intro,[status(thm)],[2341])).
% 2.22/1.76 tff(2343,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.76 inference(rewrite,[status(thm)],[])).
% 2.22/1.76 tff(2344,plain,
% 2.22/1.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp31) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp31))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp31) <=> (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 2.22/1.76 inference(bind,[status(th)],[])).
% 2.22/1.76 tff(2345,plain,
% 2.22/1.76 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp31) <=> ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.76 inference(quant_intro,[status(thm)],[2344])).
% 2.22/1.76 tff(2346,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(V)) | hskp31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 2.22/1.76 tff(2347,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.76 inference(modus_ponens,[status(thm)],[2346, 2345])).
% 2.22/1.76 tff(2348,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.76 inference(modus_ponens,[status(thm)],[2347, 2343])).
% 2.22/1.76 tff(2349,plain,(
% 2.22/1.76 ![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.76 inference(skolemize,[status(sab)],[2348])).
% 2.22/1.76 tff(2350,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 2.22/1.76 inference(modus_ponens,[status(thm)],[2349, 2342])).
% 2.22/1.76 tff(2351,plain,
% 2.22/1.76 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 2.22/1.76 inference(bind,[status(th)],[])).
% 2.22/1.76 tff(2352,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.22/1.76 inference(quant_intro,[status(thm)],[2351])).
% 2.22/1.76 tff(2353,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.22/1.76 inference(rewrite,[status(thm)],[])).
% 2.22/1.76 tff(2354,plain,
% 2.22/1.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp1))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 2.22/1.76 inference(bind,[status(th)],[])).
% 2.22/1.76 tff(2355,plain,
% 2.22/1.76 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.22/1.76 inference(quant_intro,[status(thm)],[2354])).
% 2.22/1.76 tff(2356,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 2.22/1.76 tff(2357,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.22/1.76 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 2.22/1.76 tff(2358,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.22/1.76 inference(modus_ponens,[status(thm)],[2357, 2353])).
% 2.22/1.76 tff(2359,plain,(
% 2.22/1.76 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.22/1.76 inference(skolemize,[status(sab)],[2358])).
% 2.22/1.76 tff(2360,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 2.22/1.76 inference(modus_ponens,[status(thm)],[2359, 2352])).
% 2.22/1.76 tff(2361,plain,
% 2.22/1.76 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~c1_1(a163)) | c2_1(a163) | c3_1(a163) | (~ndr1_0))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | (~c1_1(a163)) | c2_1(a163) | c3_1(a163) | (~ndr1_0))),
% 2.22/1.76 inference(rewrite,[status(thm)],[])).
% 2.22/1.76 tff(2362,plain,
% 2.22/1.76 ((hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c1_1(a163))) <=> (hskp19 | (~c1_1(a163)) | c2_1(a163) | c3_1(a163) | (~ndr1_0))),
% 2.22/1.76 inference(rewrite,[status(thm)],[])).
% 2.22/1.76 tff(2363,plain,
% 2.22/1.76 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c1_1(a163)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~c1_1(a163)) | c2_1(a163) | c3_1(a163) | (~ndr1_0)))),
% 2.22/1.76 inference(monotonicity,[status(thm)],[2362])).
% 2.22/1.76 tff(2364,plain,
% 2.22/1.76 (((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c1_1(a163)))) <=> ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | (~c1_1(a163)) | c2_1(a163) | c3_1(a163) | (~ndr1_0))),
% 2.22/1.76 inference(transitivity,[status(thm)],[2363, 2361])).
% 2.22/1.76 tff(2365,plain,
% 2.22/1.76 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp19 | (~ndr1_0) | c3_1(a163) | c2_1(a163) | (~c1_1(a163)))),
% 2.22/1.76 inference(quant_inst,[status(thm)],[])).
% 2.22/1.76 tff(2366,plain,
% 2.22/1.76 ((~![U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp19 | (~c1_1(a163)) | c2_1(a163) | c3_1(a163) | (~ndr1_0)),
% 2.22/1.76 inference(modus_ponens,[status(thm)],[2365, 2364])).
% 2.22/1.76 tff(2367,plain,
% 2.22/1.76 (hskp19 | c2_1(a163) | c3_1(a163)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[2366, 160, 2258, 11])).
% 2.22/1.76 tff(2368,plain,
% 2.22/1.76 (hskp19),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[2367, 97, 98])).
% 2.22/1.76 tff(2369,plain,
% 2.22/1.76 (c0_1(a135)),
% 2.22/1.76 inference(unit_resolution,[status(thm)],[459, 2368])).
% 2.22/1.76 tff(2370,plain,
% 2.22/1.76 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 2.22/1.76 inference(bind,[status(th)],[])).
% 2.22/1.76 tff(2371,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 2.22/1.76 inference(quant_intro,[status(thm)],[2370])).
% 2.22/1.76 tff(2372,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 2.22/1.76 inference(rewrite,[status(thm)],[])).
% 2.22/1.76 tff(2373,plain,
% 2.22/1.76 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 2.22/1.76 inference(bind,[status(th)],[])).
% 2.22/1.76 tff(2374,plain,
% 2.22/1.76 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 2.22/1.76 inference(quant_intro,[status(thm)],[2373])).
% 2.22/1.76 tff(2375,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 2.22/1.76 tff(2376,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 2.22/1.76 inference(modus_ponens,[status(thm)],[2375, 2374])).
% 2.22/1.76 tff(2377,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 2.22/1.76 inference(modus_ponens,[status(thm)],[2376, 2372])).
% 2.22/1.76 tff(2378,plain,(
% 2.22/1.76 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 2.22/1.76 inference(skolemize,[status(sab)],[2377])).
% 2.22/1.76 tff(2379,plain,
% 2.22/1.76 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 2.22/1.76 inference(modus_ponens,[status(thm)],[2378, 2371])).
% 2.22/1.76 tff(2380,plain,
% 2.22/1.76 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.22/1.76 inference(rewrite,[status(thm)],[])).
% 2.22/1.76 tff(2381,plain,
% 2.22/1.76 ((hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a163) | c3_1(a163) | (~c1_1(a163))) <=> (hskp8 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.22/1.76 inference(rewrite,[status(thm)],[])).
% 2.22/1.76 tff(2382,plain,
% 2.22/1.76 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a163) | c3_1(a163) | (~c1_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)))),
% 2.22/1.76 inference(monotonicity,[status(thm)],[2381])).
% 2.22/1.76 tff(2383,plain,
% 2.30/1.76 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a163) | c3_1(a163) | (~c1_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.30/1.76 inference(transitivity,[status(thm)],[2382, 2380])).
% 2.30/1.76 tff(2384,plain,
% 2.30/1.76 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a163) | c3_1(a163) | (~c1_1(a163)))),
% 2.30/1.76 inference(quant_inst,[status(thm)],[])).
% 2.30/1.76 tff(2385,plain,
% 2.30/1.76 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)),
% 2.30/1.76 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 2.30/1.76 tff(2386,plain,
% 2.30/1.76 (hskp8),
% 2.30/1.76 inference(unit_resolution,[status(thm)],[2385, 160, 86, 75, 64, 2258, 97, 2379, 245])).
% 2.30/1.76 tff(2387,plain,
% 2.30/1.76 (~c3_1(a109)),
% 2.30/1.76 inference(unit_resolution,[status(thm)],[173, 2386])).
% 2.30/1.76 tff(2388,plain,
% 2.30/1.76 (~c0_1(a109)),
% 2.30/1.76 inference(unit_resolution,[status(thm)],[207, 2386])).
% 2.30/1.76 tff(2389,plain,
% 2.30/1.76 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.30/1.76 inference(rewrite,[status(thm)],[])).
% 2.30/1.76 tff(2390,plain,
% 2.30/1.76 ((hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | c3_1(a163)) <=> (hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.30/1.76 inference(rewrite,[status(thm)],[])).
% 2.30/1.76 tff(2391,plain,
% 2.30/1.76 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | c3_1(a163))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)))),
% 2.30/1.76 inference(monotonicity,[status(thm)],[2390])).
% 2.30/1.76 tff(2392,plain,
% 2.30/1.76 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | c3_1(a163))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163))),
% 2.30/1.76 inference(transitivity,[status(thm)],[2391, 2389])).
% 2.30/1.76 tff(2393,plain,
% 2.30/1.76 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | c3_1(a163))),
% 2.30/1.76 inference(quant_inst,[status(thm)],[])).
% 2.30/1.76 tff(2394,plain,
% 2.30/1.76 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | c0_1(a163)),
% 2.30/1.76 inference(modus_ponens,[status(thm)],[2393, 2392])).
% 2.30/1.76 tff(2395,plain,
% 2.30/1.76 (hskp13),
% 2.30/1.76 inference(unit_resolution,[status(thm)],[2394, 160, 86, 75, 64, 98, 97, 1328, 245])).
% 2.30/1.76 tff(2396,plain,
% 2.30/1.76 (~c3_1(a114)),
% 2.30/1.76 inference(unit_resolution,[status(thm)],[629, 2395])).
% 2.30/1.76 tff(2397,plain,
% 2.30/1.77 (~c3_1(a135)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[432, 2368])).
% 2.30/1.77 tff(2398,plain,
% 2.30/1.77 (~c2_1(a135)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[438, 2368])).
% 2.30/1.77 tff(2399,plain,
% 2.30/1.77 (c1_1(a109)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[184, 2386])).
% 2.30/1.77 tff(2400,plain,
% 2.30/1.77 (c2_1(a114)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[640, 2395])).
% 2.30/1.77 tff(2401,plain,
% 2.30/1.77 (c1_1(a114)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[651, 2395])).
% 2.30/1.77 tff(2402,plain,
% 2.30/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c1_1(a109)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c1_1(a109)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2403,plain,
% 2.30/1.77 (((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109))) <=> (c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c1_1(a109)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2404,plain,
% 2.30/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c1_1(a109)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135))))),
% 2.30/1.77 inference(monotonicity,[status(thm)],[2403])).
% 2.30/1.77 tff(2405,plain,
% 2.30/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c1_1(a109)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135)))),
% 2.30/1.77 inference(transitivity,[status(thm)],[2404, 2402])).
% 2.30/1.77 tff(2406,plain,
% 2.30/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a109) | c0_1(a109) | (~c1_1(a109)))),
% 2.30/1.77 inference(quant_inst,[status(thm)],[])).
% 2.30/1.77 tff(2407,plain,
% 2.30/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c3_1(a114) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c1_1(a109)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a135))),
% 2.30/1.77 inference(modus_ponens,[status(thm)],[2406, 2405])).
% 2.30/1.77 tff(2408,plain,
% 2.30/1.77 ($false),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2407, 160, 2369, 2401, 2400, 2399, 2398, 2397, 2396, 2388, 2387, 202])).
% 2.30/1.77 tff(2409,plain,((~hskp31) | c2_1(a163) | c3_1(a163) | c0_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.30/1.77 tff(2410,plain,
% 2.30/1.77 (~hskp31),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2409, 245, 97, 98])).
% 2.30/1.77 tff(2411,plain,
% 2.30/1.77 (^[U: $i] : refl((hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))),
% 2.30/1.77 inference(bind,[status(th)],[])).
% 2.30/1.77 tff(2412,plain,
% 2.30/1.77 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.30/1.77 inference(quant_intro,[status(thm)],[2411])).
% 2.30/1.77 tff(2413,plain,
% 2.30/1.77 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2414,plain,
% 2.30/1.77 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp10) <=> ((hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp10))), rewrite(((hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp10) <=> (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp10) <=> (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))))),
% 2.30/1.77 inference(bind,[status(th)],[])).
% 2.30/1.77 tff(2415,plain,
% 2.30/1.77 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp10) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.30/1.77 inference(quant_intro,[status(thm)],[2414])).
% 2.30/1.77 tff(2416,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 2.30/1.77 tff(2417,plain,
% 2.30/1.77 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.30/1.77 inference(modus_ponens,[status(thm)],[2416, 2415])).
% 2.30/1.77 tff(2418,plain,
% 2.30/1.77 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.30/1.77 inference(modus_ponens,[status(thm)],[2417, 2413])).
% 2.30/1.77 tff(2419,plain,(
% 2.30/1.77 ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.30/1.77 inference(skolemize,[status(sab)],[2418])).
% 2.30/1.77 tff(2420,plain,
% 2.30/1.77 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 2.30/1.77 inference(modus_ponens,[status(thm)],[2419, 2412])).
% 2.30/1.77 tff(2421,plain,
% 2.30/1.77 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp10 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | c0_1(a163))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp10 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2422,plain,
% 2.30/1.77 ((hskp15 | hskp10 | (~ndr1_0) | c3_1(a163) | c0_1(a163) | (~c1_1(a163))) <=> (hskp15 | hskp10 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2423,plain,
% 2.30/1.77 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c3_1(a163) | c0_1(a163) | (~c1_1(a163)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp10 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | c0_1(a163)))),
% 2.30/1.77 inference(monotonicity,[status(thm)],[2422])).
% 2.30/1.77 tff(2424,plain,
% 2.30/1.77 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c3_1(a163) | c0_1(a163) | (~c1_1(a163)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp10 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | c0_1(a163))),
% 2.30/1.77 inference(transitivity,[status(thm)],[2423, 2421])).
% 2.30/1.77 tff(2425,plain,
% 2.30/1.77 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | c3_1(a163) | c0_1(a163) | (~c1_1(a163)))),
% 2.30/1.77 inference(quant_inst,[status(thm)],[])).
% 2.30/1.77 tff(2426,plain,
% 2.30/1.77 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp15 | hskp10 | (~c1_1(a163)) | c3_1(a163) | (~ndr1_0) | c0_1(a163)),
% 2.30/1.77 inference(modus_ponens,[status(thm)],[2425, 2424])).
% 2.30/1.77 tff(2427,plain,
% 2.30/1.77 (hskp15 | hskp10 | c3_1(a163) | c0_1(a163)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2426, 160, 2258, 2420])).
% 2.30/1.77 tff(2428,plain,
% 2.30/1.77 (hskp15),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2427, 22, 97, 245])).
% 2.30/1.77 tff(2429,plain,
% 2.30/1.77 (~c1_1(a117)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[563, 2428])).
% 2.30/1.77 tff(2430,plain,
% 2.30/1.77 (c3_1(a117)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[585, 2428])).
% 2.30/1.77 tff(2431,plain,
% 2.30/1.77 (c0_1(a117)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[574, 2428])).
% 2.30/1.77 tff(2432,plain,
% 2.30/1.77 (hskp28),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[608, 2428, 23])).
% 2.30/1.77 tff(2433,plain,
% 2.30/1.77 (~hskp4),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2220, 2432, 2263, 2262, 2261])).
% 2.30/1.77 tff(2434,plain,
% 2.30/1.77 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2435,plain,
% 2.30/1.77 ((hskp10 | hskp4 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117))) <=> (hskp10 | hskp4 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2436,plain,
% 2.30/1.77 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117))))),
% 2.30/1.77 inference(monotonicity,[status(thm)],[2435])).
% 2.30/1.77 tff(2437,plain,
% 2.30/1.77 (((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117)))) <=> ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117)))),
% 2.30/1.77 inference(transitivity,[status(thm)],[2436, 2434])).
% 2.30/1.77 tff(2438,plain,
% 2.30/1.77 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp10 | hskp4 | (~ndr1_0) | c1_1(a117) | (~c3_1(a117)) | (~c0_1(a117)))),
% 2.30/1.77 inference(quant_inst,[status(thm)],[])).
% 2.30/1.77 tff(2439,plain,
% 2.30/1.77 ((~![U: $i] : (hskp10 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp10 | hskp4 | c1_1(a117) | (~ndr1_0) | (~c0_1(a117)) | (~c3_1(a117))),
% 2.30/1.77 inference(modus_ponens,[status(thm)],[2438, 2437])).
% 2.30/1.77 tff(2440,plain,
% 2.30/1.77 ($false),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2439, 160, 22, 2433, 2431, 2430, 2429, 1848])).
% 2.30/1.77 tff(2441,plain,(hskp10 | hskp31 | c3_1(a163) | c0_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.30/1.77 tff(2442,plain,
% 2.30/1.77 (hskp10),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2441, 2410, 97, 245])).
% 2.30/1.77 tff(2443,plain,
% 2.30/1.77 (~c0_1(a111)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1346, 2442])).
% 2.30/1.77 tff(2444,plain,
% 2.30/1.77 (~c3_1(a111)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1334, 2442])).
% 2.30/1.77 tff(2445,plain,
% 2.30/1.77 (hskp30),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[158, 2410, 2259])).
% 2.30/1.77 tff(2446,plain,
% 2.30/1.77 (c2_1(a131)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1012, 2445])).
% 2.30/1.77 tff(2447,plain,
% 2.30/1.77 (c0_1(a131)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1023, 2445])).
% 2.30/1.77 tff(2448,plain,
% 2.30/1.77 (c3_1(a131)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1001, 2445])).
% 2.30/1.77 tff(2449,plain,
% 2.30/1.77 (hskp28 | c1_1(a131)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1576, 2410, 160, 2447, 2448, 596])).
% 2.30/1.77 tff(2450,plain,
% 2.30/1.77 (c1_1(a131)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2449, 557])).
% 2.30/1.77 tff(2451,plain,
% 2.30/1.77 (~hskp15),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[608, 557, 2410])).
% 2.30/1.77 tff(2452,plain,
% 2.30/1.77 (hskp10),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2427, 2451, 97, 245])).
% 2.30/1.77 tff(2453,plain,
% 2.30/1.77 (~c2_1(a111)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1340, 2452])).
% 2.30/1.77 tff(2454,plain,
% 2.30/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111) | (~c0_1(a135)))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2455,plain,
% 2.30/1.77 (((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111)) <=> (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111) | (~c0_1(a135)))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2456,plain,
% 2.30/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111) | (~c0_1(a135))))),
% 2.30/1.77 inference(monotonicity,[status(thm)],[2455])).
% 2.30/1.77 tff(2457,plain,
% 2.30/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111) | (~c0_1(a135)))),
% 2.30/1.77 inference(transitivity,[status(thm)],[2456, 2454])).
% 2.30/1.77 tff(2458,plain,
% 2.30/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c2_1(a131)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))),
% 2.30/1.77 inference(quant_inst,[status(thm)],[])).
% 2.30/1.77 tff(2459,plain,
% 2.30/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c2_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111) | (~c0_1(a135))),
% 2.30/1.77 inference(modus_ponens,[status(thm)],[2458, 2457])).
% 2.30/1.77 tff(2460,plain,
% 2.30/1.77 (c1_1(a111)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2459, 160, 2446, 2448, 2369, 2398, 2397, 2453, 1476, 108, 2450])).
% 2.30/1.77 tff(2461,plain,
% 2.30/1.77 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2462,plain,
% 2.30/1.77 ((hskp13 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c2_1(a163) | c0_1(a163) | c3_1(a163)) <=> (hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2463,plain,
% 2.30/1.77 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c2_1(a163) | c0_1(a163) | c3_1(a163))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163)))),
% 2.30/1.77 inference(monotonicity,[status(thm)],[2462])).
% 2.30/1.77 tff(2464,plain,
% 2.30/1.77 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c2_1(a163) | c0_1(a163) | c3_1(a163))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163))),
% 2.30/1.77 inference(transitivity,[status(thm)],[2463, 2461])).
% 2.30/1.77 tff(2465,plain,
% 2.30/1.77 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c2_1(a163) | c0_1(a163) | c3_1(a163))),
% 2.30/1.77 inference(quant_inst,[status(thm)],[])).
% 2.30/1.77 tff(2466,plain,
% 2.30/1.77 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp13 | c2_1(a163) | c3_1(a163) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c0_1(a163)),
% 2.30/1.77 inference(modus_ponens,[status(thm)],[2465, 2464])).
% 2.30/1.77 tff(2467,plain,
% 2.30/1.77 (hskp13),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2466, 160, 2447, 2448, 98, 97, 1328, 245, 2450])).
% 2.30/1.77 tff(2468,plain,
% 2.30/1.77 ($false),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1489, 2467, 2460, 2398, 2397, 1477, 1476, 2369])).
% 2.30/1.77 tff(2469,plain,(hskp28 | c0_1(a111) | c3_1(a111) | c2_1(a163) | c3_1(a163) | c0_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.30/1.77 tff(2470,plain,
% 2.30/1.77 (hskp28),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2469, 1476, 1477, 98, 97, 245])).
% 2.30/1.77 tff(2471,plain,
% 2.30/1.77 (~hskp4),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2220, 2470, 2448, 2447, 2446])).
% 2.30/1.77 tff(2472,plain,
% 2.30/1.77 (c3_1(a118)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[524, 2470])).
% 2.30/1.77 tff(2473,plain,
% 2.30/1.77 (c2_1(a118)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[535, 2470])).
% 2.30/1.77 tff(2474,plain,
% 2.30/1.77 (c1_1(a118)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[546, 2470])).
% 2.30/1.77 tff(2475,plain,
% 2.30/1.77 (c2_1(a111)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1965, 2474, 2397, 1477, 2471, 2369, 2398, 1476, 2473, 2472])).
% 2.30/1.77 tff(2476,plain,
% 2.30/1.77 (~hskp10),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1340, 2475])).
% 2.30/1.77 tff(2477,plain,
% 2.30/1.77 (hskp10 | hskp4 | c1_1(a131)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1854, 160, 2447, 2448, 1848])).
% 2.30/1.77 tff(2478,plain,
% 2.30/1.77 (c1_1(a131)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2477, 2476, 2471])).
% 2.30/1.77 tff(2479,plain,
% 2.30/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c0_1(a111) | (~c2_1(a111)) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c0_1(a111) | (~c2_1(a111)) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c0_1(a135)))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2480,plain,
% 2.30/1.77 (((~ndr1_0) | c3_1(a111) | (~c1_1(a111)) | (~c2_1(a111)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111))) <=> (c2_1(a135) | c3_1(a135) | c0_1(a111) | (~c2_1(a111)) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c0_1(a135)))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2481,plain,
% 2.30/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a111) | (~c1_1(a111)) | (~c2_1(a111)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a135) | c3_1(a135) | c0_1(a111) | (~c2_1(a111)) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c0_1(a135))))),
% 2.30/1.77 inference(monotonicity,[status(thm)],[2480])).
% 2.30/1.77 tff(2482,plain,
% 2.30/1.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a111) | (~c1_1(a111)) | (~c2_1(a111)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c0_1(a111) | (~c2_1(a111)) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c0_1(a135)))),
% 2.30/1.77 inference(transitivity,[status(thm)],[2481, 2479])).
% 2.30/1.77 tff(2483,plain,
% 2.30/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a111) | (~c1_1(a111)) | (~c2_1(a111)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c0_1(a111) | (~c1_1(a111)))),
% 2.30/1.77 inference(quant_inst,[status(thm)],[])).
% 2.30/1.77 tff(2484,plain,
% 2.30/1.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a135) | c3_1(a135) | c0_1(a111) | (~c2_1(a111)) | c3_1(a111) | (~ndr1_0) | (~c1_1(a111)) | (~c0_1(a135))),
% 2.30/1.77 inference(modus_ponens,[status(thm)],[2483, 2482])).
% 2.30/1.77 tff(2485,plain,
% 2.30/1.77 ((~c2_1(a111)) | (~c1_1(a111))),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2484, 160, 2369, 2398, 2397, 1477, 1476, 202])).
% 2.30/1.77 tff(2486,plain,
% 2.30/1.77 (~c1_1(a111)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2485, 2475])).
% 2.30/1.77 tff(2487,plain,
% 2.30/1.77 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a111) | (~c2_1(a111)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a111) | (~c2_1(a111)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2488,plain,
% 2.30/1.77 ((hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a111) | c0_1(a111) | (~c2_1(a111))) <=> (hskp10 | c0_1(a111) | (~c2_1(a111)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2489,plain,
% 2.30/1.77 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a111) | c0_1(a111) | (~c2_1(a111)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c0_1(a111) | (~c2_1(a111)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111)))),
% 2.30/1.77 inference(monotonicity,[status(thm)],[2488])).
% 2.30/1.77 tff(2490,plain,
% 2.30/1.77 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a111) | c0_1(a111) | (~c2_1(a111)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a111) | (~c2_1(a111)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111))),
% 2.30/1.77 inference(transitivity,[status(thm)],[2489, 2487])).
% 2.30/1.77 tff(2491,plain,
% 2.30/1.77 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | (~c1_1(a131)) | (~c3_1(a131)) | (~c0_1(a131)) | c1_1(a111) | c0_1(a111) | (~c2_1(a111)))),
% 2.30/1.77 inference(quant_inst,[status(thm)],[])).
% 2.30/1.77 tff(2492,plain,
% 2.30/1.77 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c0_1(a111) | (~c2_1(a111)) | (~ndr1_0) | (~c0_1(a131)) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a111)),
% 2.30/1.77 inference(modus_ponens,[status(thm)],[2491, 2490])).
% 2.30/1.77 tff(2493,plain,
% 2.30/1.77 ($false),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2492, 160, 2476, 2447, 2448, 1477, 2475, 1400, 2486, 2478])).
% 2.30/1.77 tff(2494,plain,(c3_1(a111) | c0_1(a111) | c2_1(a163) | c3_1(a163) | c0_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.30/1.77 tff(2495,plain,
% 2.30/1.77 ($false),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2494, 2444, 2443, 98, 97, 245])).
% 2.30/1.77 tff(2496,plain,(c0_1(a163) | c2_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.30/1.77 tff(2497,plain,
% 2.30/1.77 (c0_1(a163)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2496, 97, 98])).
% 2.30/1.77 tff(2498,plain,
% 2.30/1.77 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2499,plain,
% 2.30/1.77 ((hskp24 | hskp1 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163))) <=> (hskp24 | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 2.30/1.77 inference(rewrite,[status(thm)],[])).
% 2.30/1.77 tff(2500,plain,
% 2.30/1.77 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163))))),
% 2.30/1.77 inference(monotonicity,[status(thm)],[2499])).
% 2.30/1.77 tff(2501,plain,
% 2.30/1.77 (((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 2.30/1.77 inference(transitivity,[status(thm)],[2500, 2498])).
% 2.30/1.77 tff(2502,plain,
% 2.30/1.77 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp1 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))),
% 2.30/1.77 inference(quant_inst,[status(thm)],[])).
% 2.30/1.77 tff(2503,plain,
% 2.30/1.77 ((~![U: $i] : (hskp24 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163))),
% 2.30/1.77 inference(modus_ponens,[status(thm)],[2502, 2501])).
% 2.30/1.77 tff(2504,plain,
% 2.30/1.77 (hskp1 | c2_1(a163) | (~c0_1(a163))),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2503, 160, 2259, 2258, 21])).
% 2.30/1.77 tff(2505,plain,
% 2.30/1.77 (hskp1),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[2504, 2497, 98])).
% 2.30/1.77 tff(2506,plain,
% 2.30/1.77 (~c1_1(a102)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1254, 2505])).
% 2.30/1.77 tff(2507,plain,
% 2.30/1.77 (~c0_1(a102)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1260, 2505])).
% 2.30/1.77 tff(2508,plain,
% 2.30/1.77 (c2_1(a102)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1307, 2505])).
% 2.30/1.77 tff(2509,plain,
% 2.30/1.77 (hskp10),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1416, 160, 86, 75, 64, 2508, 2507, 2506, 1400])).
% 2.30/1.77 tff(2510,plain,
% 2.30/1.77 (~c3_1(a111)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1334, 2509])).
% 2.30/1.77 tff(2511,plain,
% 2.30/1.77 (~c2_1(a111)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1340, 2509])).
% 2.30/1.77 tff(2512,plain,
% 2.30/1.77 (~c0_1(a111)),
% 2.30/1.77 inference(unit_resolution,[status(thm)],[1346, 2509])).
% 2.30/1.77 tff(2513,plain,
% 2.30/1.77 (hskp13),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1353, 160, 86, 75, 64, 2512, 2511, 2510, 1328])).
% 2.31/1.78 tff(2514,plain,
% 2.31/1.78 (~c3_1(a114)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[629, 2513])).
% 2.31/1.78 tff(2515,plain,
% 2.31/1.78 (c2_1(a114)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[640, 2513])).
% 2.31/1.78 tff(2516,plain,
% 2.31/1.78 (c1_1(a114)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[651, 2513])).
% 2.31/1.78 tff(2517,plain,
% 2.31/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a163) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a163) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a163)))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2518,plain,
% 2.31/1.78 (((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114))) <=> (c2_1(a163) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a163)))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2519,plain,
% 2.31/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a163) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a163))))),
% 2.31/1.78 inference(monotonicity,[status(thm)],[2518])).
% 2.31/1.78 tff(2520,plain,
% 2.31/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a163) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a163)))),
% 2.31/1.78 inference(transitivity,[status(thm)],[2519, 2517])).
% 2.31/1.78 tff(2521,plain,
% 2.31/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))),
% 2.31/1.78 inference(quant_inst,[status(thm)],[])).
% 2.31/1.78 tff(2522,plain,
% 2.31/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a163) | c3_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | c0_1(a114) | (~c0_1(a163))),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2521, 2520])).
% 2.31/1.78 tff(2523,plain,
% 2.31/1.78 (c0_1(a114)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2522, 160, 2516, 2515, 98, 97, 2514, 202, 2497])).
% 2.31/1.78 tff(2524,plain,
% 2.31/1.78 (~c1_1(a111)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1489, 2513, 2398, 2397, 2512, 2510, 2369])).
% 2.31/1.78 tff(2525,plain,
% 2.31/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a114) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c2_1(a114)) | (~c0_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a114) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c2_1(a114)) | (~c0_1(a114)))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2526,plain,
% 2.31/1.78 (((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111)) <=> (c3_1(a114) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c2_1(a114)) | (~c0_1(a114)))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2527,plain,
% 2.31/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a114) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c2_1(a114)) | (~c0_1(a114))))),
% 2.31/1.78 inference(monotonicity,[status(thm)],[2526])).
% 2.31/1.78 tff(2528,plain,
% 2.31/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a114) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c2_1(a114)) | (~c0_1(a114)))),
% 2.31/1.78 inference(transitivity,[status(thm)],[2527, 2525])).
% 2.31/1.78 tff(2529,plain,
% 2.31/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))),
% 2.31/1.78 inference(quant_inst,[status(thm)],[])).
% 2.31/1.78 tff(2530,plain,
% 2.31/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a114) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c2_1(a114)) | (~c0_1(a114))),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2529, 2528])).
% 2.31/1.78 tff(2531,plain,
% 2.31/1.78 (c3_1(a102)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2530, 160, 2515, 2508, 2514, 2512, 2510, 2507, 367, 2524, 2523])).
% 2.31/1.78 tff(2532,plain,
% 2.31/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a163) | c3_1(a163) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a163) | c3_1(a163) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a163)))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2533,plain,
% 2.31/1.78 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a111) | c1_1(a111) | c2_1(a111)) <=> (c2_1(a163) | c3_1(a163) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a163)))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2534,plain,
% 2.31/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (c2_1(a163) | c3_1(a163) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a163))))),
% 2.31/1.78 inference(monotonicity,[status(thm)],[2533])).
% 2.31/1.78 tff(2535,plain,
% 2.31/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a163) | c3_1(a163) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a163)))),
% 2.31/1.78 inference(transitivity,[status(thm)],[2534, 2532])).
% 2.31/1.78 tff(2536,plain,
% 2.31/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)) | c2_1(a163) | c3_1(a163) | (~c0_1(a163)) | c3_1(a111) | c1_1(a111) | c2_1(a111))),
% 2.31/1.78 inference(quant_inst,[status(thm)],[])).
% 2.31/1.78 tff(2537,plain,
% 2.31/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | c2_1(a163) | c3_1(a163) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c1_1(a141)) | c1_1(a111) | (~c0_1(a163))),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 2.31/1.78 tff(2538,plain,
% 2.31/1.78 ((~c2_1(a141)) | c1_1(a111)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2537, 160, 75, 64, 98, 97, 2511, 2510, 108, 2497])).
% 2.31/1.78 tff(2539,plain,
% 2.31/1.78 (~c2_1(a141)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2538, 2524])).
% 2.31/1.78 tff(2540,plain,
% 2.31/1.78 (hskp12),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2052, 160, 86, 75, 2516, 2515, 2514, 2027, 2539])).
% 2.31/1.78 tff(2541,plain,
% 2.31/1.78 (~c2_1(a113)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1702, 2540])).
% 2.31/1.78 tff(2542,plain,
% 2.31/1.78 (~c0_1(a113)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1736, 2540])).
% 2.31/1.78 tff(2543,plain,
% 2.31/1.78 (c3_1(a113)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1713, 2540])).
% 2.31/1.78 tff(2544,plain,
% 2.31/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a113) | c2_1(a113) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | (~c3_1(a113)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a113) | c2_1(a113) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | (~c3_1(a113)))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2545,plain,
% 2.31/1.78 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102))) <=> (c0_1(a113) | c2_1(a113) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | (~c3_1(a113)))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2546,plain,
% 2.31/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a113) | c2_1(a113) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | (~c3_1(a113))))),
% 2.31/1.78 inference(monotonicity,[status(thm)],[2545])).
% 2.31/1.78 tff(2547,plain,
% 2.31/1.78 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a113) | c2_1(a113) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | (~c3_1(a113)))),
% 2.31/1.78 inference(transitivity,[status(thm)],[2546, 2544])).
% 2.31/1.78 tff(2548,plain,
% 2.31/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a113) | c0_1(a113) | (~c3_1(a113)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))),
% 2.31/1.78 inference(quant_inst,[status(thm)],[])).
% 2.31/1.78 tff(2549,plain,
% 2.31/1.78 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a113) | c2_1(a113) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | (~c3_1(a113))),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2548, 2547])).
% 2.31/1.78 tff(2550,plain,
% 2.31/1.78 ($false),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2549, 160, 86, 75, 64, 2543, 2542, 2541, 2507, 2506, 804, 2531])).
% 2.31/1.78 tff(2551,plain,((~hskp31) | c2_1(a163) | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.31/1.78 tff(2552,plain,
% 2.31/1.78 (~hskp31),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2551, 97, 98])).
% 2.31/1.78 tff(2553,plain,
% 2.31/1.78 (~hskp4),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2282, 2552])).
% 2.31/1.78 tff(2554,plain,
% 2.31/1.78 (hskp30),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[158, 2552, 2259])).
% 2.31/1.78 tff(2555,plain,
% 2.31/1.78 (c3_1(a131)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1001, 2554])).
% 2.31/1.78 tff(2556,plain,
% 2.31/1.78 (c0_1(a131)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1023, 2554])).
% 2.31/1.78 tff(2557,plain,
% 2.31/1.78 (hskp10),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2311, 2556, 2555, 2508, 2507, 2506, 2553])).
% 2.31/1.78 tff(2558,plain,
% 2.31/1.78 (~c3_1(a111)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1334, 2557])).
% 2.31/1.78 tff(2559,plain,
% 2.31/1.78 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2560,plain,
% 2.31/1.78 ((hskp29 | hskp4 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163))) <=> (hskp29 | hskp4 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2561,plain,
% 2.31/1.78 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163))))),
% 2.31/1.78 inference(monotonicity,[status(thm)],[2560])).
% 2.31/1.78 tff(2562,plain,
% 2.31/1.78 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163)))),
% 2.31/1.78 inference(transitivity,[status(thm)],[2561, 2559])).
% 2.31/1.78 tff(2563,plain,
% 2.31/1.78 ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))),
% 2.31/1.78 inference(quant_inst,[status(thm)],[])).
% 2.31/1.78 tff(2564,plain,
% 2.31/1.78 ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | (~c1_1(a163)) | c2_1(a163) | (~ndr1_0) | (~c0_1(a163))),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2563, 2562])).
% 2.31/1.78 tff(2565,plain,
% 2.31/1.78 (hskp29 | hskp4 | c2_1(a163) | (~c0_1(a163))),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2564, 160, 2258, 1888])).
% 2.31/1.78 tff(2566,plain,
% 2.31/1.78 (hskp29),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2565, 2553, 98, 2497])).
% 2.31/1.78 tff(2567,plain,
% 2.31/1.78 (c2_1(a128)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1929, 2566])).
% 2.31/1.78 tff(2568,plain,
% 2.31/1.78 (~c0_1(a111)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1346, 2557])).
% 2.31/1.78 tff(2569,plain,
% 2.31/1.78 (c0_1(a128)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1906, 2566])).
% 2.31/1.78 tff(2570,plain,
% 2.31/1.78 (c1_1(a128)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1918, 2566])).
% 2.31/1.78 tff(2571,plain,
% 2.31/1.78 (~c2_1(a111)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1340, 2557])).
% 2.31/1.78 tff(2572,plain,
% 2.31/1.78 (hskp13),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1960, 2571, 2570, 2553, 2569, 2568, 2567, 2558])).
% 2.31/1.78 tff(2573,plain,
% 2.31/1.78 (~c1_1(a111)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[1489, 2558, 2398, 2397, 2568, 2572, 2369])).
% 2.31/1.78 tff(2574,plain,
% 2.31/1.78 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U)) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U)))),
% 2.31/1.78 inference(bind,[status(th)],[])).
% 2.31/1.78 tff(2575,plain,
% 2.31/1.78 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))),
% 2.31/1.78 inference(quant_intro,[status(thm)],[2574])).
% 2.31/1.78 tff(2576,plain,
% 2.31/1.78 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2577,plain,
% 2.31/1.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_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))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U)) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U)) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))))),
% 2.31/1.78 inference(bind,[status(th)],[])).
% 2.31/1.78 tff(2578,plain,
% 2.31/1.78 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))),
% 2.31/1.78 inference(quant_intro,[status(thm)],[2577])).
% 2.31/1.78 tff(2579,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 2.31/1.78 tff(2580,plain,
% 2.31/1.78 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2579, 2578])).
% 2.31/1.78 tff(2581,plain,
% 2.31/1.78 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2580, 2576])).
% 2.31/1.78 tff(2582,plain,(
% 2.31/1.78 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))),
% 2.31/1.78 inference(skolemize,[status(sab)],[2581])).
% 2.31/1.78 tff(2583,plain,
% 2.31/1.78 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2582, 2575])).
% 2.31/1.78 tff(2584,plain,
% 2.31/1.78 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | (hskp4 | hskp3 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | hskp4 | hskp3 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2585,plain,
% 2.31/1.78 ((hskp4 | hskp3 | (~ndr1_0) | c1_1(a111) | c0_1(a111) | c2_1(a111)) <=> (hskp4 | hskp3 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2586,plain,
% 2.31/1.78 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a111) | c0_1(a111) | c2_1(a111))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | (hskp4 | hskp3 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111)))),
% 2.31/1.78 inference(monotonicity,[status(thm)],[2585])).
% 2.31/1.78 tff(2587,plain,
% 2.31/1.78 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a111) | c0_1(a111) | c2_1(a111))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | hskp4 | hskp3 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))),
% 2.31/1.78 inference(transitivity,[status(thm)],[2586, 2584])).
% 2.31/1.78 tff(2588,plain,
% 2.31/1.78 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c1_1(a111) | c0_1(a111) | c2_1(a111))),
% 2.31/1.78 inference(quant_inst,[status(thm)],[])).
% 2.31/1.78 tff(2589,plain,
% 2.31/1.78 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | c2_1(U))) | hskp4 | hskp3 | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2588, 2587])).
% 2.31/1.78 tff(2590,plain,
% 2.31/1.78 (hskp3),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2589, 160, 2553, 2568, 2571, 2583, 2573])).
% 2.31/1.78 tff(2591,plain,
% 2.31/1.78 (((~hskp3) | (~c1_1(a104))) <=> ((~hskp3) | (~c1_1(a104)))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2592,plain,
% 2.31/1.78 (((~c1_1(a104)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a104)))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2593,axiom,((~c1_1(a104)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 2.31/1.78 tff(2594,plain,
% 2.31/1.78 ((~hskp3) | (~c1_1(a104))),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2593, 2592])).
% 2.31/1.78 tff(2595,plain,
% 2.31/1.78 ((~hskp3) | (~c1_1(a104))),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2594, 2591])).
% 2.31/1.78 tff(2596,plain,
% 2.31/1.78 (~c1_1(a104)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2595, 2590])).
% 2.31/1.78 tff(2597,plain,
% 2.31/1.78 (((~hskp3) | c2_1(a104)) <=> ((~hskp3) | c2_1(a104))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2598,axiom,((~hskp3) | c2_1(a104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 2.31/1.78 tff(2599,plain,
% 2.31/1.78 ((~hskp3) | c2_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2598, 2597])).
% 2.31/1.78 tff(2600,plain,
% 2.31/1.78 ((~hskp3) | c2_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2599, 2597])).
% 2.31/1.78 tff(2601,plain,
% 2.31/1.78 ((~hskp3) | c2_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2600, 2597])).
% 2.31/1.78 tff(2602,plain,
% 2.31/1.78 ((~hskp3) | c2_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2601, 2597])).
% 2.31/1.78 tff(2603,plain,
% 2.31/1.78 ((~hskp3) | c2_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2602, 2597])).
% 2.31/1.78 tff(2604,plain,
% 2.31/1.78 ((~hskp3) | c2_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2603, 2597])).
% 2.31/1.78 tff(2605,plain,
% 2.31/1.78 ((~hskp3) | c2_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2604, 2597])).
% 2.31/1.78 tff(2606,plain,
% 2.31/1.78 ((~hskp3) | c2_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2605, 2597])).
% 2.31/1.78 tff(2607,plain,
% 2.31/1.78 (c2_1(a104)),
% 2.31/1.78 inference(unit_resolution,[status(thm)],[2606, 2590])).
% 2.31/1.78 tff(2608,plain,
% 2.31/1.78 (((~hskp3) | c0_1(a104)) <=> ((~hskp3) | c0_1(a104))),
% 2.31/1.78 inference(rewrite,[status(thm)],[])).
% 2.31/1.78 tff(2609,axiom,((~hskp3) | c0_1(a104)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 2.31/1.78 tff(2610,plain,
% 2.31/1.78 ((~hskp3) | c0_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2609, 2608])).
% 2.31/1.78 tff(2611,plain,
% 2.31/1.78 ((~hskp3) | c0_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2610, 2608])).
% 2.31/1.78 tff(2612,plain,
% 2.31/1.78 ((~hskp3) | c0_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2611, 2608])).
% 2.31/1.78 tff(2613,plain,
% 2.31/1.78 ((~hskp3) | c0_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2612, 2608])).
% 2.31/1.78 tff(2614,plain,
% 2.31/1.78 ((~hskp3) | c0_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2613, 2608])).
% 2.31/1.78 tff(2615,plain,
% 2.31/1.78 ((~hskp3) | c0_1(a104)),
% 2.31/1.78 inference(modus_ponens,[status(thm)],[2614, 2608])).
% 2.31/1.79 tff(2616,plain,
% 2.31/1.79 ((~hskp3) | c0_1(a104)),
% 2.31/1.79 inference(modus_ponens,[status(thm)],[2615, 2608])).
% 2.31/1.79 tff(2617,plain,
% 2.31/1.79 ((~hskp3) | c0_1(a104)),
% 2.31/1.79 inference(modus_ponens,[status(thm)],[2616, 2608])).
% 2.31/1.79 tff(2618,plain,
% 2.31/1.79 (c0_1(a104)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2617, 2590])).
% 2.31/1.79 tff(2619,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2620,plain,
% 2.31/1.79 ((hskp31 | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a128)) | (~c0_1(a128)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104))) <=> (hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2621,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a128)) | (~c0_1(a128)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128))))),
% 2.31/1.79 inference(monotonicity,[status(thm)],[2620])).
% 2.31/1.79 tff(2622,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a128)) | (~c0_1(a128)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)))),
% 2.31/1.79 inference(transitivity,[status(thm)],[2621, 2619])).
% 2.31/1.79 tff(2623,plain,
% 2.31/1.79 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a128)) | (~c0_1(a128)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104)))),
% 2.31/1.79 inference(quant_inst,[status(thm)],[])).
% 2.31/1.79 tff(2624,plain,
% 2.31/1.79 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128))),
% 2.31/1.79 inference(modus_ponens,[status(thm)],[2623, 2622])).
% 2.31/1.79 tff(2625,plain,
% 2.31/1.79 ($false),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2624, 2552, 160, 2569, 2570, 2567, 2618, 2607, 2596, 2350])).
% 2.31/1.79 tff(2626,plain,(c3_1(a163) | c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.31/1.79 tff(2627,plain,
% 2.31/1.79 (c3_1(a163)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2626, 98])).
% 2.31/1.79 tff(2628,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2629,plain,
% 2.31/1.79 ((hskp1 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163))) <=> (hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2630,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131))))),
% 2.31/1.79 inference(monotonicity,[status(thm)],[2629])).
% 2.31/1.79 tff(2631,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)))),
% 2.31/1.79 inference(transitivity,[status(thm)],[2630, 2628])).
% 2.31/1.79 tff(2632,plain,
% 2.31/1.79 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)))),
% 2.31/1.79 inference(quant_inst,[status(thm)],[])).
% 2.31/1.79 tff(2633,plain,
% 2.31/1.79 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131))),
% 2.31/1.79 inference(modus_ponens,[status(thm)],[2632, 2631])).
% 2.31/1.79 tff(2634,plain,
% 2.31/1.79 (hskp1),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2633, 160, 2262, 2261, 2263, 2258, 98, 2627, 2360])).
% 2.31/1.79 tff(2635,plain,
% 2.31/1.79 (~c1_1(a102)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1254, 2634])).
% 2.31/1.79 tff(2636,plain,
% 2.31/1.79 (~c0_1(a102)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1260, 2634])).
% 2.31/1.79 tff(2637,plain,
% 2.31/1.79 (c2_1(a102)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1307, 2634])).
% 2.31/1.79 tff(2638,plain,
% 2.31/1.79 (hskp10),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2311, 2637, 2263, 2262, 2636, 2635, 2283])).
% 2.31/1.79 tff(2639,plain,
% 2.31/1.79 (~c0_1(a111)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1346, 2638])).
% 2.31/1.79 tff(2640,plain,
% 2.31/1.79 (~c3_1(a111)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1334, 2638])).
% 2.31/1.79 tff(2641,plain,
% 2.31/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a135) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a135) | (~c0_1(a135)))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2642,plain,
% 2.31/1.79 (((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)) | c3_1(a135) | c1_1(a135) | (~c0_1(a135))) <=> ((~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a135) | (~c0_1(a135)))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2643,plain,
% 2.31/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)) | c3_1(a135) | c1_1(a135) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a135) | (~c0_1(a135))))),
% 2.31/1.79 inference(monotonicity,[status(thm)],[2642])).
% 2.31/1.79 tff(2644,plain,
% 2.31/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)) | c3_1(a135) | c1_1(a135) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a135) | (~c0_1(a135)))),
% 2.31/1.79 inference(transitivity,[status(thm)],[2643, 2641])).
% 2.31/1.79 tff(2645,plain,
% 2.31/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a131)) | (~c2_1(a131)) | (~c0_1(a131)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)) | c3_1(a135) | c1_1(a135) | (~c0_1(a135)))),
% 2.31/1.79 inference(quant_inst,[status(thm)],[])).
% 2.31/1.79 tff(2646,plain,
% 2.31/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c3_1(a135) | (~ndr1_0) | (~c0_1(a131)) | (~c2_1(a131)) | (~c3_1(a131)) | c1_1(a135) | (~c0_1(a135))),
% 2.31/1.79 inference(modus_ponens,[status(thm)],[2645, 2644])).
% 2.31/1.79 tff(2647,plain,
% 2.31/1.79 (c1_1(a135)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2646, 160, 2262, 2261, 2263, 2288, 2258, 98, 2627, 2286, 1679])).
% 2.31/1.79 tff(2648,plain,
% 2.31/1.79 (~c2_1(a111)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1340, 2638])).
% 2.31/1.79 tff(2649,plain,
% 2.31/1.79 (hskp13),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1962, 2648, 2283, 2647, 2640, 2639, 2288, 2287])).
% 2.31/1.79 tff(2650,plain,
% 2.31/1.79 (~c1_1(a111)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1489, 2640, 2286, 2287, 2639, 2649, 2288])).
% 2.31/1.79 tff(2651,plain,
% 2.31/1.79 (hskp3),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2589, 160, 2283, 2639, 2648, 2583, 2650])).
% 2.31/1.79 tff(2652,plain,
% 2.31/1.79 (~c1_1(a104)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2595, 2651])).
% 2.31/1.79 tff(2653,plain,
% 2.31/1.79 (c2_1(a104)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2606, 2651])).
% 2.31/1.79 tff(2654,plain,
% 2.31/1.79 (c0_1(a104)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2617, 2651])).
% 2.31/1.79 tff(2655,plain,
% 2.31/1.79 (hskp29 | (~c1_1(a135))),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1894, 160, 2283, 2288, 2287, 1888])).
% 2.31/1.79 tff(2656,plain,
% 2.31/1.79 (hskp29),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2655, 2647])).
% 2.31/1.79 tff(2657,plain,
% 2.31/1.79 (c2_1(a128)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1929, 2656])).
% 2.31/1.79 tff(2658,plain,
% 2.31/1.79 (c1_1(a128)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1918, 2656])).
% 2.31/1.79 tff(2659,plain,
% 2.31/1.79 (c0_1(a128)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1906, 2656])).
% 2.31/1.79 tff(2660,plain,
% 2.31/1.79 ($false),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2624, 23, 160, 2659, 2658, 2657, 2654, 2653, 2652, 2350])).
% 2.31/1.79 tff(2661,plain,(hskp31 | c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.31/1.79 tff(2662,plain,
% 2.31/1.79 (hskp31),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2661, 98])).
% 2.31/1.79 tff(2663,plain,
% 2.31/1.79 (c1_1(a141)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[74, 2662])).
% 2.31/1.79 tff(2664,plain,
% 2.31/1.79 (c3_1(a141)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[63, 2662])).
% 2.31/1.79 tff(2665,plain,
% 2.31/1.79 (c0_1(a141)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[85, 2662])).
% 2.31/1.79 tff(2666,assumption,(~hskp1), introduced(assumption)).
% 2.31/1.79 tff(2667,plain,
% 2.31/1.79 (hskp1 | c2_1(a141)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1406, 160, 2259, 818, 817, 21])).
% 2.31/1.79 tff(2668,plain,
% 2.31/1.79 (c2_1(a141)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2667, 2666])).
% 2.31/1.79 tff(2669,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2670,plain,
% 2.31/1.79 ((hskp1 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163))) <=> (hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2671,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141))))),
% 2.31/1.79 inference(monotonicity,[status(thm)],[2670])).
% 2.31/1.79 tff(2672,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141)))),
% 2.31/1.79 inference(transitivity,[status(thm)],[2671, 2669])).
% 2.31/1.79 tff(2673,plain,
% 2.31/1.79 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp1 | (~ndr1_0) | (~c3_1(a141)) | (~c2_1(a141)) | (~c0_1(a141)) | c2_1(a163) | (~c3_1(a163)) | (~c1_1(a163)))),
% 2.31/1.79 inference(quant_inst,[status(thm)],[])).
% 2.31/1.79 tff(2674,plain,
% 2.31/1.79 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp1 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c2_1(a141))),
% 2.31/1.79 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 2.31/1.79 tff(2675,plain,
% 2.31/1.79 (hskp1 | (~c2_1(a141))),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2674, 160, 818, 851, 2258, 98, 2627, 2360])).
% 2.31/1.79 tff(2676,plain,
% 2.31/1.79 ($false),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2675, 2668, 2666])).
% 2.31/1.79 tff(2677,plain,(hskp1 | (~c0_1(a141)) | (~c3_1(a141)) | c2_1(a163) | (~c1_1(a141))), inference(lemma,lemma(discharge,[]))).
% 2.31/1.79 tff(2678,plain,
% 2.31/1.79 (hskp1),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2677, 2665, 2664, 98, 2663])).
% 2.31/1.79 tff(2679,plain,
% 2.31/1.79 (~c1_1(a102)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1254, 2678])).
% 2.31/1.79 tff(2680,plain,
% 2.31/1.79 (~c0_1(a102)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1260, 2678])).
% 2.31/1.79 tff(2681,plain,
% 2.31/1.79 (hskp1),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2677, 86, 64, 98, 75])).
% 2.31/1.79 tff(2682,plain,
% 2.31/1.79 (~c1_1(a102)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1254, 2681])).
% 2.31/1.79 tff(2683,plain,
% 2.31/1.79 (~c0_1(a102)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1260, 2681])).
% 2.31/1.79 tff(2684,plain,
% 2.31/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a163) | (~c3_1(a163)) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a163) | (~c3_1(a163)) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | c0_1(a163))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2685,plain,
% 2.31/1.79 (((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102))) <=> (c2_1(a163) | (~c3_1(a163)) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | c0_1(a163))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2686,plain,
% 2.31/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a163) | (~c3_1(a163)) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | c0_1(a163)))),
% 2.31/1.79 inference(monotonicity,[status(thm)],[2685])).
% 2.31/1.79 tff(2687,plain,
% 2.31/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a163) | (~c3_1(a163)) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | c0_1(a163))),
% 2.31/1.79 inference(transitivity,[status(thm)],[2686, 2684])).
% 2.31/1.79 tff(2688,plain,
% 2.31/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c2_1(a163) | c0_1(a163) | (~c3_1(a163)) | c1_1(a102) | c0_1(a102) | (~c3_1(a102)))),
% 2.31/1.79 inference(quant_inst,[status(thm)],[])).
% 2.31/1.79 tff(2689,plain,
% 2.31/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a163) | (~c3_1(a163)) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c3_1(a102)) | c0_1(a163)),
% 2.31/1.79 inference(modus_ponens,[status(thm)],[2688, 2687])).
% 2.31/1.79 tff(2690,plain,
% 2.31/1.79 (~c3_1(a102)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2689, 160, 86, 75, 64, 98, 2627, 2683, 2682, 804, 245])).
% 2.31/1.79 tff(2691,plain,
% 2.31/1.79 (hskp10),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2323, 2681, 86, 75, 64])).
% 2.31/1.79 tff(2692,plain,
% 2.31/1.79 (~c3_1(a111)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1334, 2691])).
% 2.31/1.79 tff(2693,plain,
% 2.31/1.79 (~c2_1(a111)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1340, 2691])).
% 2.31/1.79 tff(2694,plain,
% 2.31/1.79 (~c0_1(a111)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1346, 2691])).
% 2.31/1.79 tff(2695,plain,
% 2.31/1.79 (hskp13),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1353, 160, 86, 75, 64, 2694, 2693, 2692, 1328])).
% 2.31/1.79 tff(2696,plain,
% 2.31/1.79 (~c3_1(a114)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[629, 2695])).
% 2.31/1.79 tff(2697,plain,
% 2.31/1.79 (c2_1(a102)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1307, 2681])).
% 2.31/1.79 tff(2698,plain,
% 2.31/1.79 (c2_1(a114)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[640, 2695])).
% 2.31/1.79 tff(2699,plain,
% 2.31/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a114) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a114)) | (~c0_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a114) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a114)) | (~c0_1(a114)))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2700,plain,
% 2.31/1.79 (((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102)) <=> (c3_1(a114) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a114)) | (~c0_1(a114)))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2701,plain,
% 2.31/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a114) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a114)) | (~c0_1(a114))))),
% 2.31/1.79 inference(monotonicity,[status(thm)],[2700])).
% 2.31/1.79 tff(2702,plain,
% 2.31/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a114) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a114)) | (~c0_1(a114)))),
% 2.31/1.79 inference(transitivity,[status(thm)],[2701, 2699])).
% 2.31/1.79 tff(2703,plain,
% 2.31/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a114) | (~c2_1(a114)) | (~c0_1(a114)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a102) | c1_1(a102) | c0_1(a102))),
% 2.31/1.79 inference(quant_inst,[status(thm)],[])).
% 2.31/1.79 tff(2704,plain,
% 2.31/1.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c3_1(a114) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a114)) | (~c0_1(a114))),
% 2.31/1.79 inference(modus_ponens,[status(thm)],[2703, 2702])).
% 2.31/1.79 tff(2705,plain,
% 2.31/1.79 (~c0_1(a114)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2704, 160, 2698, 2697, 2696, 2683, 2682, 367, 2690])).
% 2.31/1.79 tff(2706,plain,
% 2.31/1.79 (c1_1(a114)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[651, 2695])).
% 2.31/1.79 tff(2707,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c1_1(a114)) | c0_1(a114))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c1_1(a114)) | c0_1(a114))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2708,plain,
% 2.31/1.79 ((hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a114) | c3_1(a114) | (~c1_1(a114))) <=> (hskp8 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c1_1(a114)) | c0_1(a114))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2709,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a114) | c3_1(a114) | (~c1_1(a114)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c1_1(a114)) | c0_1(a114)))),
% 2.31/1.79 inference(monotonicity,[status(thm)],[2708])).
% 2.31/1.79 tff(2710,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a114) | c3_1(a114) | (~c1_1(a114)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c1_1(a114)) | c0_1(a114))),
% 2.31/1.79 inference(transitivity,[status(thm)],[2709, 2707])).
% 2.31/1.79 tff(2711,plain,
% 2.31/1.79 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c1_1(a141)) | (~c3_1(a141)) | (~c0_1(a141)) | c0_1(a114) | c3_1(a114) | (~c1_1(a114)))),
% 2.31/1.79 inference(quant_inst,[status(thm)],[])).
% 2.31/1.79 tff(2712,plain,
% 2.31/1.79 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp8 | c3_1(a114) | (~ndr1_0) | (~c0_1(a141)) | (~c3_1(a141)) | (~c1_1(a141)) | (~c1_1(a114)) | c0_1(a114)),
% 2.31/1.79 inference(modus_ponens,[status(thm)],[2711, 2710])).
% 2.31/1.79 tff(2713,plain,
% 2.31/1.79 (hskp8),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2712, 160, 86, 75, 64, 2706, 2696, 2379, 2705])).
% 2.31/1.79 tff(2714,plain,
% 2.31/1.79 (c1_1(a109)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[184, 2713])).
% 2.31/1.79 tff(2715,plain,
% 2.31/1.79 (~c3_1(a109)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[173, 2713])).
% 2.31/1.79 tff(2716,plain,
% 2.31/1.79 (~c0_1(a109)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[207, 2713])).
% 2.31/1.79 tff(2717,assumption,(~c3_1(a109)), introduced(assumption)).
% 2.31/1.79 tff(2718,assumption,(c1_1(a109)), introduced(assumption)).
% 2.31/1.79 tff(2719,plain,
% 2.31/1.79 (hskp19 | c2_1(a109)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[191, 160, 2718, 2717, 11])).
% 2.31/1.79 tff(2720,plain,
% 2.31/1.79 (c2_1(a109)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2719, 1])).
% 2.31/1.79 tff(2721,plain,
% 2.31/1.79 (hskp19 | (~c1_1(a111))),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[1425, 160, 1868, 1476, 11])).
% 2.31/1.79 tff(2722,plain,
% 2.31/1.79 (~c1_1(a111)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2721, 1])).
% 2.31/1.79 tff(2723,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2724,plain,
% 2.31/1.79 ((hskp2 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c1_1(a111) | c0_1(a111)) <=> (hskp2 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))),
% 2.31/1.79 inference(rewrite,[status(thm)],[])).
% 2.31/1.79 tff(2725,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111)))),
% 2.31/1.79 inference(monotonicity,[status(thm)],[2724])).
% 2.31/1.79 tff(2726,plain,
% 2.31/1.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111))),
% 2.31/1.79 inference(transitivity,[status(thm)],[2725, 2723])).
% 2.31/1.79 tff(2727,plain,
% 2.31/1.79 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp2 | (~ndr1_0) | c2_1(a163) | (~c1_1(a163)) | (~c3_1(a163)) | c2_1(a111) | c1_1(a111) | c0_1(a111))),
% 2.31/1.79 inference(quant_inst,[status(thm)],[])).
% 2.31/1.79 tff(2728,plain,
% 2.31/1.79 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp2 | (~c1_1(a163)) | c2_1(a163) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | (~ndr1_0) | c1_1(a111)),
% 2.31/1.79 inference(modus_ponens,[status(thm)],[2727, 2726])).
% 2.31/1.79 tff(2729,plain,
% 2.31/1.79 (hskp2 | c1_1(a111)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2728, 160, 2258, 98, 2627, 1477, 1868, 270])).
% 2.31/1.79 tff(2730,plain,
% 2.31/1.79 (hskp2),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[2729, 2722])).
% 2.31/1.79 tff(2731,plain,
% 2.31/1.79 (~c3_1(a103)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[419, 2730])).
% 2.31/1.79 tff(2732,assumption,(~c0_1(a109)), introduced(assumption)).
% 2.31/1.79 tff(2733,plain,
% 2.31/1.79 (c0_1(a103)),
% 2.31/1.79 inference(unit_resolution,[status(thm)],[308, 2730])).
% 2.31/1.79 tff(2734,plain,
% 2.31/1.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2735,plain,
% 2.31/1.80 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a111) | c1_1(a111) | c0_1(a111)) <=> (c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2736,plain,
% 2.31/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111)))),
% 2.31/1.80 inference(monotonicity,[status(thm)],[2735])).
% 2.31/1.80 tff(2737,plain,
% 2.31/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))),
% 2.31/1.80 inference(transitivity,[status(thm)],[2736, 2734])).
% 2.31/1.80 tff(2738,plain,
% 2.31/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a109) | c3_1(a109) | (~c2_1(a109)) | c3_1(a111) | c1_1(a111) | c0_1(a111))),
% 2.31/1.80 inference(quant_inst,[status(thm)],[])).
% 2.31/1.80 tff(2739,plain,
% 2.31/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c3_1(a103) | (~ndr1_0) | (~c2_1(a109)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111)),
% 2.31/1.80 inference(modus_ponens,[status(thm)],[2738, 2737])).
% 2.31/1.80 tff(2740,plain,
% 2.31/1.80 (~c2_1(a103)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2739, 160, 2733, 1477, 1476, 2732, 2717, 2731, 367, 2722, 2720])).
% 2.31/1.80 tff(2741,assumption,(~c3_1(a102)), introduced(assumption)).
% 2.31/1.80 tff(2742,plain,
% 2.31/1.80 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp17 | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2743,plain,
% 2.31/1.80 ((hskp19 | hskp17 | (~ndr1_0) | c3_1(a102) | c1_1(a102) | (~c2_1(a102))) <=> (hskp19 | hskp17 | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2744,plain,
% 2.31/1.80 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c3_1(a102) | c1_1(a102) | (~c2_1(a102)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102))))),
% 2.31/1.80 inference(monotonicity,[status(thm)],[2743])).
% 2.31/1.80 tff(2745,plain,
% 2.31/1.80 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c3_1(a102) | c1_1(a102) | (~c2_1(a102)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp17 | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)))),
% 2.31/1.80 inference(transitivity,[status(thm)],[2744, 2742])).
% 2.31/1.80 tff(2746,plain,
% 2.31/1.80 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c3_1(a102) | c1_1(a102) | (~c2_1(a102)))),
% 2.31/1.80 inference(quant_inst,[status(thm)],[])).
% 2.31/1.80 tff(2747,plain,
% 2.31/1.80 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp19 | hskp17 | c1_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102))),
% 2.31/1.80 inference(modus_ponens,[status(thm)],[2746, 2745])).
% 2.31/1.80 tff(2748,plain,
% 2.31/1.80 (hskp19 | hskp17 | c3_1(a102)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2747, 160, 2303, 2301, 1365])).
% 2.31/1.80 tff(2749,plain,
% 2.31/1.80 (hskp17),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2748, 1, 2741])).
% 2.31/1.80 tff(2750,plain,
% 2.31/1.80 (~c1_1(a132)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[831, 2749])).
% 2.31/1.80 tff(2751,plain,
% 2.31/1.80 (~c0_1(a132)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[837, 2749])).
% 2.31/1.80 tff(2752,plain,
% 2.31/1.80 (c1_1(a103)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[288, 2730])).
% 2.31/1.80 tff(2753,plain,
% 2.31/1.80 (c3_1(a132)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[849, 2749])).
% 2.31/1.80 tff(2754,plain,
% 2.31/1.80 ($false),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1465, 160, 1071, 2753, 2752, 2751, 2750, 2731, 1458, 2740])).
% 2.31/1.80 tff(2755,plain,(hskp19 | c0_1(a111) | c3_1(a111) | c0_1(a109) | c3_1(a109) | c2_1(a163) | c2_1(a111) | (~c1_1(a109)) | c3_1(a102) | (~c2_1(a102)) | c1_1(a102)), inference(lemma,lemma(discharge,[]))).
% 2.31/1.80 tff(2756,plain,
% 2.31/1.80 (hskp19),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2755, 2694, 2692, 2716, 2715, 98, 2693, 2714, 2690, 2697, 2682])).
% 2.31/1.80 tff(2757,plain,
% 2.31/1.80 (~c3_1(a135)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[432, 2756])).
% 2.31/1.80 tff(2758,plain,
% 2.31/1.80 (~c2_1(a135)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[438, 2756])).
% 2.31/1.80 tff(2759,plain,
% 2.31/1.80 (c0_1(a135)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[459, 2756])).
% 2.31/1.80 tff(2760,plain,
% 2.31/1.80 ($false),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[658, 160, 2759, 2706, 2698, 2758, 2757, 2696, 202, 2705])).
% 2.31/1.80 tff(2761,plain,((~hskp31) | c2_1(a163) | c0_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.31/1.80 tff(2762,plain,
% 2.31/1.80 (c0_1(a163)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2761, 2662, 98])).
% 2.31/1.80 tff(2763,plain,
% 2.31/1.80 (hskp10),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2323, 2665, 2678, 2663, 2664])).
% 2.31/1.80 tff(2764,plain,
% 2.31/1.80 (~c3_1(a111)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1334, 2763])).
% 2.31/1.80 tff(2765,plain,
% 2.31/1.80 (~c2_1(a111)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1340, 2763])).
% 2.31/1.80 tff(2766,plain,
% 2.31/1.80 (~c0_1(a111)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1346, 2763])).
% 2.31/1.80 tff(2767,plain,
% 2.31/1.80 (hskp13),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1353, 160, 2665, 2663, 2664, 2766, 2765, 2764, 1328])).
% 2.31/1.80 tff(2768,plain,
% 2.31/1.80 (~c3_1(a114)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[629, 2767])).
% 2.31/1.80 tff(2769,plain,
% 2.31/1.80 (c2_1(a114)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[640, 2767])).
% 2.31/1.80 tff(2770,plain,
% 2.31/1.80 (c1_1(a114)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[651, 2767])).
% 2.31/1.80 tff(2771,plain,
% 2.31/1.80 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~c1_1(a163)) | c2_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | c2_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a163)))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2772,plain,
% 2.31/1.80 ((hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163))) <=> (hskp12 | (~c1_1(a163)) | c2_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a163)))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2773,plain,
% 2.31/1.80 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~c1_1(a163)) | c2_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a163))))),
% 2.31/1.80 inference(monotonicity,[status(thm)],[2772])).
% 2.31/1.80 tff(2774,plain,
% 2.31/1.80 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | c2_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a163)))),
% 2.31/1.80 inference(transitivity,[status(thm)],[2773, 2771])).
% 2.31/1.80 tff(2775,plain,
% 2.31/1.80 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a114) | (~c1_1(a114)) | (~c2_1(a114)) | c2_1(a163) | (~c1_1(a163)) | (~c0_1(a163)))),
% 2.31/1.80 inference(quant_inst,[status(thm)],[])).
% 2.31/1.80 tff(2776,plain,
% 2.31/1.80 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | c2_1(a163) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a163))),
% 2.31/1.80 inference(modus_ponens,[status(thm)],[2775, 2774])).
% 2.31/1.80 tff(2777,plain,
% 2.31/1.80 (hskp12),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2776, 160, 2770, 2769, 2258, 98, 2768, 2027, 2762])).
% 2.31/1.80 tff(2778,plain,
% 2.31/1.80 (~c2_1(a113)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1702, 2777])).
% 2.31/1.80 tff(2779,plain,
% 2.31/1.80 (~c0_1(a113)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1736, 2777])).
% 2.31/1.80 tff(2780,plain,
% 2.31/1.80 (c3_1(a113)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1713, 2777])).
% 2.31/1.80 tff(2781,plain,
% 2.31/1.80 (~c3_1(a102)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2549, 160, 2665, 2663, 2664, 2780, 2779, 2778, 2680, 2679, 804])).
% 2.31/1.80 tff(2782,plain,
% 2.31/1.80 (c2_1(a102)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1307, 2678])).
% 2.31/1.80 tff(2783,plain,
% 2.31/1.80 (~c0_1(a114)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2704, 160, 2769, 2782, 2768, 2680, 2679, 367, 2781])).
% 2.31/1.80 tff(2784,plain,
% 2.31/1.80 (hskp8),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2712, 160, 2665, 2663, 2664, 2770, 2768, 2379, 2783])).
% 2.31/1.80 tff(2785,plain,
% 2.31/1.80 (~c3_1(a109)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[173, 2784])).
% 2.31/1.80 tff(2786,plain,
% 2.31/1.80 (~c0_1(a109)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[207, 2784])).
% 2.31/1.80 tff(2787,plain,
% 2.31/1.80 (c1_1(a109)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[184, 2784])).
% 2.31/1.80 tff(2788,plain,
% 2.31/1.80 (hskp19),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2755, 2786, 2764, 2679, 2785, 98, 2765, 2787, 2781, 2782, 2766])).
% 2.31/1.80 tff(2789,plain,
% 2.31/1.80 (~c3_1(a135)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[432, 2788])).
% 2.31/1.80 tff(2790,plain,
% 2.31/1.80 (~c2_1(a135)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[438, 2788])).
% 2.31/1.80 tff(2791,plain,
% 2.31/1.80 (c0_1(a135)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[459, 2788])).
% 2.31/1.80 tff(2792,plain,
% 2.31/1.80 ($false),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2407, 160, 2791, 2770, 2769, 2787, 2790, 2789, 2768, 2786, 2785, 202])).
% 2.31/1.80 tff(2793,plain,(c2_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.31/1.80 tff(2794,plain,
% 2.31/1.80 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp13 | hskp4 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2795,plain,
% 2.31/1.80 ((hskp13 | hskp4 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163))) <=> (hskp13 | hskp4 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2796,plain,
% 2.31/1.80 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0)))),
% 2.31/1.80 inference(monotonicity,[status(thm)],[2795])).
% 2.31/1.80 tff(2797,plain,
% 2.31/1.80 (((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)))) <=> ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp13 | hskp4 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0))),
% 2.31/1.80 inference(transitivity,[status(thm)],[2796, 2794])).
% 2.31/1.80 tff(2798,plain,
% 2.31/1.80 ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | (hskp13 | hskp4 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)))),
% 2.31/1.80 inference(quant_inst,[status(thm)],[])).
% 2.31/1.80 tff(2799,plain,
% 2.31/1.80 ((~![U: $i] : (hskp13 | hskp4 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)))) | hskp13 | hskp4 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0)),
% 2.31/1.80 inference(modus_ponens,[status(thm)],[2798, 2797])).
% 2.31/1.80 tff(2800,plain,
% 2.31/1.80 (hskp13 | hskp4 | (~c2_1(a163)) | c3_1(a163)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2799, 160, 2258, 1950])).
% 2.31/1.80 tff(2801,plain,
% 2.31/1.80 (hskp13),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2800, 2283, 2793, 97])).
% 2.31/1.80 tff(2802,plain,
% 2.31/1.80 (~c3_1(a114)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[629, 2801])).
% 2.31/1.80 tff(2803,plain,
% 2.31/1.80 (c1_1(a114)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[651, 2801])).
% 2.31/1.80 tff(2804,plain,
% 2.31/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | c0_1(a114) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | c0_1(a114) | (~c0_1(a135)))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2805,plain,
% 2.31/1.80 (((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114))) <=> ((~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | c0_1(a114) | (~c0_1(a135)))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2806,plain,
% 2.31/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | c0_1(a114) | (~c0_1(a135))))),
% 2.31/1.80 inference(monotonicity,[status(thm)],[2805])).
% 2.31/1.80 tff(2807,plain,
% 2.31/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | c0_1(a114) | (~c0_1(a135)))),
% 2.31/1.80 inference(transitivity,[status(thm)],[2806, 2804])).
% 2.31/1.80 tff(2808,plain,
% 2.31/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a114) | c0_1(a114) | (~c1_1(a114)))),
% 2.31/1.80 inference(quant_inst,[status(thm)],[])).
% 2.31/1.80 tff(2809,plain,
% 2.31/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | c3_1(a114) | (~ndr1_0) | (~c1_1(a114)) | c0_1(a114) | (~c0_1(a135))),
% 2.31/1.80 inference(modus_ponens,[status(thm)],[2808, 2807])).
% 2.31/1.80 tff(2810,plain,
% 2.31/1.80 (c0_1(a114)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2809, 160, 2288, 2803, 2258, 2793, 97, 2287, 2286, 2802, 202])).
% 2.31/1.80 tff(2811,plain,
% 2.31/1.80 (~c1_1(a111)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1489, 2286, 2336, 2287, 2340, 2801, 2288])).
% 2.31/1.80 tff(2812,plain,
% 2.31/1.80 (hskp4 | hskp3 | c1_1(a111)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2589, 160, 2340, 2337, 2583])).
% 2.31/1.80 tff(2813,plain,
% 2.31/1.80 (hskp3),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2812, 2811, 2283])).
% 2.31/1.80 tff(2814,plain,
% 2.31/1.80 (~c1_1(a104)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2595, 2813])).
% 2.31/1.80 tff(2815,plain,
% 2.31/1.80 (c2_1(a104)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2606, 2813])).
% 2.31/1.80 tff(2816,plain,
% 2.31/1.80 (c0_1(a104)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2617, 2813])).
% 2.31/1.80 tff(2817,plain,
% 2.31/1.80 (c2_1(a114)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[640, 2801])).
% 2.31/1.80 tff(2818,plain,
% 2.31/1.80 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2819,plain,
% 2.31/1.80 ((hskp31 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104))) <=> (hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2820,plain,
% 2.31/1.80 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114))))),
% 2.31/1.80 inference(monotonicity,[status(thm)],[2819])).
% 2.31/1.80 tff(2821,plain,
% 2.31/1.80 (((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)))),
% 2.31/1.80 inference(transitivity,[status(thm)],[2820, 2818])).
% 2.31/1.80 tff(2822,plain,
% 2.31/1.80 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp31 | (~ndr1_0) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114)) | c1_1(a104) | (~c0_1(a104)) | (~c2_1(a104)))),
% 2.31/1.80 inference(quant_inst,[status(thm)],[])).
% 2.31/1.80 tff(2823,plain,
% 2.31/1.80 ((~![V: $i, U: $i] : (hskp31 | (~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp31 | c1_1(a104) | (~ndr1_0) | (~c0_1(a104)) | (~c2_1(a104)) | (~c1_1(a114)) | (~c2_1(a114)) | (~c0_1(a114))),
% 2.31/1.80 inference(modus_ponens,[status(thm)],[2822, 2821])).
% 2.31/1.80 tff(2824,plain,
% 2.31/1.80 ($false),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2823, 23, 160, 2803, 2817, 2816, 2815, 2814, 2350, 2810])).
% 2.31/1.80 tff(2825,plain,(hskp31 | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.31/1.80 tff(2826,plain,
% 2.31/1.80 (hskp31),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2825, 97])).
% 2.31/1.80 tff(2827,plain,
% 2.31/1.80 (c3_1(a141)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[63, 2826])).
% 2.31/1.80 tff(2828,plain,
% 2.31/1.80 (c0_1(a141)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[85, 2826])).
% 2.31/1.80 tff(2829,plain,
% 2.31/1.80 (~c2_1(a141)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2328, 1, 2828, 2827])).
% 2.31/1.80 tff(2830,plain,
% 2.31/1.80 (c1_1(a141)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[74, 2826])).
% 2.31/1.80 tff(2831,plain,
% 2.31/1.80 (hskp2),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2129, 160, 2830, 2827, 2340, 2337, 270, 2829, 2339])).
% 2.31/1.80 tff(2832,plain,
% 2.31/1.80 (~c3_1(a103)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[419, 2831])).
% 2.31/1.80 tff(2833,plain,
% 2.31/1.80 (c1_1(a103)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[288, 2831])).
% 2.31/1.80 tff(2834,plain,
% 2.31/1.80 (c2_1(a103)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[296, 160, 1, 2833, 2832, 11])).
% 2.31/1.80 tff(2835,plain,
% 2.31/1.80 (hskp1 | c2_1(a141)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1406, 160, 2259, 2828, 2830, 21])).
% 2.31/1.80 tff(2836,plain,
% 2.31/1.80 (hskp1),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2835, 2829])).
% 2.31/1.80 tff(2837,plain,
% 2.31/1.80 (~c1_1(a102)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1254, 2836])).
% 2.31/1.80 tff(2838,plain,
% 2.31/1.80 (~c0_1(a102)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1260, 2836])).
% 2.31/1.80 tff(2839,plain,
% 2.31/1.80 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2840,plain,
% 2.31/1.80 ((hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141))) <=> (hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2841,plain,
% 2.31/1.80 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141))))),
% 2.31/1.80 inference(monotonicity,[status(thm)],[2840])).
% 2.31/1.80 tff(2842,plain,
% 2.31/1.80 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141)))),
% 2.31/1.80 inference(transitivity,[status(thm)],[2841, 2839])).
% 2.31/1.80 tff(2843,plain,
% 2.31/1.80 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a141) | (~c1_1(a141)) | (~c0_1(a141)))),
% 2.31/1.80 inference(quant_inst,[status(thm)],[])).
% 2.31/1.80 tff(2844,plain,
% 2.31/1.80 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | (~ndr1_0) | (~c0_1(a141)) | c2_1(a141) | (~c1_1(a141))),
% 2.31/1.80 inference(modus_ponens,[status(thm)],[2843, 2842])).
% 2.31/1.80 tff(2845,plain,
% 2.31/1.80 (hskp12),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2844, 160, 2828, 2830, 2258, 2793, 97, 2027, 2829])).
% 2.31/1.80 tff(2846,plain,
% 2.31/1.80 (~c2_1(a113)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1702, 2845])).
% 2.31/1.80 tff(2847,plain,
% 2.31/1.80 (~c0_1(a113)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1736, 2845])).
% 2.31/1.80 tff(2848,plain,
% 2.31/1.80 (c3_1(a113)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1713, 2845])).
% 2.31/1.80 tff(2849,plain,
% 2.31/1.80 (~c3_1(a102)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2549, 160, 2828, 2830, 2827, 2848, 2847, 2846, 2838, 2837, 804])).
% 2.31/1.80 tff(2850,plain,
% 2.31/1.80 (c2_1(a102)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1307, 2836])).
% 2.31/1.80 tff(2851,plain,
% 2.31/1.80 (c0_1(a103)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[308, 2831])).
% 2.31/1.80 tff(2852,plain,
% 2.31/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a111) | c3_1(a111) | c3_1(a103) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a111) | c3_1(a111) | c3_1(a103) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2853,plain,
% 2.31/1.80 (((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111)) <=> (c0_1(a111) | c3_1(a111) | c3_1(a103) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))),
% 2.31/1.80 inference(rewrite,[status(thm)],[])).
% 2.31/1.80 tff(2854,plain,
% 2.31/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a111) | c3_1(a111) | c3_1(a103) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111)))),
% 2.31/1.80 inference(monotonicity,[status(thm)],[2853])).
% 2.31/1.80 tff(2855,plain,
% 2.31/1.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a111) | c3_1(a111) | c3_1(a103) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111))),
% 2.31/1.80 inference(transitivity,[status(thm)],[2854, 2852])).
% 2.31/1.80 tff(2856,plain,
% 2.31/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a103) | (~c2_1(a103)) | (~c0_1(a103)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))),
% 2.31/1.80 inference(quant_inst,[status(thm)],[])).
% 2.31/1.80 tff(2857,plain,
% 2.31/1.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a111) | c3_1(a111) | c3_1(a103) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c2_1(a103)) | (~c0_1(a103)) | c1_1(a111)),
% 2.31/1.80 inference(modus_ponens,[status(thm)],[2856, 2855])).
% 2.31/1.80 tff(2858,plain,
% 2.31/1.80 (c3_1(a102) | (~c2_1(a103))),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2857, 160, 2851, 2850, 2340, 2336, 2832, 2838, 367, 2339])).
% 2.31/1.80 tff(2859,plain,
% 2.31/1.80 ($false),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2858, 2849, 2834])).
% 2.31/1.80 tff(2860,plain,(hskp19 | c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.31/1.80 tff(2861,plain,
% 2.31/1.80 (hskp19),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[2860, 97])).
% 2.31/1.80 tff(2862,plain,
% 2.31/1.80 (c0_1(a135)),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[459, 2861])).
% 2.31/1.80 tff(2863,plain,
% 2.31/1.80 (hskp13),
% 2.31/1.80 inference(unit_resolution,[status(thm)],[1353, 160, 2828, 2830, 2827, 2340, 2337, 2336, 1328])).
% 2.31/1.81 tff(2864,plain,
% 2.31/1.81 (~c2_1(a135)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[438, 2861])).
% 2.31/1.81 tff(2865,plain,
% 2.31/1.81 (~c3_1(a135)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[432, 2861])).
% 2.31/1.81 tff(2866,plain,
% 2.31/1.81 (~c1_1(a111)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1489, 2865, 2336, 2864, 2340, 2863, 2862])).
% 2.31/1.81 tff(2867,plain,
% 2.31/1.81 (hskp5 | c1_1(a111)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1787, 160, 2340, 2336, 227])).
% 2.31/1.81 tff(2868,plain,
% 2.31/1.81 (hskp5),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[2867, 2866])).
% 2.31/1.81 tff(2869,plain,
% 2.31/1.81 (~c2_1(a106)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[976, 2868])).
% 2.31/1.81 tff(2870,plain,
% 2.31/1.81 (c1_1(a106)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[257, 2868])).
% 2.31/1.81 tff(2871,plain,
% 2.31/1.81 (c0_1(a106)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[337, 2868])).
% 2.31/1.81 tff(2872,plain,
% 2.31/1.81 (hskp1),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1818, 160, 2259, 2871, 2870, 2869, 21])).
% 2.31/1.81 tff(2873,plain,
% 2.31/1.81 (~c1_1(a102)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1254, 2872])).
% 2.31/1.81 tff(2874,plain,
% 2.31/1.81 (~c0_1(a102)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1260, 2872])).
% 2.31/1.81 tff(2875,plain,
% 2.31/1.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))),
% 2.31/1.81 inference(rewrite,[status(thm)],[])).
% 2.31/1.81 tff(2876,plain,
% 2.31/1.81 ((hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106))) <=> (hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))),
% 2.31/1.81 inference(rewrite,[status(thm)],[])).
% 2.31/1.81 tff(2877,plain,
% 2.31/1.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106))))),
% 2.31/1.81 inference(monotonicity,[status(thm)],[2876])).
% 2.31/1.81 tff(2878,plain,
% 2.31/1.81 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106)))),
% 2.31/1.81 inference(transitivity,[status(thm)],[2877, 2875])).
% 2.31/1.81 tff(2879,plain,
% 2.31/1.81 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a106) | (~c1_1(a106)) | (~c0_1(a106)))),
% 2.31/1.81 inference(quant_inst,[status(thm)],[])).
% 2.31/1.81 tff(2880,plain,
% 2.31/1.81 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a106) | (~ndr1_0) | (~c0_1(a106)) | (~c1_1(a106))),
% 2.31/1.81 inference(modus_ponens,[status(thm)],[2879, 2878])).
% 2.31/1.81 tff(2881,plain,
% 2.31/1.81 (hskp12),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[2880, 160, 2871, 2870, 2258, 2793, 97, 2869, 2027])).
% 2.31/1.81 tff(2882,plain,
% 2.31/1.81 (~c2_1(a113)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1702, 2881])).
% 2.31/1.81 tff(2883,plain,
% 2.31/1.81 (~c0_1(a113)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1736, 2881])).
% 2.31/1.81 tff(2884,plain,
% 2.31/1.81 (c3_1(a113)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1713, 2881])).
% 2.31/1.81 tff(2885,plain,
% 2.31/1.81 (~c3_1(a102)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[2549, 160, 2828, 2830, 2827, 2884, 2883, 2882, 2874, 2873, 804])).
% 2.31/1.81 tff(2886,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | c0_1(a163))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | c0_1(a163))),
% 2.31/1.81 inference(rewrite,[status(thm)],[])).
% 2.31/1.81 tff(2887,plain,
% 2.31/1.81 (((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c0_1(a163) | (~c1_1(a163))) <=> ((~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | c0_1(a163))),
% 2.31/1.81 inference(rewrite,[status(thm)],[])).
% 2.31/1.81 tff(2888,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c0_1(a163) | (~c1_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | c0_1(a163)))),
% 2.31/1.81 inference(monotonicity,[status(thm)],[2887])).
% 2.31/1.81 tff(2889,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c0_1(a163) | (~c1_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | c0_1(a163))),
% 2.31/1.81 inference(transitivity,[status(thm)],[2888, 2886])).
% 2.31/1.81 tff(2890,plain,
% 2.31/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a163) | (~c1_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a163) | c0_1(a163) | (~c1_1(a163)))),
% 2.31/1.81 inference(quant_inst,[status(thm)],[])).
% 2.31/1.81 tff(2891,plain,
% 2.31/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (~c1_1(a163)) | (~c2_1(a163)) | c3_1(a163) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | (~c0_1(a135)) | c0_1(a163)),
% 2.31/1.81 inference(modus_ponens,[status(thm)],[2890, 2889])).
% 2.31/1.81 tff(2892,plain,
% 2.31/1.81 (c0_1(a163)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[2891, 160, 2862, 2258, 2793, 97, 2864, 2865, 202])).
% 2.31/1.81 tff(2893,plain,
% 2.31/1.81 (c2_1(a102)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1307, 2872])).
% 2.31/1.81 tff(2894,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~c2_1(a163)) | c3_1(a163) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c0_1(a163)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c2_1(a163)) | c3_1(a163) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c0_1(a163)))),
% 2.31/1.81 inference(rewrite,[status(thm)],[])).
% 2.31/1.81 tff(2895,plain,
% 2.31/1.81 (((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111)) <=> ((~c2_1(a163)) | c3_1(a163) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c0_1(a163)))),
% 2.31/1.81 inference(rewrite,[status(thm)],[])).
% 2.31/1.81 tff(2896,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~c2_1(a163)) | c3_1(a163) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c0_1(a163))))),
% 2.31/1.81 inference(monotonicity,[status(thm)],[2895])).
% 2.31/1.81 tff(2897,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c2_1(a163)) | c3_1(a163) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c0_1(a163)))),
% 2.31/1.81 inference(transitivity,[status(thm)],[2896, 2894])).
% 2.31/1.81 tff(2898,plain,
% 2.31/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a163) | (~c2_1(a163)) | (~c0_1(a163)) | c0_1(a102) | c3_1(a102) | (~c2_1(a102)) | c3_1(a111) | c1_1(a111) | c0_1(a111))),
% 2.31/1.81 inference(quant_inst,[status(thm)],[])).
% 2.31/1.81 tff(2899,plain,
% 2.31/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (~c2_1(a163)) | c3_1(a163) | c0_1(a111) | c3_1(a111) | c0_1(a102) | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | c1_1(a111) | (~c0_1(a163))),
% 2.31/1.81 inference(modus_ponens,[status(thm)],[2898, 2897])).
% 2.31/1.81 tff(2900,plain,
% 2.31/1.81 ($false),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[2899, 160, 2893, 2793, 97, 2340, 2336, 2874, 367, 2892, 2866, 2885])).
% 2.31/1.81 tff(2901,plain,(c3_1(a163)), inference(lemma,lemma(discharge,[]))).
% 2.31/1.81 tff(2902,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)))),
% 2.31/1.81 inference(rewrite,[status(thm)],[])).
% 2.31/1.81 tff(2903,plain,
% 2.31/1.81 (((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111)) <=> ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)))),
% 2.31/1.81 inference(rewrite,[status(thm)],[])).
% 2.31/1.81 tff(2904,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135))))),
% 2.31/1.81 inference(monotonicity,[status(thm)],[2903])).
% 2.31/1.81 tff(2905,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135)))),
% 2.31/1.81 inference(transitivity,[status(thm)],[2904, 2902])).
% 2.31/1.81 tff(2906,plain,
% 2.31/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a111) | c1_1(a111) | c2_1(a111))),
% 2.31/1.81 inference(quant_inst,[status(thm)],[])).
% 2.31/1.81 tff(2907,plain,
% 2.31/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | c2_1(a111) | c3_1(a111) | (~ndr1_0) | c1_1(a111) | (~c0_1(a135))),
% 2.31/1.81 inference(modus_ponens,[status(thm)],[2906, 2905])).
% 2.31/1.81 tff(2908,plain,
% 2.31/1.81 (c1_1(a111)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[2907, 160, 2288, 2258, 2793, 2901, 2287, 2286, 2337, 2336, 108])).
% 2.31/1.81 tff(2909,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)))),
% 2.31/1.81 inference(rewrite,[status(thm)],[])).
% 2.31/1.81 tff(2910,plain,
% 2.31/1.81 (((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135)) <=> ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)))),
% 2.31/1.81 inference(rewrite,[status(thm)],[])).
% 2.31/1.81 tff(2911,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135))))),
% 2.31/1.81 inference(monotonicity,[status(thm)],[2910])).
% 2.31/1.81 tff(2912,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135)))),
% 2.31/1.81 inference(transitivity,[status(thm)],[2911, 2909])).
% 2.31/1.81 tff(2913,plain,
% 2.31/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c2_1(a135) | c3_1(a135) | (~c0_1(a135)) | c3_1(a135) | c1_1(a135) | c2_1(a135))),
% 2.31/1.81 inference(quant_inst,[status(thm)],[])).
% 2.31/1.81 tff(2914,plain,
% 2.31/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c1_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c2_1(a135) | c3_1(a135) | (~ndr1_0) | c1_1(a135) | (~c0_1(a135))),
% 2.31/1.81 inference(modus_ponens,[status(thm)],[2913, 2912])).
% 2.31/1.81 tff(2915,plain,
% 2.31/1.81 (c1_1(a135)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[2914, 160, 2288, 2258, 2793, 2901, 2287, 2286, 108])).
% 2.31/1.81 tff(2916,plain,
% 2.31/1.81 (hskp13),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1962, 2915, 2337, 2283, 2336, 2340, 2288, 2287])).
% 2.31/1.81 tff(2917,plain,
% 2.31/1.81 ($false),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1489, 2916, 2908, 2336, 2287, 2340, 2286, 2288])).
% 2.31/1.81 tff(2918,plain,(hskp31), inference(lemma,lemma(discharge,[]))).
% 2.31/1.81 tff(2919,plain,
% 2.31/1.81 (c3_1(a141)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[63, 2918])).
% 2.31/1.81 tff(2920,plain,
% 2.31/1.81 (c0_1(a141)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[85, 2918])).
% 2.31/1.81 tff(2921,plain,
% 2.31/1.81 (~c2_1(a141)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[2328, 1, 2920, 2919])).
% 2.31/1.81 tff(2922,plain,
% 2.31/1.81 (c1_1(a141)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[74, 2918])).
% 2.31/1.81 tff(2923,plain,
% 2.31/1.81 (hskp1 | c2_1(a141)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1406, 160, 2259, 2920, 2922, 21])).
% 2.31/1.81 tff(2924,plain,
% 2.31/1.81 (hskp1),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[2923, 2921])).
% 2.31/1.81 tff(2925,plain,
% 2.31/1.81 (~c1_1(a102)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1254, 2924])).
% 2.31/1.81 tff(2926,plain,
% 2.31/1.81 (~c0_1(a102)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1260, 2924])).
% 2.31/1.81 tff(2927,plain,
% 2.31/1.81 (c2_1(a102)),
% 2.31/1.81 inference(unit_resolution,[status(thm)],[1307, 2924])).
% 2.31/1.81 tff(2928,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | c1_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | c1_1(a111))),
% 2.31/1.81 inference(rewrite,[status(thm)],[])).
% 2.31/1.81 tff(2929,plain,
% 2.31/1.81 (((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a111) | c0_1(a111) | c2_1(a111)) <=> ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | c1_1(a111))),
% 2.31/1.81 inference(rewrite,[status(thm)],[])).
% 2.31/1.81 tff(2930,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a111) | c0_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | c1_1(a111)))),
% 2.31/1.81 inference(monotonicity,[status(thm)],[2929])).
% 2.31/1.81 tff(2931,plain,
% 2.31/1.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a111) | c0_1(a111) | c2_1(a111))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | c1_1(a111))),
% 2.31/1.81 inference(transitivity,[status(thm)],[2930, 2928])).
% 2.31/1.81 tff(2932,plain,
% 2.31/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a163)) | (~c3_1(a163)) | (~c2_1(a163)) | c1_1(a102) | c0_1(a102) | (~c2_1(a102)) | c1_1(a111) | c0_1(a111) | c2_1(a111))),
% 2.31/1.81 inference(quant_inst,[status(thm)],[])).
% 2.31/1.81 tff(2933,plain,
% 2.31/1.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W) | c2_1(W))) | (~c1_1(a163)) | (~c2_1(a163)) | (~c3_1(a163)) | c0_1(a111) | c2_1(a111) | c0_1(a102) | c1_1(a102) | (~ndr1_0) | (~c2_1(a102)) | c1_1(a111)),
% 2.31/1.82 inference(modus_ponens,[status(thm)],[2932, 2931])).
% 2.31/1.82 tff(2934,plain,
% 2.31/1.82 ($false),
% 2.31/1.82 inference(unit_resolution,[status(thm)],[2933, 160, 2927, 2258, 2793, 2901, 2340, 2337, 2926, 2925, 1233, 2339])).
% 2.31/1.82 tff(2935,plain,(hskp19), inference(lemma,lemma(discharge,[]))).
% 2.31/1.82 tff(2936,plain,
% 2.31/1.82 (c0_1(a135)),
% 2.31/1.82 inference(unit_resolution,[status(thm)],[459, 2935])).
% 2.31/1.82 tff(2937,plain,
% 2.31/1.82 (~c2_1(a135)),
% 2.31/1.82 inference(unit_resolution,[status(thm)],[438, 2935])).
% 2.31/1.82 tff(2938,plain,
% 2.31/1.82 (hskp13),
% 2.31/1.82 inference(unit_resolution,[status(thm)],[1353, 160, 2920, 2922, 2919, 2340, 2337, 2336, 1328])).
% 2.31/1.82 tff(2939,plain,
% 2.31/1.82 (~c3_1(a135)),
% 2.31/1.82 inference(unit_resolution,[status(thm)],[432, 2935])).
% 2.31/1.82 tff(2940,plain,
% 2.31/1.82 (~c1_1(a111)),
% 2.31/1.82 inference(unit_resolution,[status(thm)],[1489, 2939, 2336, 2938, 2340, 2937, 2936])).
% 2.31/1.82 tff(2941,plain,
% 2.31/1.82 ($false),
% 2.31/1.82 inference(unit_resolution,[status(thm)],[2907, 160, 2936, 2258, 2793, 2901, 2937, 2939, 2337, 2336, 108, 2940])).
% 2.31/1.82 % SZS output end Proof
%------------------------------------------------------------------------------