TSTP Solution File: SYN483-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN483-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 23:55:49 EDT 2022
% Result : Unsatisfiable 0.83s 0.77s
% Output : Proof 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN483-1 : TPTP v8.1.0. Released v2.1.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 04:22:18 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.83/0.77 % SZS status Unsatisfiable
% 0.83/0.77 % SZS output start Proof
% 0.83/0.77 tff(c3_1_type, type, (
% 0.83/0.77 c3_1: $i > $o)).
% 0.83/0.77 tff(a1862_type, type, (
% 0.83/0.77 a1862: $i)).
% 0.83/0.77 tff(c2_1_type, type, (
% 0.83/0.77 c2_1: $i > $o)).
% 0.83/0.77 tff(c0_1_type, type, (
% 0.83/0.77 c0_1: $i > $o)).
% 0.83/0.77 tff(c1_1_type, type, (
% 0.83/0.77 c1_1: $i > $o)).
% 0.83/0.77 tff(ndr1_0_type, type, (
% 0.83/0.77 ndr1_0: $o)).
% 0.83/0.77 tff(hskp8_type, type, (
% 0.83/0.77 hskp8: $o)).
% 0.83/0.77 tff(hskp9_type, type, (
% 0.83/0.77 hskp9: $o)).
% 0.83/0.77 tff(a1890_type, type, (
% 0.83/0.77 a1890: $i)).
% 0.83/0.77 tff(hskp20_type, type, (
% 0.83/0.77 hskp20: $o)).
% 0.83/0.77 tff(a1864_type, type, (
% 0.83/0.77 a1864: $i)).
% 0.83/0.77 tff(hskp24_type, type, (
% 0.83/0.77 hskp24: $o)).
% 0.83/0.77 tff(a1919_type, type, (
% 0.83/0.77 a1919: $i)).
% 0.83/0.77 tff(a1853_type, type, (
% 0.83/0.77 a1853: $i)).
% 0.83/0.77 tff(hskp1_type, type, (
% 0.83/0.77 hskp1: $o)).
% 0.83/0.77 tff(a1877_type, type, (
% 0.83/0.77 a1877: $i)).
% 0.83/0.77 tff(a1852_type, type, (
% 0.83/0.77 a1852: $i)).
% 0.83/0.77 tff(hskp0_type, type, (
% 0.83/0.77 hskp0: $o)).
% 0.83/0.77 tff(a1858_type, type, (
% 0.83/0.77 a1858: $i)).
% 0.83/0.77 tff(hskp26_type, type, (
% 0.83/0.77 hskp26: $o)).
% 0.83/0.77 tff(hskp23_type, type, (
% 0.83/0.77 hskp23: $o)).
% 0.83/0.77 tff(a1878_type, type, (
% 0.83/0.77 a1878: $i)).
% 0.83/0.77 tff(hskp28_type, type, (
% 0.83/0.77 hskp28: $o)).
% 0.83/0.77 tff(hskp27_type, type, (
% 0.83/0.77 hskp27: $o)).
% 0.83/0.77 tff(hskp29_type, type, (
% 0.83/0.77 hskp29: $o)).
% 0.83/0.77 tff(a1885_type, type, (
% 0.83/0.77 a1885: $i)).
% 0.83/0.77 tff(a1911_type, type, (
% 0.83/0.77 a1911: $i)).
% 0.83/0.77 tff(a1899_type, type, (
% 0.83/0.77 a1899: $i)).
% 0.83/0.77 tff(hskp22_type, type, (
% 0.83/0.77 hskp22: $o)).
% 0.83/0.77 tff(hskp3_type, type, (
% 0.83/0.77 hskp3: $o)).
% 0.83/0.77 tff(a1855_type, type, (
% 0.83/0.77 a1855: $i)).
% 0.83/0.77 tff(a1872_type, type, (
% 0.83/0.77 a1872: $i)).
% 0.83/0.77 tff(hskp16_type, type, (
% 0.83/0.77 hskp16: $o)).
% 0.83/0.77 tff(hskp10_type, type, (
% 0.83/0.77 hskp10: $o)).
% 0.83/0.77 tff(hskp13_type, type, (
% 0.83/0.77 hskp13: $o)).
% 0.83/0.77 tff(a1898_type, type, (
% 0.83/0.77 a1898: $i)).
% 0.83/0.77 tff(hskp21_type, type, (
% 0.83/0.77 hskp21: $o)).
% 0.83/0.77 tff(a1875_type, type, (
% 0.83/0.77 a1875: $i)).
% 0.83/0.77 tff(a1867_type, type, (
% 0.83/0.77 a1867: $i)).
% 0.83/0.77 tff(a1863_type, type, (
% 0.83/0.77 a1863: $i)).
% 0.83/0.77 tff(a1866_type, type, (
% 0.83/0.77 a1866: $i)).
% 0.83/0.77 tff(hskp12_type, type, (
% 0.83/0.77 hskp12: $o)).
% 0.83/0.77 tff(hskp18_type, type, (
% 0.83/0.77 hskp18: $o)).
% 0.83/0.77 tff(a1874_type, type, (
% 0.83/0.77 a1874: $i)).
% 0.83/0.77 tff(hskp17_type, type, (
% 0.83/0.77 hskp17: $o)).
% 0.83/0.77 tff(a1870_type, type, (
% 0.83/0.77 a1870: $i)).
% 0.83/0.77 tff(hskp15_type, type, (
% 0.83/0.77 hskp15: $o)).
% 0.83/0.77 tff(1,plain,
% 0.83/0.77 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 0.83/0.77 inference(bind,[status(th)],[])).
% 0.83/0.77 tff(2,plain,
% 0.83/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.77 inference(quant_intro,[status(thm)],[1])).
% 0.83/0.77 tff(3,plain,
% 0.83/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.77 inference(rewrite,[status(thm)],[])).
% 0.83/0.77 tff(4,plain,
% 0.83/0.77 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 0.83/0.77 inference(bind,[status(th)],[])).
% 0.83/0.77 tff(5,plain,
% 0.83/0.77 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.77 inference(quant_intro,[status(thm)],[4])).
% 0.83/0.77 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.83/0.77 tff(7,plain,
% 0.83/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.83/0.77 tff(8,plain,
% 0.83/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.83/0.77 tff(9,plain,(
% 0.83/0.77 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.77 inference(skolemize,[status(sab)],[8])).
% 0.83/0.77 tff(10,plain,
% 0.83/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.83/0.77 tff(11,plain,
% 0.83/0.77 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.83/0.77 inference(bind,[status(th)],[])).
% 0.83/0.77 tff(12,plain,
% 0.83/0.77 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.83/0.77 inference(quant_intro,[status(thm)],[11])).
% 0.83/0.77 tff(13,plain,
% 0.83/0.77 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.83/0.77 inference(rewrite,[status(thm)],[])).
% 0.83/0.77 tff(14,plain,
% 0.83/0.77 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.83/0.77 inference(bind,[status(th)],[])).
% 0.83/0.77 tff(15,plain,
% 0.83/0.77 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.83/0.77 inference(quant_intro,[status(thm)],[14])).
% 0.83/0.77 tff(16,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.83/0.77 tff(17,plain,
% 0.83/0.77 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.83/0.77 tff(18,plain,
% 0.83/0.77 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.83/0.77 tff(19,plain,(
% 0.83/0.77 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.83/0.77 inference(skolemize,[status(sab)],[18])).
% 0.83/0.77 tff(20,plain,
% 0.83/0.77 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.83/0.77 tff(21,assumption,(~hskp8), introduced(assumption)).
% 0.83/0.77 tff(22,plain,
% 0.83/0.77 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.83/0.77 inference(bind,[status(th)],[])).
% 0.83/0.77 tff(23,plain,
% 0.83/0.77 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.83/0.77 inference(quant_intro,[status(thm)],[22])).
% 0.83/0.77 tff(24,plain,
% 0.83/0.77 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.83/0.77 inference(rewrite,[status(thm)],[])).
% 0.83/0.77 tff(25,plain,
% 0.83/0.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.83/0.77 inference(bind,[status(th)],[])).
% 0.83/0.77 tff(26,plain,
% 0.83/0.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.83/0.77 inference(quant_intro,[status(thm)],[25])).
% 0.83/0.77 tff(27,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 0.83/0.77 tff(28,plain,
% 0.83/0.77 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.83/0.77 tff(29,plain,
% 0.83/0.77 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.83/0.77 tff(30,plain,(
% 0.83/0.77 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.83/0.77 inference(skolemize,[status(sab)],[29])).
% 0.83/0.77 tff(31,plain,
% 0.83/0.77 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.83/0.77 tff(32,assumption,(~hskp1), introduced(assumption)).
% 0.83/0.77 tff(33,plain,
% 0.83/0.77 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 0.83/0.77 inference(bind,[status(th)],[])).
% 0.83/0.77 tff(34,plain,
% 0.83/0.77 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.83/0.77 inference(quant_intro,[status(thm)],[33])).
% 0.83/0.77 tff(35,plain,
% 0.83/0.77 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.83/0.77 inference(rewrite,[status(thm)],[])).
% 0.83/0.77 tff(36,plain,
% 0.83/0.77 (^[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(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | 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))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | 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))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | 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)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | 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)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | 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)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 0.83/0.77 inference(bind,[status(th)],[])).
% 0.83/0.77 tff(37,plain,
% 0.83/0.77 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.83/0.77 inference(quant_intro,[status(thm)],[36])).
% 0.83/0.77 tff(38,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause163')).
% 0.83/0.77 tff(39,plain,
% 0.83/0.77 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.83/0.77 tff(40,plain,
% 0.83/0.77 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.83/0.77 tff(41,plain,(
% 0.83/0.77 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.83/0.77 inference(skolemize,[status(sab)],[40])).
% 0.83/0.77 tff(42,plain,
% 0.83/0.77 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.83/0.77 tff(43,assumption,(~hskp0), introduced(assumption)).
% 0.83/0.77 tff(44,plain,
% 0.83/0.77 (^[U: $i] : refl((hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.83/0.77 inference(bind,[status(th)],[])).
% 0.83/0.77 tff(45,plain,
% 0.83/0.77 (![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.77 inference(quant_intro,[status(thm)],[44])).
% 0.83/0.77 tff(46,plain,
% 0.83/0.77 (![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.77 inference(rewrite,[status(thm)],[])).
% 0.83/0.77 tff(47,plain,
% 0.83/0.77 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp24) <=> ((hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp24) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.83/0.77 inference(bind,[status(th)],[])).
% 0.83/0.77 tff(48,plain,
% 0.83/0.77 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp24) <=> ![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.77 inference(quant_intro,[status(thm)],[47])).
% 0.83/0.77 tff(49,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp0) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 0.83/0.77 tff(50,plain,
% 0.83/0.77 (![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.83/0.77 tff(51,plain,
% 0.83/0.77 (![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.77 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.83/0.77 tff(52,plain,(
% 0.83/0.77 ![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.77 inference(skolemize,[status(sab)],[51])).
% 0.83/0.78 tff(53,plain,
% 0.83/0.78 (![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.83/0.78 tff(54,plain,
% 0.83/0.78 (^[U: $i] : refl((hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(55,plain,
% 0.83/0.78 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[54])).
% 0.83/0.78 tff(56,plain,
% 0.83/0.78 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(57,plain,
% 0.83/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) | hskp0) <=> ((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp0))), rewrite(((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp0) <=> (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) | hskp0) <=> (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(58,plain,
% 0.83/0.78 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) | hskp0) <=> ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[57])).
% 0.83/0.78 tff(59,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp28) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 0.83/0.78 tff(60,plain,
% 0.83/0.78 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.83/0.78 tff(61,plain,
% 0.83/0.78 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.83/0.78 tff(62,plain,(
% 0.83/0.78 ![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.78 inference(skolemize,[status(sab)],[61])).
% 0.83/0.78 tff(63,plain,
% 0.83/0.78 (![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.83/0.78 tff(64,assumption,(~hskp24), introduced(assumption)).
% 0.83/0.78 tff(65,assumption,(hskp29), introduced(assumption)).
% 0.83/0.78 tff(66,plain,
% 0.83/0.78 (((~hskp29) | c2_1(a1885)) <=> ((~hskp29) | c2_1(a1885))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(67,axiom,((~hskp29) | c2_1(a1885)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.83/0.78 tff(68,plain,
% 0.83/0.78 ((~hskp29) | c2_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.83/0.78 tff(69,plain,
% 0.83/0.78 ((~hskp29) | c2_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[68, 66])).
% 0.83/0.78 tff(70,plain,
% 0.83/0.78 ((~hskp29) | c2_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.83/0.78 tff(71,plain,
% 0.83/0.78 ((~hskp29) | c2_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.83/0.78 tff(72,plain,
% 0.83/0.78 ((~hskp29) | c2_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[71, 66])).
% 0.83/0.78 tff(73,plain,
% 0.83/0.78 ((~hskp29) | c2_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[72, 66])).
% 0.83/0.78 tff(74,plain,
% 0.83/0.78 ((~hskp29) | c2_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.83/0.78 tff(75,plain,
% 0.83/0.78 ((~hskp29) | c2_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[74, 66])).
% 0.83/0.78 tff(76,plain,
% 0.83/0.78 (c2_1(a1885)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[75, 65])).
% 0.83/0.78 tff(77,plain,
% 0.83/0.78 (((~hskp29) | c1_1(a1885)) <=> ((~hskp29) | c1_1(a1885))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(78,axiom,((~hskp29) | c1_1(a1885)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.83/0.78 tff(79,plain,
% 0.83/0.78 ((~hskp29) | c1_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.83/0.78 tff(80,plain,
% 0.83/0.78 ((~hskp29) | c1_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[79, 77])).
% 0.83/0.78 tff(81,plain,
% 0.83/0.78 ((~hskp29) | c1_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[80, 77])).
% 0.83/0.78 tff(82,plain,
% 0.83/0.78 ((~hskp29) | c1_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.83/0.78 tff(83,plain,
% 0.83/0.78 ((~hskp29) | c1_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[82, 77])).
% 0.83/0.78 tff(84,plain,
% 0.83/0.78 ((~hskp29) | c1_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[83, 77])).
% 0.83/0.78 tff(85,plain,
% 0.83/0.78 ((~hskp29) | c1_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.83/0.78 tff(86,plain,
% 0.83/0.78 ((~hskp29) | c1_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[85, 77])).
% 0.83/0.78 tff(87,plain,
% 0.83/0.78 (c1_1(a1885)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[86, 65])).
% 0.83/0.78 tff(88,plain,
% 0.83/0.78 (((~hskp29) | c0_1(a1885)) <=> ((~hskp29) | c0_1(a1885))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(89,axiom,((~hskp29) | c0_1(a1885)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.83/0.78 tff(90,plain,
% 0.83/0.78 ((~hskp29) | c0_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.83/0.78 tff(91,plain,
% 0.83/0.78 ((~hskp29) | c0_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[90, 88])).
% 0.83/0.78 tff(92,plain,
% 0.83/0.78 ((~hskp29) | c0_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[91, 88])).
% 0.83/0.78 tff(93,plain,
% 0.83/0.78 ((~hskp29) | c0_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.83/0.78 tff(94,plain,
% 0.83/0.78 ((~hskp29) | c0_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[93, 88])).
% 0.83/0.78 tff(95,plain,
% 0.83/0.78 ((~hskp29) | c0_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[94, 88])).
% 0.83/0.78 tff(96,plain,
% 0.83/0.78 ((~hskp29) | c0_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.83/0.78 tff(97,plain,
% 0.83/0.78 ((~hskp29) | c0_1(a1885)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[96, 88])).
% 0.83/0.78 tff(98,plain,
% 0.83/0.78 (c0_1(a1885)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[97, 65])).
% 0.83/0.78 tff(99,assumption,(~ndr1_0), introduced(assumption)).
% 0.83/0.78 tff(100,plain,
% 0.83/0.78 ((ndr1_0 | (~hskp1)) <=> (ndr1_0 | (~hskp1))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(101,plain,
% 0.83/0.78 (((~hskp1) | ndr1_0) <=> (ndr1_0 | (~hskp1))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(102,axiom,((~hskp1) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause29')).
% 0.83/0.78 tff(103,plain,
% 0.83/0.78 (ndr1_0 | (~hskp1)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.83/0.78 tff(104,plain,
% 0.83/0.78 (ndr1_0 | (~hskp1)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[103, 100])).
% 0.83/0.78 tff(105,plain,
% 0.83/0.78 (~hskp1),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[104, 99])).
% 0.83/0.78 tff(106,plain,
% 0.83/0.78 (((~hskp29) | ndr1_0) <=> ((~hskp29) | ndr1_0)),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(107,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.83/0.78 tff(108,plain,
% 0.83/0.78 ((~hskp29) | ndr1_0),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.83/0.78 tff(109,plain,
% 0.83/0.78 ((~hskp29) | ndr1_0),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[108, 106])).
% 0.83/0.78 tff(110,plain,
% 0.83/0.78 ((~hskp29) | ndr1_0),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[109, 106])).
% 0.83/0.78 tff(111,plain,
% 0.83/0.78 ((~hskp29) | ndr1_0),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.83/0.78 tff(112,plain,
% 0.83/0.78 ((~hskp29) | ndr1_0),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[111, 106])).
% 0.83/0.78 tff(113,plain,
% 0.83/0.78 ((~hskp29) | ndr1_0),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[112, 106])).
% 0.83/0.78 tff(114,plain,
% 0.83/0.78 ((~hskp29) | ndr1_0),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.83/0.78 tff(115,plain,
% 0.83/0.78 ((~hskp29) | ndr1_0),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[114, 106])).
% 0.83/0.78 tff(116,plain,
% 0.83/0.78 (~hskp29),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[115, 99])).
% 0.83/0.78 tff(117,plain,
% 0.83/0.78 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(118,plain,
% 0.83/0.78 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(119,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.83/0.78 tff(120,plain,
% 0.83/0.78 (ndr1_0 | (~hskp27)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.83/0.78 tff(121,plain,
% 0.83/0.78 (ndr1_0 | (~hskp27)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[120, 117])).
% 0.83/0.78 tff(122,plain,
% 0.83/0.78 (~hskp27),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[121, 99])).
% 0.83/0.78 tff(123,plain,
% 0.83/0.78 ((hskp29 | hskp27 | hskp1) <=> (hskp29 | hskp27 | hskp1)),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(124,plain,
% 0.83/0.78 (((hskp29 | hskp27) | hskp1) <=> (hskp29 | hskp27 | hskp1)),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(125,plain,
% 0.83/0.78 ((hskp29 | hskp27) <=> (hskp29 | hskp27)),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(126,plain,
% 0.83/0.78 (((hskp29 | hskp27) | hskp1) <=> ((hskp29 | hskp27) | hskp1)),
% 0.83/0.78 inference(monotonicity,[status(thm)],[125])).
% 0.83/0.78 tff(127,plain,
% 0.83/0.78 (((hskp29 | hskp27) | hskp1) <=> (hskp29 | hskp27 | hskp1)),
% 0.83/0.78 inference(transitivity,[status(thm)],[126, 124])).
% 0.83/0.78 tff(128,axiom,((hskp29 | hskp27) | hskp1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause31')).
% 0.83/0.78 tff(129,plain,
% 0.83/0.78 (hskp29 | hskp27 | hskp1),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.83/0.78 tff(130,plain,
% 0.83/0.78 (hskp29 | hskp27 | hskp1),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[129, 123])).
% 0.83/0.78 tff(131,plain,
% 0.83/0.78 (hskp29 | hskp27 | hskp1),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.83/0.78 tff(132,plain,
% 0.83/0.78 (hskp29 | hskp27 | hskp1),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[131, 123])).
% 0.83/0.78 tff(133,plain,
% 0.83/0.78 (hskp29 | hskp27 | hskp1),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[132, 123])).
% 0.83/0.78 tff(134,plain,
% 0.83/0.78 (hskp29 | hskp27 | hskp1),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[133, 123])).
% 0.83/0.78 tff(135,plain,
% 0.83/0.78 (hskp29 | hskp27 | hskp1),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[134, 123])).
% 0.83/0.78 tff(136,plain,
% 0.83/0.78 (hskp29 | hskp27 | hskp1),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[135, 123])).
% 0.83/0.78 tff(137,plain,
% 0.83/0.78 ($false),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[136, 122, 116, 32])).
% 0.83/0.78 tff(138,plain,(ndr1_0 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.83/0.78 tff(139,plain,
% 0.83/0.78 ($false),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[138, 105, 99])).
% 0.83/0.78 tff(140,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.83/0.78 tff(141,plain,
% 0.83/0.78 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(142,plain,
% 0.83/0.78 ((hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885))) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(143,plain,
% 0.83/0.78 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885))))),
% 0.83/0.78 inference(monotonicity,[status(thm)],[142])).
% 0.83/0.78 tff(144,plain,
% 0.83/0.78 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)))),
% 0.83/0.78 inference(transitivity,[status(thm)],[143, 141])).
% 0.83/0.78 tff(145,plain,
% 0.83/0.78 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)))),
% 0.83/0.78 inference(quant_inst,[status(thm)],[])).
% 0.83/0.78 tff(146,plain,
% 0.83/0.78 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.83/0.78 tff(147,plain,
% 0.83/0.78 ($false),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[146, 140, 64, 43, 98, 87, 76, 53])).
% 0.83/0.78 tff(148,plain,((~hskp29) | hskp24 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.83/0.78 tff(149,plain,
% 0.83/0.78 (~hskp29),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[148, 64, 43])).
% 0.83/0.78 tff(150,plain,
% 0.83/0.78 (hskp27),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[136, 149, 32])).
% 0.83/0.78 tff(151,plain,
% 0.83/0.78 (((~hskp27) | c3_1(a1877)) <=> ((~hskp27) | c3_1(a1877))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(152,axiom,((~hskp27) | c3_1(a1877)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.83/0.78 tff(153,plain,
% 0.83/0.78 ((~hskp27) | c3_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.83/0.78 tff(154,plain,
% 0.83/0.78 ((~hskp27) | c3_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[153, 151])).
% 0.83/0.78 tff(155,plain,
% 0.83/0.78 ((~hskp27) | c3_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[154, 151])).
% 0.83/0.78 tff(156,plain,
% 0.83/0.78 ((~hskp27) | c3_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.83/0.78 tff(157,plain,
% 0.83/0.78 ((~hskp27) | c3_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[156, 151])).
% 0.83/0.78 tff(158,plain,
% 0.83/0.78 ((~hskp27) | c3_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[157, 151])).
% 0.83/0.78 tff(159,plain,
% 0.83/0.78 ((~hskp27) | c3_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.83/0.78 tff(160,plain,
% 0.83/0.78 ((~hskp27) | c3_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[159, 151])).
% 0.83/0.78 tff(161,plain,
% 0.83/0.78 (c3_1(a1877)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[160, 150])).
% 0.83/0.78 tff(162,plain,
% 0.83/0.78 (((~hskp27) | c2_1(a1877)) <=> ((~hskp27) | c2_1(a1877))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(163,axiom,((~hskp27) | c2_1(a1877)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.83/0.78 tff(164,plain,
% 0.83/0.78 ((~hskp27) | c2_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.83/0.78 tff(165,plain,
% 0.83/0.78 ((~hskp27) | c2_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[164, 162])).
% 0.83/0.78 tff(166,plain,
% 0.83/0.78 ((~hskp27) | c2_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[165, 162])).
% 0.83/0.78 tff(167,plain,
% 0.83/0.78 ((~hskp27) | c2_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.83/0.78 tff(168,plain,
% 0.83/0.78 ((~hskp27) | c2_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[167, 162])).
% 0.83/0.78 tff(169,plain,
% 0.83/0.78 ((~hskp27) | c2_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[168, 162])).
% 0.83/0.78 tff(170,plain,
% 0.83/0.78 ((~hskp27) | c2_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.83/0.78 tff(171,plain,
% 0.83/0.78 ((~hskp27) | c2_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[170, 162])).
% 0.83/0.78 tff(172,plain,
% 0.83/0.78 (c2_1(a1877)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[171, 150])).
% 0.83/0.78 tff(173,plain,
% 0.83/0.78 (((~hskp27) | c0_1(a1877)) <=> ((~hskp27) | c0_1(a1877))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(174,axiom,((~hskp27) | c0_1(a1877)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.83/0.78 tff(175,plain,
% 0.83/0.78 ((~hskp27) | c0_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.83/0.78 tff(176,plain,
% 0.83/0.78 ((~hskp27) | c0_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[175, 173])).
% 0.83/0.78 tff(177,plain,
% 0.83/0.78 ((~hskp27) | c0_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[176, 173])).
% 0.83/0.78 tff(178,plain,
% 0.83/0.78 ((~hskp27) | c0_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.83/0.78 tff(179,plain,
% 0.83/0.78 ((~hskp27) | c0_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[178, 173])).
% 0.83/0.78 tff(180,plain,
% 0.83/0.78 ((~hskp27) | c0_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[179, 173])).
% 0.83/0.78 tff(181,plain,
% 0.83/0.78 ((~hskp27) | c0_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.83/0.78 tff(182,plain,
% 0.83/0.78 ((~hskp27) | c0_1(a1877)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[181, 173])).
% 0.83/0.78 tff(183,plain,
% 0.83/0.78 (c0_1(a1877)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[182, 150])).
% 0.83/0.78 tff(184,plain,
% 0.83/0.78 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(185,plain,
% 0.83/0.78 ((hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877))) <=> (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(186,plain,
% 0.83/0.78 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.83/0.78 inference(monotonicity,[status(thm)],[185])).
% 0.83/0.78 tff(187,plain,
% 0.83/0.78 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.83/0.78 inference(transitivity,[status(thm)],[186, 184])).
% 0.83/0.78 tff(188,plain,
% 0.83/0.78 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)))),
% 0.83/0.78 inference(quant_inst,[status(thm)],[])).
% 0.83/0.78 tff(189,plain,
% 0.83/0.78 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.83/0.78 tff(190,plain,
% 0.83/0.78 (hskp28),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[189, 140, 43, 183, 172, 161, 63])).
% 0.83/0.78 tff(191,plain,
% 0.83/0.78 (((~hskp28) | c2_1(a1878)) <=> ((~hskp28) | c2_1(a1878))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(192,axiom,((~hskp28) | c2_1(a1878)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.83/0.78 tff(193,plain,
% 0.83/0.78 ((~hskp28) | c2_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.83/0.78 tff(194,plain,
% 0.83/0.78 ((~hskp28) | c2_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[193, 191])).
% 0.83/0.78 tff(195,plain,
% 0.83/0.78 ((~hskp28) | c2_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[194, 191])).
% 0.83/0.78 tff(196,plain,
% 0.83/0.78 ((~hskp28) | c2_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[195, 191])).
% 0.83/0.78 tff(197,plain,
% 0.83/0.78 ((~hskp28) | c2_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[196, 191])).
% 0.83/0.78 tff(198,plain,
% 0.83/0.78 ((~hskp28) | c2_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[197, 191])).
% 0.83/0.78 tff(199,plain,
% 0.83/0.78 ((~hskp28) | c2_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.83/0.78 tff(200,plain,
% 0.83/0.78 ((~hskp28) | c2_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[199, 191])).
% 0.83/0.78 tff(201,plain,
% 0.83/0.78 (c2_1(a1878)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[200, 190])).
% 0.83/0.78 tff(202,plain,
% 0.83/0.78 (((~hskp28) | c1_1(a1878)) <=> ((~hskp28) | c1_1(a1878))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(203,axiom,((~hskp28) | c1_1(a1878)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.83/0.78 tff(204,plain,
% 0.83/0.78 ((~hskp28) | c1_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.83/0.78 tff(205,plain,
% 0.83/0.78 ((~hskp28) | c1_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[204, 202])).
% 0.83/0.78 tff(206,plain,
% 0.83/0.78 ((~hskp28) | c1_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[205, 202])).
% 0.83/0.78 tff(207,plain,
% 0.83/0.78 ((~hskp28) | c1_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.83/0.78 tff(208,plain,
% 0.83/0.78 ((~hskp28) | c1_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[207, 202])).
% 0.83/0.78 tff(209,plain,
% 0.83/0.78 ((~hskp28) | c1_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[208, 202])).
% 0.83/0.78 tff(210,plain,
% 0.83/0.78 ((~hskp28) | c1_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.83/0.78 tff(211,plain,
% 0.83/0.78 ((~hskp28) | c1_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[210, 202])).
% 0.83/0.78 tff(212,plain,
% 0.83/0.78 (c1_1(a1878)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[211, 190])).
% 0.83/0.78 tff(213,plain,
% 0.83/0.78 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(214,plain,
% 0.83/0.78 ((hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878))) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(215,plain,
% 0.83/0.78 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878))))),
% 0.83/0.78 inference(monotonicity,[status(thm)],[214])).
% 0.83/0.78 tff(216,plain,
% 0.83/0.78 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.83/0.78 inference(transitivity,[status(thm)],[215, 213])).
% 0.83/0.78 tff(217,plain,
% 0.83/0.78 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878)))),
% 0.83/0.78 inference(quant_inst,[status(thm)],[])).
% 0.83/0.78 tff(218,plain,
% 0.83/0.78 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.83/0.78 tff(219,plain,
% 0.83/0.78 (~c0_1(a1878)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[218, 140, 64, 43, 212, 201, 53])).
% 0.83/0.78 tff(220,plain,
% 0.83/0.78 (((~hskp28) | c3_1(a1878)) <=> ((~hskp28) | c3_1(a1878))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(221,axiom,((~hskp28) | c3_1(a1878)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.83/0.78 tff(222,plain,
% 0.83/0.78 ((~hskp28) | c3_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.83/0.78 tff(223,plain,
% 0.83/0.78 ((~hskp28) | c3_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[222, 220])).
% 0.83/0.78 tff(224,plain,
% 0.83/0.78 ((~hskp28) | c3_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[223, 220])).
% 0.83/0.78 tff(225,plain,
% 0.83/0.78 ((~hskp28) | c3_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.83/0.78 tff(226,plain,
% 0.83/0.78 ((~hskp28) | c3_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[225, 220])).
% 0.83/0.78 tff(227,plain,
% 0.83/0.78 ((~hskp28) | c3_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[226, 220])).
% 0.83/0.78 tff(228,plain,
% 0.83/0.78 ((~hskp28) | c3_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[227, 220])).
% 0.83/0.78 tff(229,plain,
% 0.83/0.78 ((~hskp28) | c3_1(a1878)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[228, 220])).
% 0.83/0.78 tff(230,plain,
% 0.83/0.78 (c3_1(a1878)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[229, 190])).
% 0.83/0.78 tff(231,assumption,(~c0_1(a1878)), introduced(assumption)).
% 0.83/0.78 tff(232,plain,
% 0.83/0.78 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(233,plain,
% 0.83/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[232])).
% 0.83/0.78 tff(234,plain,
% 0.83/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(235,plain,
% 0.83/0.78 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_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) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | 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) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | 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) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 0.83/0.78 inference(bind,[status(th)],[])).
% 0.83/0.78 tff(236,plain,
% 0.83/0.78 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.83/0.78 inference(quant_intro,[status(thm)],[235])).
% 0.83/0.78 tff(237,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.83/0.78 tff(238,plain,
% 0.83/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.83/0.78 tff(239,plain,
% 0.83/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[238, 234])).
% 0.83/0.78 tff(240,plain,(
% 0.83/0.78 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.83/0.78 inference(skolemize,[status(sab)],[239])).
% 0.83/0.78 tff(241,plain,
% 0.83/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[240, 233])).
% 0.83/0.78 tff(242,assumption,(hskp23), introduced(assumption)).
% 0.83/0.78 tff(243,plain,
% 0.83/0.78 (((~hskp23) | (~c3_1(a1911))) <=> ((~hskp23) | (~c3_1(a1911)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(244,plain,
% 0.83/0.78 (((~c3_1(a1911)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1911)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(245,axiom,((~c3_1(a1911)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.83/0.78 tff(246,plain,
% 0.83/0.78 ((~hskp23) | (~c3_1(a1911))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.83/0.78 tff(247,plain,
% 0.83/0.78 ((~hskp23) | (~c3_1(a1911))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[246, 243])).
% 0.83/0.78 tff(248,plain,
% 0.83/0.78 (~c3_1(a1911)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[247, 242])).
% 0.83/0.78 tff(249,plain,
% 0.83/0.78 (((~hskp23) | (~c1_1(a1911))) <=> ((~hskp23) | (~c1_1(a1911)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(250,plain,
% 0.83/0.78 (((~c1_1(a1911)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a1911)))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(251,axiom,((~c1_1(a1911)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.83/0.78 tff(252,plain,
% 0.83/0.78 ((~hskp23) | (~c1_1(a1911))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.83/0.78 tff(253,plain,
% 0.83/0.78 ((~hskp23) | (~c1_1(a1911))),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[252, 249])).
% 0.83/0.78 tff(254,plain,
% 0.83/0.78 (~c1_1(a1911)),
% 0.83/0.78 inference(unit_resolution,[status(thm)],[253, 242])).
% 0.83/0.78 tff(255,plain,
% 0.83/0.78 (((~hskp23) | c0_1(a1911)) <=> ((~hskp23) | c0_1(a1911))),
% 0.83/0.78 inference(rewrite,[status(thm)],[])).
% 0.83/0.78 tff(256,axiom,((~hskp23) | c0_1(a1911)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.83/0.78 tff(257,plain,
% 0.83/0.78 ((~hskp23) | c0_1(a1911)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.83/0.78 tff(258,plain,
% 0.83/0.78 ((~hskp23) | c0_1(a1911)),
% 0.83/0.78 inference(modus_ponens,[status(thm)],[257, 255])).
% 0.83/0.78 tff(259,plain,
% 0.83/0.78 ((~hskp23) | c0_1(a1911)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[258, 255])).
% 0.83/0.79 tff(260,plain,
% 0.83/0.79 ((~hskp23) | c0_1(a1911)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[259, 255])).
% 0.83/0.79 tff(261,plain,
% 0.83/0.79 ((~hskp23) | c0_1(a1911)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[260, 255])).
% 0.83/0.79 tff(262,plain,
% 0.83/0.79 ((~hskp23) | c0_1(a1911)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[261, 255])).
% 0.83/0.79 tff(263,plain,
% 0.83/0.79 ((~hskp23) | c0_1(a1911)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[262, 255])).
% 0.83/0.79 tff(264,plain,
% 0.83/0.79 ((~hskp23) | c0_1(a1911)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[263, 255])).
% 0.83/0.79 tff(265,plain,
% 0.83/0.79 (c0_1(a1911)),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[264, 242])).
% 0.83/0.79 tff(266,assumption,(c3_1(a1878)), introduced(assumption)).
% 0.83/0.79 tff(267,assumption,(c1_1(a1878)), introduced(assumption)).
% 0.83/0.79 tff(268,plain,
% 0.83/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c0_1(a1911)) | (~c2_1(a1911)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(269,plain,
% 0.83/0.79 (((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1911) | c1_1(a1911) | (~c2_1(a1911)) | c0_1(a1878) | (~c3_1(a1878)) | (~c1_1(a1878))) <=> (c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(270,plain,
% 0.83/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1911) | c1_1(a1911) | (~c2_1(a1911)) | c0_1(a1878) | (~c3_1(a1878)) | (~c1_1(a1878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c0_1(a1911)) | (~c2_1(a1911))))),
% 0.83/0.79 inference(monotonicity,[status(thm)],[269])).
% 0.83/0.79 tff(271,plain,
% 0.83/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1911) | c1_1(a1911) | (~c2_1(a1911)) | c0_1(a1878) | (~c3_1(a1878)) | (~c1_1(a1878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.83/0.79 inference(transitivity,[status(thm)],[270, 268])).
% 0.83/0.79 tff(272,plain,
% 0.83/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1911) | c1_1(a1911) | (~c2_1(a1911)) | c0_1(a1878) | (~c3_1(a1878)) | (~c1_1(a1878)))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(273,plain,
% 0.83/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c0_1(a1911)) | (~c2_1(a1911))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.83/0.79 tff(274,plain,
% 0.83/0.79 (~c2_1(a1911)),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[273, 140, 267, 266, 265, 254, 248, 241, 231])).
% 0.83/0.79 tff(275,plain,
% 0.83/0.79 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.83/0.79 inference(bind,[status(th)],[])).
% 0.83/0.79 tff(276,plain,
% 0.83/0.79 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.83/0.79 inference(quant_intro,[status(thm)],[275])).
% 0.83/0.79 tff(277,plain,
% 0.83/0.79 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(278,plain,
% 0.83/0.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp24) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp24))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.83/0.79 inference(bind,[status(th)],[])).
% 0.83/0.79 tff(279,plain,
% 0.83/0.79 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.83/0.79 inference(quant_intro,[status(thm)],[278])).
% 0.83/0.79 tff(280,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.83/0.79 tff(281,plain,
% 0.83/0.79 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.83/0.79 tff(282,plain,
% 0.83/0.79 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[281, 277])).
% 0.83/0.79 tff(283,plain,(
% 0.83/0.79 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.83/0.79 inference(skolemize,[status(sab)],[282])).
% 0.83/0.79 tff(284,plain,
% 0.83/0.79 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[283, 276])).
% 0.83/0.79 tff(285,assumption,(c3_1(a1877)), introduced(assumption)).
% 0.83/0.79 tff(286,assumption,(c2_1(a1877)), introduced(assumption)).
% 0.83/0.79 tff(287,assumption,(c0_1(a1877)), introduced(assumption)).
% 0.83/0.79 tff(288,plain,
% 0.83/0.79 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c3_1(a1911) | (~ndr1_0) | (~c0_1(a1911)) | c2_1(a1911) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1911) | (~ndr1_0) | (~c0_1(a1911)) | c2_1(a1911) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(289,plain,
% 0.83/0.79 ((hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1911) | c2_1(a1911) | (~c0_1(a1911))) <=> (hskp24 | c3_1(a1911) | (~ndr1_0) | (~c0_1(a1911)) | c2_1(a1911) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(290,plain,
% 0.83/0.79 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1911) | c2_1(a1911) | (~c0_1(a1911)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c3_1(a1911) | (~ndr1_0) | (~c0_1(a1911)) | c2_1(a1911) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.83/0.79 inference(monotonicity,[status(thm)],[289])).
% 0.83/0.79 tff(291,plain,
% 0.83/0.79 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1911) | c2_1(a1911) | (~c0_1(a1911)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1911) | (~ndr1_0) | (~c0_1(a1911)) | c2_1(a1911) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.83/0.79 inference(transitivity,[status(thm)],[290, 288])).
% 0.83/0.79 tff(292,plain,
% 0.83/0.79 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1911) | c2_1(a1911) | (~c0_1(a1911)))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(293,plain,
% 0.83/0.79 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1911) | (~ndr1_0) | (~c0_1(a1911)) | c2_1(a1911) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.83/0.79 tff(294,plain,
% 0.83/0.79 ($false),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[293, 140, 64, 287, 286, 285, 265, 248, 284, 274])).
% 0.83/0.79 tff(295,plain,((~hskp23) | hskp24 | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1878)) | (~c3_1(a1878)) | c0_1(a1878)), inference(lemma,lemma(discharge,[]))).
% 0.83/0.79 tff(296,plain,
% 0.83/0.79 (~hskp23),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[295, 64, 183, 172, 161, 212, 230, 219])).
% 0.83/0.79 tff(297,plain,
% 0.83/0.79 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(298,plain,
% 0.83/0.79 ((hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877))) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(299,plain,
% 0.83/0.79 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))))),
% 0.83/0.79 inference(monotonicity,[status(thm)],[298])).
% 0.83/0.79 tff(300,plain,
% 0.83/0.79 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.83/0.79 inference(transitivity,[status(thm)],[299, 297])).
% 0.83/0.79 tff(301,plain,
% 0.83/0.79 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877)))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(302,plain,
% 0.83/0.79 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.83/0.79 tff(303,plain,
% 0.83/0.79 (~c1_1(a1877)),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[302, 140, 64, 43, 183, 172, 53])).
% 0.83/0.79 tff(304,plain,
% 0.83/0.79 (^[U: $i] : refl((hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.83/0.79 inference(bind,[status(th)],[])).
% 0.83/0.79 tff(305,plain,
% 0.83/0.79 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.79 inference(quant_intro,[status(thm)],[304])).
% 0.83/0.79 tff(306,plain,
% 0.83/0.79 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(307,plain,
% 0.83/0.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23) <=> ((hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23) <=> (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.83/0.79 inference(bind,[status(th)],[])).
% 0.83/0.79 tff(308,plain,
% 0.83/0.79 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23) <=> ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.79 inference(quant_intro,[status(thm)],[307])).
% 0.83/0.79 tff(309,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 0.83/0.79 tff(310,plain,
% 0.83/0.79 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.83/0.79 tff(311,plain,
% 0.83/0.79 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[310, 306])).
% 0.83/0.79 tff(312,plain,(
% 0.83/0.79 ![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.79 inference(skolemize,[status(sab)],[311])).
% 0.83/0.79 tff(313,plain,
% 0.83/0.79 (![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[312, 305])).
% 0.83/0.79 tff(314,plain,
% 0.83/0.79 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(315,plain,
% 0.83/0.79 ((hskp26 | hskp23 | (~ndr1_0) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877))) <=> (hskp26 | hskp23 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(316,plain,
% 0.83/0.79 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877)))),
% 0.83/0.79 inference(monotonicity,[status(thm)],[315])).
% 0.83/0.79 tff(317,plain,
% 0.83/0.79 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.83/0.79 inference(transitivity,[status(thm)],[316, 314])).
% 0.83/0.79 tff(318,plain,
% 0.83/0.79 ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)))),
% 0.83/0.79 inference(quant_inst,[status(thm)],[])).
% 0.83/0.79 tff(319,plain,
% 0.83/0.79 ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | (~ndr1_0) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.83/0.79 tff(320,plain,
% 0.83/0.79 (hskp26 | hskp23),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[319, 140, 183, 161, 313, 303])).
% 0.83/0.79 tff(321,plain,
% 0.83/0.79 (hskp26),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[320, 296])).
% 0.83/0.79 tff(322,plain,
% 0.83/0.79 (((~hskp26) | c1_1(a1858)) <=> ((~hskp26) | c1_1(a1858))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(323,axiom,((~hskp26) | c1_1(a1858)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.83/0.79 tff(324,plain,
% 0.83/0.79 ((~hskp26) | c1_1(a1858)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.83/0.79 tff(325,plain,
% 0.83/0.79 ((~hskp26) | c1_1(a1858)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[324, 322])).
% 0.83/0.79 tff(326,plain,
% 0.83/0.79 ((~hskp26) | c1_1(a1858)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[325, 322])).
% 0.83/0.79 tff(327,plain,
% 0.83/0.79 ((~hskp26) | c1_1(a1858)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[326, 322])).
% 0.83/0.79 tff(328,plain,
% 0.83/0.79 ((~hskp26) | c1_1(a1858)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[327, 322])).
% 0.83/0.79 tff(329,plain,
% 0.83/0.79 ((~hskp26) | c1_1(a1858)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[328, 322])).
% 0.83/0.79 tff(330,plain,
% 0.83/0.79 ((~hskp26) | c1_1(a1858)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[329, 322])).
% 0.83/0.79 tff(331,plain,
% 0.83/0.79 ((~hskp26) | c1_1(a1858)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[330, 322])).
% 0.83/0.79 tff(332,plain,
% 0.83/0.79 (c1_1(a1858)),
% 0.83/0.79 inference(unit_resolution,[status(thm)],[331, 321])).
% 0.83/0.79 tff(333,plain,
% 0.83/0.79 (((~hskp26) | c0_1(a1858)) <=> ((~hskp26) | c0_1(a1858))),
% 0.83/0.79 inference(rewrite,[status(thm)],[])).
% 0.83/0.79 tff(334,axiom,((~hskp26) | c0_1(a1858)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.83/0.79 tff(335,plain,
% 0.83/0.79 ((~hskp26) | c0_1(a1858)),
% 0.83/0.79 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.83/0.80 tff(336,plain,
% 0.83/0.80 ((~hskp26) | c0_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[335, 333])).
% 0.83/0.80 tff(337,plain,
% 0.83/0.80 ((~hskp26) | c0_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[336, 333])).
% 0.83/0.80 tff(338,plain,
% 0.83/0.80 ((~hskp26) | c0_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[337, 333])).
% 0.83/0.80 tff(339,plain,
% 0.83/0.80 ((~hskp26) | c0_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[338, 333])).
% 0.83/0.80 tff(340,plain,
% 0.83/0.80 ((~hskp26) | c0_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[339, 333])).
% 0.83/0.80 tff(341,plain,
% 0.83/0.80 ((~hskp26) | c0_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[340, 333])).
% 0.83/0.80 tff(342,plain,
% 0.83/0.80 ((~hskp26) | c0_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[341, 333])).
% 0.83/0.80 tff(343,plain,
% 0.83/0.80 (c0_1(a1858)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[342, 321])).
% 0.83/0.80 tff(344,plain,
% 0.83/0.80 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1858)) | (~c2_1(a1858)) | (~c1_1(a1858)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1858)) | (~c2_1(a1858)) | (~c1_1(a1858)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(345,plain,
% 0.83/0.80 ((hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858))) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1858)) | (~c2_1(a1858)) | (~c1_1(a1858)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(346,plain,
% 0.83/0.80 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1858)) | (~c2_1(a1858)) | (~c1_1(a1858))))),
% 0.83/0.80 inference(monotonicity,[status(thm)],[345])).
% 0.83/0.80 tff(347,plain,
% 0.83/0.80 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1858)) | (~c2_1(a1858)) | (~c1_1(a1858)))),
% 0.83/0.80 inference(transitivity,[status(thm)],[346, 344])).
% 0.83/0.80 tff(348,plain,
% 0.83/0.80 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)))),
% 0.83/0.80 inference(quant_inst,[status(thm)],[])).
% 0.83/0.80 tff(349,plain,
% 0.83/0.80 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c0_1(a1858)) | (~c2_1(a1858)) | (~c1_1(a1858))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.83/0.80 tff(350,plain,
% 0.83/0.80 (~c2_1(a1858)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[349, 140, 64, 43, 343, 332, 53])).
% 0.83/0.80 tff(351,plain,
% 0.83/0.80 (((~hskp26) | c3_1(a1858)) <=> ((~hskp26) | c3_1(a1858))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(352,axiom,((~hskp26) | c3_1(a1858)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 0.83/0.80 tff(353,plain,
% 0.83/0.80 ((~hskp26) | c3_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.83/0.80 tff(354,plain,
% 0.83/0.80 ((~hskp26) | c3_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[353, 351])).
% 0.83/0.80 tff(355,plain,
% 0.83/0.80 ((~hskp26) | c3_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[354, 351])).
% 0.83/0.80 tff(356,plain,
% 0.83/0.80 ((~hskp26) | c3_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[355, 351])).
% 0.83/0.80 tff(357,plain,
% 0.83/0.80 ((~hskp26) | c3_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[356, 351])).
% 0.83/0.80 tff(358,plain,
% 0.83/0.80 ((~hskp26) | c3_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[357, 351])).
% 0.83/0.80 tff(359,plain,
% 0.83/0.80 ((~hskp26) | c3_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[358, 351])).
% 0.83/0.80 tff(360,plain,
% 0.83/0.80 ((~hskp26) | c3_1(a1858)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[359, 351])).
% 0.83/0.80 tff(361,plain,
% 0.83/0.80 (c3_1(a1858)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[360, 321])).
% 0.83/0.80 tff(362,plain,
% 0.83/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c3_1(a1858)) | c2_1(a1858) | (~c1_1(a1858)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~ndr1_0) | (~c2_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c3_1(a1858)) | c2_1(a1858) | (~c1_1(a1858)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(363,plain,
% 0.83/0.80 (((~ndr1_0) | c2_1(a1858) | (~c3_1(a1858)) | (~c1_1(a1858)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1878) | (~c3_1(a1878)) | (~c2_1(a1878))) <=> ((~ndr1_0) | (~c2_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c3_1(a1858)) | c2_1(a1858) | (~c1_1(a1858)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(364,plain,
% 0.83/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1858) | (~c3_1(a1858)) | (~c1_1(a1858)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1878) | (~c3_1(a1878)) | (~c2_1(a1878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c3_1(a1858)) | c2_1(a1858) | (~c1_1(a1858)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877)))),
% 0.83/0.80 inference(monotonicity,[status(thm)],[363])).
% 0.83/0.80 tff(365,plain,
% 0.83/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1858) | (~c3_1(a1858)) | (~c1_1(a1858)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1878) | (~c3_1(a1878)) | (~c2_1(a1878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~ndr1_0) | (~c2_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c3_1(a1858)) | c2_1(a1858) | (~c1_1(a1858)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.83/0.80 inference(transitivity,[status(thm)],[364, 362])).
% 0.83/0.80 tff(366,plain,
% 0.83/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1858) | (~c3_1(a1858)) | (~c1_1(a1858)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1878) | (~c3_1(a1878)) | (~c2_1(a1878)))),
% 0.83/0.80 inference(quant_inst,[status(thm)],[])).
% 0.83/0.80 tff(367,plain,
% 0.83/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~ndr1_0) | (~c2_1(a1878)) | c0_1(a1878) | (~c3_1(a1878)) | (~c3_1(a1858)) | c2_1(a1858) | (~c1_1(a1858)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.83/0.80 tff(368,plain,
% 0.83/0.80 ($false),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[367, 140, 201, 230, 183, 161, 332, 361, 10, 303, 219, 350])).
% 0.83/0.80 tff(369,plain,(hskp24 | hskp0 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.83/0.80 tff(370,plain,
% 0.83/0.80 (hskp24),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[369, 43, 32])).
% 0.83/0.80 tff(371,plain,
% 0.83/0.80 (((~hskp24) | (~c2_1(a1919))) <=> ((~hskp24) | (~c2_1(a1919)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(372,plain,
% 0.83/0.80 (((~c2_1(a1919)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a1919)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(373,axiom,((~c2_1(a1919)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 0.83/0.80 tff(374,plain,
% 0.83/0.80 ((~hskp24) | (~c2_1(a1919))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.83/0.80 tff(375,plain,
% 0.83/0.80 ((~hskp24) | (~c2_1(a1919))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[374, 371])).
% 0.83/0.80 tff(376,plain,
% 0.83/0.80 (~c2_1(a1919)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[375, 370])).
% 0.83/0.80 tff(377,plain,
% 0.83/0.80 (((~hskp24) | (~c1_1(a1919))) <=> ((~hskp24) | (~c1_1(a1919)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(378,plain,
% 0.83/0.80 (((~c1_1(a1919)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a1919)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(379,axiom,((~c1_1(a1919)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 0.83/0.80 tff(380,plain,
% 0.83/0.80 ((~hskp24) | (~c1_1(a1919))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.83/0.80 tff(381,plain,
% 0.83/0.80 ((~hskp24) | (~c1_1(a1919))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[380, 377])).
% 0.83/0.80 tff(382,plain,
% 0.83/0.80 (~c1_1(a1919)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[381, 370])).
% 0.83/0.80 tff(383,plain,
% 0.83/0.80 (((~hskp24) | c3_1(a1919)) <=> ((~hskp24) | c3_1(a1919))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(384,axiom,((~hskp24) | c3_1(a1919)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.83/0.80 tff(385,plain,
% 0.83/0.80 ((~hskp24) | c3_1(a1919)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.83/0.80 tff(386,plain,
% 0.83/0.80 ((~hskp24) | c3_1(a1919)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[385, 383])).
% 0.83/0.80 tff(387,plain,
% 0.83/0.80 ((~hskp24) | c3_1(a1919)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[386, 383])).
% 0.83/0.80 tff(388,plain,
% 0.83/0.80 ((~hskp24) | c3_1(a1919)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[387, 383])).
% 0.83/0.80 tff(389,plain,
% 0.83/0.80 ((~hskp24) | c3_1(a1919)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[388, 383])).
% 0.83/0.80 tff(390,plain,
% 0.83/0.80 ((~hskp24) | c3_1(a1919)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[389, 383])).
% 0.83/0.80 tff(391,plain,
% 0.83/0.80 ((~hskp24) | c3_1(a1919)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[390, 383])).
% 0.83/0.80 tff(392,plain,
% 0.83/0.80 ((~hskp24) | c3_1(a1919)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[391, 383])).
% 0.83/0.80 tff(393,plain,
% 0.83/0.80 (c3_1(a1919)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[392, 370])).
% 0.83/0.80 tff(394,plain,
% 0.83/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | c0_1(a1919))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | c0_1(a1919))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(395,plain,
% 0.83/0.80 ((hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919)) <=> (hskp1 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | c0_1(a1919))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(396,plain,
% 0.83/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | c0_1(a1919)))),
% 0.83/0.80 inference(monotonicity,[status(thm)],[395])).
% 0.83/0.80 tff(397,plain,
% 0.83/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | c0_1(a1919))),
% 0.83/0.80 inference(transitivity,[status(thm)],[396, 394])).
% 0.83/0.80 tff(398,plain,
% 0.83/0.80 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919))),
% 0.83/0.80 inference(quant_inst,[status(thm)],[])).
% 0.83/0.80 tff(399,plain,
% 0.83/0.80 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | c0_1(a1919)),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.83/0.80 tff(400,plain,
% 0.83/0.80 (c0_1(a1919)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[399, 140, 32, 393, 382, 376, 42])).
% 0.83/0.80 tff(401,plain,
% 0.83/0.80 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))))),
% 0.83/0.80 inference(bind,[status(th)],[])).
% 0.83/0.80 tff(402,plain,
% 0.83/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.83/0.80 inference(quant_intro,[status(thm)],[401])).
% 0.83/0.80 tff(403,plain,
% 0.83/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(404,plain,
% 0.83/0.80 (^[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))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c2_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))))),
% 0.83/0.80 inference(bind,[status(th)],[])).
% 0.83/0.80 tff(405,plain,
% 0.83/0.80 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.83/0.80 inference(quant_intro,[status(thm)],[404])).
% 0.83/0.80 tff(406,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c3_1(U)) | c2_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 0.83/0.80 tff(407,plain,
% 0.83/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.83/0.80 tff(408,plain,
% 0.83/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[407, 403])).
% 0.83/0.80 tff(409,plain,(
% 0.83/0.80 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.83/0.80 inference(skolemize,[status(sab)],[408])).
% 0.83/0.80 tff(410,plain,
% 0.83/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[409, 402])).
% 0.83/0.80 tff(411,assumption,(hskp3), introduced(assumption)).
% 0.83/0.80 tff(412,plain,
% 0.83/0.80 (((~hskp3) | (~c2_1(a1855))) <=> ((~hskp3) | (~c2_1(a1855)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(413,plain,
% 0.83/0.80 (((~c2_1(a1855)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a1855)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(414,axiom,((~c2_1(a1855)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.83/0.80 tff(415,plain,
% 0.83/0.80 ((~hskp3) | (~c2_1(a1855))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.83/0.80 tff(416,plain,
% 0.83/0.80 ((~hskp3) | (~c2_1(a1855))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[415, 412])).
% 0.83/0.80 tff(417,plain,
% 0.83/0.80 (~c2_1(a1855)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[416, 411])).
% 0.83/0.80 tff(418,assumption,(hskp24), introduced(assumption)).
% 0.83/0.80 tff(419,plain,
% 0.83/0.80 (((~hskp3) | (~c0_1(a1855))) <=> ((~hskp3) | (~c0_1(a1855)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(420,plain,
% 0.83/0.80 (((~c0_1(a1855)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a1855)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(421,axiom,((~c0_1(a1855)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.83/0.80 tff(422,plain,
% 0.83/0.80 ((~hskp3) | (~c0_1(a1855))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.83/0.80 tff(423,plain,
% 0.83/0.80 ((~hskp3) | (~c0_1(a1855))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[422, 419])).
% 0.83/0.80 tff(424,plain,
% 0.83/0.80 (~c0_1(a1855)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[423, 411])).
% 0.83/0.80 tff(425,plain,
% 0.83/0.80 (((~hskp3) | (~c1_1(a1855))) <=> ((~hskp3) | (~c1_1(a1855)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(426,plain,
% 0.83/0.80 (((~c1_1(a1855)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a1855)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(427,axiom,((~c1_1(a1855)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.83/0.80 tff(428,plain,
% 0.83/0.80 ((~hskp3) | (~c1_1(a1855))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.83/0.80 tff(429,plain,
% 0.83/0.80 ((~hskp3) | (~c1_1(a1855))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[428, 425])).
% 0.83/0.80 tff(430,plain,
% 0.83/0.80 (~c1_1(a1855)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[429, 411])).
% 0.83/0.80 tff(431,assumption,(~c2_1(a1855)), introduced(assumption)).
% 0.83/0.80 tff(432,assumption,(~c1_1(a1855)), introduced(assumption)).
% 0.83/0.80 tff(433,assumption,(~c0_1(a1855)), introduced(assumption)).
% 0.83/0.80 tff(434,plain,
% 0.83/0.80 (~c2_1(a1919)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[375, 418])).
% 0.83/0.80 tff(435,plain,
% 0.83/0.80 (~c1_1(a1919)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[381, 418])).
% 0.83/0.80 tff(436,plain,
% 0.83/0.80 (c3_1(a1919)),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[392, 418])).
% 0.83/0.80 tff(437,plain,
% 0.83/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1855) | c1_1(a1855) | c2_1(a1855) | (~ndr1_0) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1855) | c1_1(a1855) | c2_1(a1855) | (~ndr1_0) | (~c3_1(a1919)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(438,plain,
% 0.83/0.80 ((hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1855) | c0_1(a1855) | c2_1(a1855)) <=> (hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1855) | c1_1(a1855) | c2_1(a1855) | (~ndr1_0) | (~c3_1(a1919)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(439,plain,
% 0.83/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1855) | c0_1(a1855) | c2_1(a1855))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1855) | c1_1(a1855) | c2_1(a1855) | (~ndr1_0) | (~c3_1(a1919))))),
% 0.83/0.80 inference(monotonicity,[status(thm)],[438])).
% 0.83/0.80 tff(440,plain,
% 0.83/0.80 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1855) | c0_1(a1855) | c2_1(a1855))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1855) | c1_1(a1855) | c2_1(a1855) | (~ndr1_0) | (~c3_1(a1919)))),
% 0.83/0.80 inference(transitivity,[status(thm)],[439, 437])).
% 0.83/0.80 tff(441,plain,
% 0.83/0.80 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1855) | c0_1(a1855) | c2_1(a1855))),
% 0.83/0.80 inference(quant_inst,[status(thm)],[])).
% 0.83/0.80 tff(442,plain,
% 0.83/0.80 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1855) | c1_1(a1855) | c2_1(a1855) | (~ndr1_0) | (~c3_1(a1919))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.83/0.80 tff(443,plain,
% 0.83/0.80 ($false),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[442, 140, 32, 436, 435, 434, 433, 432, 431, 42])).
% 0.83/0.80 tff(444,plain,((~hskp24) | hskp1 | c0_1(a1855) | c1_1(a1855) | c2_1(a1855)), inference(lemma,lemma(discharge,[]))).
% 0.83/0.80 tff(445,plain,
% 0.83/0.80 ($false),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[444, 430, 424, 418, 417, 32])).
% 0.83/0.80 tff(446,plain,((~hskp3) | (~hskp24) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.83/0.80 tff(447,plain,
% 0.83/0.80 (~hskp3),
% 0.83/0.80 inference(unit_resolution,[status(thm)],[446, 370, 32])).
% 0.83/0.80 tff(448,assumption,(c0_1(a1919)), introduced(assumption)).
% 0.83/0.80 tff(449,assumption,(~hskp22), introduced(assumption)).
% 0.83/0.80 tff(450,plain,
% 0.83/0.80 (^[U: $i] : refl((hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.83/0.80 inference(bind,[status(th)],[])).
% 0.83/0.80 tff(451,plain,
% 0.83/0.80 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.80 inference(quant_intro,[status(thm)],[450])).
% 0.83/0.80 tff(452,plain,
% 0.83/0.80 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(453,plain,
% 0.83/0.80 (^[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)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp22) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp22))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp22) <=> (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.83/0.80 inference(bind,[status(th)],[])).
% 0.83/0.80 tff(454,plain,
% 0.83/0.80 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp22) <=> ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.80 inference(quant_intro,[status(thm)],[453])).
% 0.83/0.80 tff(455,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp27) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.83/0.80 tff(456,plain,
% 0.83/0.80 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[455, 454])).
% 0.83/0.80 tff(457,plain,
% 0.83/0.80 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[456, 452])).
% 0.83/0.80 tff(458,plain,(
% 0.83/0.80 ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.80 inference(skolemize,[status(sab)],[457])).
% 0.83/0.80 tff(459,plain,
% 0.83/0.80 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.83/0.80 inference(modus_ponens,[status(thm)],[458, 451])).
% 0.83/0.80 tff(460,assumption,(~c2_1(a1919)), introduced(assumption)).
% 0.83/0.80 tff(461,assumption,(c3_1(a1919)), introduced(assumption)).
% 0.83/0.80 tff(462,plain,
% 0.83/0.80 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(463,plain,
% 0.83/0.80 ((hskp27 | hskp22 | (~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919))) <=> (hskp27 | hskp22 | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.83/0.80 inference(rewrite,[status(thm)],[])).
% 0.83/0.80 tff(464,plain,
% 0.83/0.80 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919))))),
% 0.83/0.81 inference(monotonicity,[status(thm)],[463])).
% 0.83/0.81 tff(465,plain,
% 0.83/0.81 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.83/0.81 inference(transitivity,[status(thm)],[464, 462])).
% 0.83/0.81 tff(466,plain,
% 0.83/0.81 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.83/0.81 inference(quant_inst,[status(thm)],[])).
% 0.83/0.81 tff(467,plain,
% 0.83/0.81 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.83/0.81 tff(468,plain,
% 0.83/0.81 (hskp27 | hskp22 | (~c0_1(a1919))),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[467, 140, 461, 460, 459])).
% 0.83/0.81 tff(469,plain,
% 0.83/0.81 (hskp27),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[468, 449, 448])).
% 0.83/0.81 tff(470,plain,
% 0.83/0.81 (c3_1(a1877)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[160, 469])).
% 0.83/0.81 tff(471,plain,
% 0.83/0.81 (c2_1(a1877)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[171, 469])).
% 0.83/0.81 tff(472,plain,
% 0.83/0.81 (c0_1(a1877)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[182, 469])).
% 0.83/0.81 tff(473,assumption,(~c1_1(a1919)), introduced(assumption)).
% 0.83/0.81 tff(474,assumption,(~hskp28), introduced(assumption)).
% 0.83/0.81 tff(475,plain,
% 0.83/0.81 ((hskp28 | hskp10 | hskp0) <=> (hskp28 | hskp10 | hskp0)),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(476,plain,
% 0.83/0.81 (((hskp10 | hskp28) | hskp0) <=> (hskp28 | hskp10 | hskp0)),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(477,axiom,((hskp10 | hskp28) | hskp0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.83/0.81 tff(478,plain,
% 0.83/0.81 (hskp28 | hskp10 | hskp0),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.83/0.81 tff(479,plain,
% 0.83/0.81 (hskp28 | hskp10 | hskp0),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[478, 475])).
% 0.83/0.81 tff(480,plain,
% 0.83/0.81 (hskp28 | hskp10 | hskp0),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[479, 475])).
% 0.83/0.81 tff(481,plain,
% 0.83/0.81 (hskp28 | hskp10 | hskp0),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[480, 475])).
% 0.83/0.81 tff(482,plain,
% 0.83/0.81 (hskp28 | hskp10 | hskp0),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[481, 475])).
% 0.83/0.81 tff(483,plain,
% 0.83/0.81 (hskp28 | hskp10 | hskp0),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[482, 475])).
% 0.83/0.81 tff(484,plain,
% 0.83/0.81 (hskp28 | hskp10 | hskp0),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[483, 475])).
% 0.83/0.81 tff(485,plain,
% 0.83/0.81 (hskp28 | hskp10 | hskp0),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[484, 475])).
% 0.83/0.81 tff(486,plain,
% 0.83/0.81 (hskp10),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[485, 474, 43])).
% 0.83/0.81 tff(487,plain,
% 0.83/0.81 (((~hskp10) | c3_1(a1864)) <=> ((~hskp10) | c3_1(a1864))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(488,axiom,((~hskp10) | c3_1(a1864)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 0.83/0.81 tff(489,plain,
% 0.83/0.81 ((~hskp10) | c3_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.83/0.81 tff(490,plain,
% 0.83/0.81 ((~hskp10) | c3_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[489, 487])).
% 0.83/0.81 tff(491,plain,
% 0.83/0.81 ((~hskp10) | c3_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[490, 487])).
% 0.83/0.81 tff(492,plain,
% 0.83/0.81 ((~hskp10) | c3_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[491, 487])).
% 0.83/0.81 tff(493,plain,
% 0.83/0.81 ((~hskp10) | c3_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[492, 487])).
% 0.83/0.81 tff(494,plain,
% 0.83/0.81 ((~hskp10) | c3_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[493, 487])).
% 0.83/0.81 tff(495,plain,
% 0.83/0.81 ((~hskp10) | c3_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[494, 487])).
% 0.83/0.81 tff(496,plain,
% 0.83/0.81 ((~hskp10) | c3_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[495, 487])).
% 0.83/0.81 tff(497,plain,
% 0.83/0.81 (c3_1(a1864)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[496, 486])).
% 0.83/0.81 tff(498,plain,
% 0.83/0.81 (((~hskp10) | c0_1(a1864)) <=> ((~hskp10) | c0_1(a1864))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(499,axiom,((~hskp10) | c0_1(a1864)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.83/0.81 tff(500,plain,
% 0.83/0.81 ((~hskp10) | c0_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.83/0.81 tff(501,plain,
% 0.83/0.81 ((~hskp10) | c0_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[500, 498])).
% 0.83/0.81 tff(502,plain,
% 0.83/0.81 ((~hskp10) | c0_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[501, 498])).
% 0.83/0.81 tff(503,plain,
% 0.83/0.81 ((~hskp10) | c0_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[502, 498])).
% 0.83/0.81 tff(504,plain,
% 0.83/0.81 ((~hskp10) | c0_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[503, 498])).
% 0.83/0.81 tff(505,plain,
% 0.83/0.81 ((~hskp10) | c0_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[504, 498])).
% 0.83/0.81 tff(506,plain,
% 0.83/0.81 ((~hskp10) | c0_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[505, 498])).
% 0.83/0.81 tff(507,plain,
% 0.83/0.81 ((~hskp10) | c0_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[506, 498])).
% 0.83/0.81 tff(508,plain,
% 0.83/0.81 (c0_1(a1864)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[507, 486])).
% 0.83/0.81 tff(509,plain,
% 0.83/0.81 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(510,plain,
% 0.83/0.81 ((hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864))) <=> (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(511,plain,
% 0.83/0.81 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864))))),
% 0.83/0.81 inference(monotonicity,[status(thm)],[510])).
% 0.83/0.81 tff(512,plain,
% 0.83/0.81 (((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)))) <=> ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)))),
% 0.83/0.81 inference(transitivity,[status(thm)],[511, 509])).
% 0.83/0.81 tff(513,plain,
% 0.83/0.81 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)))),
% 0.83/0.81 inference(quant_inst,[status(thm)],[])).
% 0.83/0.81 tff(514,plain,
% 0.83/0.81 ((~![U: $i] : (hskp28 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp0 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.83/0.81 tff(515,plain,
% 0.83/0.81 (~c2_1(a1864)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[514, 140, 474, 43, 508, 497, 63])).
% 0.83/0.81 tff(516,plain,
% 0.83/0.81 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(517,plain,
% 0.83/0.81 ((hskp27 | hskp22 | (~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864))) <=> (hskp27 | hskp22 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(518,plain,
% 0.83/0.81 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864)))),
% 0.83/0.81 inference(monotonicity,[status(thm)],[517])).
% 0.83/0.81 tff(519,plain,
% 0.83/0.81 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864))),
% 0.83/0.81 inference(transitivity,[status(thm)],[518, 516])).
% 0.83/0.81 tff(520,plain,
% 0.83/0.81 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)))),
% 0.83/0.81 inference(quant_inst,[status(thm)],[])).
% 0.83/0.81 tff(521,plain,
% 0.83/0.81 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864)),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.83/0.81 tff(522,plain,
% 0.83/0.81 (hskp27),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[521, 140, 449, 508, 497, 459, 515])).
% 0.83/0.81 tff(523,plain,
% 0.83/0.81 (c3_1(a1877)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[160, 522])).
% 0.83/0.81 tff(524,plain,
% 0.83/0.81 (c2_1(a1877)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[171, 522])).
% 0.83/0.81 tff(525,plain,
% 0.83/0.81 (c0_1(a1877)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[182, 522])).
% 0.83/0.81 tff(526,plain,
% 0.83/0.81 ($false),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[189, 140, 474, 43, 525, 524, 523, 63])).
% 0.83/0.81 tff(527,plain,(hskp28 | hskp0 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.83/0.81 tff(528,plain,
% 0.83/0.81 (hskp28),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[527, 449, 43])).
% 0.83/0.81 tff(529,plain,
% 0.83/0.81 (c1_1(a1878)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[211, 528])).
% 0.83/0.81 tff(530,plain,
% 0.83/0.81 (c3_1(a1878)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[229, 528])).
% 0.83/0.81 tff(531,assumption,(~hskp3), introduced(assumption)).
% 0.83/0.81 tff(532,plain,
% 0.83/0.81 (c2_1(a1878)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[200, 528])).
% 0.83/0.81 tff(533,plain,
% 0.83/0.81 (^[U: $i] : refl((hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.83/0.81 inference(bind,[status(th)],[])).
% 0.83/0.81 tff(534,plain,
% 0.83/0.81 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.81 inference(quant_intro,[status(thm)],[533])).
% 0.83/0.81 tff(535,plain,
% 0.83/0.81 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(536,plain,
% 0.83/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp26) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp26) | hskp3) <=> ((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp3))), rewrite(((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp26) | hskp3) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.83/0.81 inference(bind,[status(th)],[])).
% 0.83/0.81 tff(537,plain,
% 0.83/0.81 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp26) | hskp3) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.81 inference(quant_intro,[status(thm)],[536])).
% 0.83/0.81 tff(538,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp26) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 0.83/0.81 tff(539,plain,
% 0.83/0.81 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.83/0.81 tff(540,plain,
% 0.83/0.81 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[539, 535])).
% 0.83/0.81 tff(541,plain,(
% 0.83/0.81 ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.81 inference(skolemize,[status(sab)],[540])).
% 0.83/0.81 tff(542,plain,
% 0.83/0.81 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[541, 534])).
% 0.83/0.81 tff(543,assumption,(c2_1(a1878)), introduced(assumption)).
% 0.83/0.81 tff(544,assumption,(~hskp26), introduced(assumption)).
% 0.83/0.81 tff(545,plain,
% 0.83/0.81 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(546,plain,
% 0.83/0.81 ((hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878))) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(547,plain,
% 0.83/0.81 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878))))),
% 0.83/0.81 inference(monotonicity,[status(thm)],[546])).
% 0.83/0.81 tff(548,plain,
% 0.83/0.81 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.83/0.81 inference(transitivity,[status(thm)],[547, 545])).
% 0.83/0.81 tff(549,plain,
% 0.83/0.81 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c0_1(a1878)))),
% 0.83/0.81 inference(quant_inst,[status(thm)],[])).
% 0.83/0.81 tff(550,plain,
% 0.83/0.81 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1878)) | (~c2_1(a1878)) | (~c1_1(a1878))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[549, 548])).
% 0.83/0.81 tff(551,plain,
% 0.83/0.81 (hskp3 | (~c0_1(a1878))),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[550, 140, 544, 267, 543, 542])).
% 0.83/0.81 tff(552,plain,
% 0.83/0.81 (~c0_1(a1878)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[551, 531])).
% 0.83/0.81 tff(553,plain,
% 0.83/0.81 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.83/0.81 inference(bind,[status(th)],[])).
% 0.83/0.81 tff(554,plain,
% 0.83/0.81 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.83/0.81 inference(quant_intro,[status(thm)],[553])).
% 0.83/0.81 tff(555,plain,
% 0.83/0.81 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(556,plain,
% 0.83/0.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.83/0.81 inference(bind,[status(th)],[])).
% 0.83/0.81 tff(557,plain,
% 0.83/0.81 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.83/0.81 inference(quant_intro,[status(thm)],[556])).
% 0.83/0.81 tff(558,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.83/0.81 tff(559,plain,
% 0.83/0.81 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[558, 557])).
% 0.83/0.81 tff(560,plain,
% 0.83/0.81 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[559, 555])).
% 0.83/0.81 tff(561,plain,(
% 0.83/0.81 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.83/0.81 inference(skolemize,[status(sab)],[560])).
% 0.83/0.81 tff(562,plain,
% 0.83/0.81 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[561, 554])).
% 0.83/0.81 tff(563,plain,
% 0.83/0.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1919)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(564,plain,
% 0.83/0.81 ((hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1878) | (~c2_1(a1878)) | (~c1_1(a1878))) <=> (hskp8 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1919)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(565,plain,
% 0.83/0.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1878) | (~c2_1(a1878)) | (~c1_1(a1878)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1919))))),
% 0.83/0.81 inference(monotonicity,[status(thm)],[564])).
% 0.83/0.81 tff(566,plain,
% 0.83/0.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1878) | (~c2_1(a1878)) | (~c1_1(a1878)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1919)))),
% 0.83/0.81 inference(transitivity,[status(thm)],[565, 563])).
% 0.83/0.81 tff(567,plain,
% 0.83/0.81 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1878) | (~c2_1(a1878)) | (~c1_1(a1878)))),
% 0.83/0.81 inference(quant_inst,[status(thm)],[])).
% 0.83/0.81 tff(568,plain,
% 0.83/0.81 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | c0_1(a1878) | (~c3_1(a1919))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.83/0.81 tff(569,plain,
% 0.83/0.81 (hskp8),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[568, 140, 267, 543, 461, 473, 460, 562, 552])).
% 0.83/0.81 tff(570,plain,
% 0.83/0.81 (((~hskp8) | (~c2_1(a1862))) <=> ((~hskp8) | (~c2_1(a1862)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(571,plain,
% 0.83/0.81 (((~c2_1(a1862)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a1862)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(572,axiom,((~c2_1(a1862)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.83/0.81 tff(573,plain,
% 0.83/0.81 ((~hskp8) | (~c2_1(a1862))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[572, 571])).
% 0.83/0.81 tff(574,plain,
% 0.83/0.81 ((~hskp8) | (~c2_1(a1862))),
% 0.83/0.81 inference(modus_ponens,[status(thm)],[573, 570])).
% 0.83/0.81 tff(575,plain,
% 0.83/0.81 (~c2_1(a1862)),
% 0.83/0.81 inference(unit_resolution,[status(thm)],[574, 569])).
% 0.83/0.81 tff(576,plain,
% 0.83/0.81 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | c1_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | c1_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(577,plain,
% 0.83/0.81 ((hskp26 | hskp23 | (~ndr1_0) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919))) <=> (hskp26 | hskp23 | c1_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.83/0.81 inference(rewrite,[status(thm)],[])).
% 0.83/0.81 tff(578,plain,
% 0.83/0.81 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | c1_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919))))),
% 0.83/0.82 inference(monotonicity,[status(thm)],[577])).
% 0.83/0.82 tff(579,plain,
% 0.83/0.82 (((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | c1_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.83/0.82 inference(transitivity,[status(thm)],[578, 576])).
% 0.83/0.82 tff(580,plain,
% 0.83/0.82 ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp23 | (~ndr1_0) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.83/0.82 inference(quant_inst,[status(thm)],[])).
% 0.83/0.82 tff(581,plain,
% 0.83/0.82 ((~![U: $i] : (hskp26 | hskp23 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp23 | c1_1(a1919) | (~ndr1_0) | (~c3_1(a1919)) | (~c0_1(a1919))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.83/0.82 tff(582,plain,
% 0.83/0.82 (hskp26 | hskp23 | (~c0_1(a1919))),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[581, 140, 461, 473, 313])).
% 0.83/0.82 tff(583,plain,
% 0.83/0.82 (hskp23),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[582, 544, 448])).
% 0.83/0.82 tff(584,plain,
% 0.83/0.82 (~c3_1(a1911)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[247, 583])).
% 0.83/0.82 tff(585,plain,
% 0.83/0.82 (~c1_1(a1911)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[253, 583])).
% 0.83/0.82 tff(586,plain,
% 0.83/0.82 (c0_1(a1911)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[264, 583])).
% 0.83/0.82 tff(587,plain,
% 0.83/0.82 (~c2_1(a1911)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[273, 140, 267, 266, 586, 585, 584, 241, 552])).
% 0.83/0.82 tff(588,plain,
% 0.83/0.82 (^[U: $i] : refl((hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 0.83/0.82 inference(bind,[status(th)],[])).
% 0.83/0.82 tff(589,plain,
% 0.83/0.82 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.83/0.82 inference(quant_intro,[status(thm)],[588])).
% 0.83/0.82 tff(590,plain,
% 0.83/0.82 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(591,plain,
% 0.83/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp16) <=> ((hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp16))), rewrite(((hskp22 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp16) <=> (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp16) <=> (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 0.83/0.82 inference(bind,[status(th)],[])).
% 0.83/0.82 tff(592,plain,
% 0.83/0.82 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp16) <=> ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.83/0.82 inference(quant_intro,[status(thm)],[591])).
% 0.83/0.82 tff(593,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp22) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 0.83/0.82 tff(594,plain,
% 0.83/0.82 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[593, 592])).
% 0.83/0.82 tff(595,plain,
% 0.83/0.82 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[594, 590])).
% 0.83/0.82 tff(596,plain,(
% 0.83/0.82 ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.83/0.82 inference(skolemize,[status(sab)],[595])).
% 0.83/0.82 tff(597,plain,
% 0.83/0.82 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[596, 589])).
% 0.83/0.82 tff(598,plain,
% 0.83/0.82 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | c2_1(a1911))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp22 | hskp16 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | c2_1(a1911))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(599,plain,
% 0.83/0.82 ((hskp22 | hskp16 | (~ndr1_0) | c2_1(a1911) | c1_1(a1911) | c3_1(a1911)) <=> (hskp22 | hskp16 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | c2_1(a1911))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(600,plain,
% 0.83/0.82 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | (~ndr1_0) | c2_1(a1911) | c1_1(a1911) | c3_1(a1911))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | c2_1(a1911)))),
% 0.83/0.82 inference(monotonicity,[status(thm)],[599])).
% 0.83/0.82 tff(601,plain,
% 0.83/0.82 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | (~ndr1_0) | c2_1(a1911) | c1_1(a1911) | c3_1(a1911))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp22 | hskp16 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | c2_1(a1911))),
% 0.83/0.82 inference(transitivity,[status(thm)],[600, 598])).
% 0.83/0.82 tff(602,plain,
% 0.83/0.82 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | (~ndr1_0) | c2_1(a1911) | c1_1(a1911) | c3_1(a1911))),
% 0.83/0.82 inference(quant_inst,[status(thm)],[])).
% 0.83/0.82 tff(603,plain,
% 0.83/0.82 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp22 | hskp16 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | c2_1(a1911)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.83/0.82 tff(604,plain,
% 0.83/0.82 (hskp22 | hskp16 | c2_1(a1911)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[603, 140, 585, 584, 597])).
% 0.83/0.82 tff(605,plain,
% 0.83/0.82 (hskp16),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[604, 587, 449])).
% 0.83/0.82 tff(606,plain,
% 0.83/0.82 (((~hskp16) | (~c0_1(a1872))) <=> ((~hskp16) | (~c0_1(a1872)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(607,plain,
% 0.83/0.82 (((~c0_1(a1872)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a1872)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(608,axiom,((~c0_1(a1872)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.83/0.82 tff(609,plain,
% 0.83/0.82 ((~hskp16) | (~c0_1(a1872))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.83/0.82 tff(610,plain,
% 0.83/0.82 ((~hskp16) | (~c0_1(a1872))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[609, 606])).
% 0.83/0.82 tff(611,plain,
% 0.83/0.82 (~c0_1(a1872)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[610, 605])).
% 0.83/0.82 tff(612,plain,
% 0.83/0.82 (((~hskp8) | c1_1(a1862)) <=> ((~hskp8) | c1_1(a1862))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(613,axiom,((~hskp8) | c1_1(a1862)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.83/0.82 tff(614,plain,
% 0.83/0.82 ((~hskp8) | c1_1(a1862)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.83/0.82 tff(615,plain,
% 0.83/0.82 ((~hskp8) | c1_1(a1862)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[614, 612])).
% 0.83/0.82 tff(616,plain,
% 0.83/0.82 ((~hskp8) | c1_1(a1862)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[615, 612])).
% 0.83/0.82 tff(617,plain,
% 0.83/0.82 ((~hskp8) | c1_1(a1862)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[616, 612])).
% 0.83/0.82 tff(618,plain,
% 0.83/0.82 ((~hskp8) | c1_1(a1862)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[617, 612])).
% 0.83/0.82 tff(619,plain,
% 0.83/0.82 ((~hskp8) | c1_1(a1862)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[618, 612])).
% 0.83/0.82 tff(620,plain,
% 0.83/0.82 ((~hskp8) | c1_1(a1862)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[619, 612])).
% 0.83/0.82 tff(621,plain,
% 0.83/0.82 ((~hskp8) | c1_1(a1862)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[620, 612])).
% 0.83/0.82 tff(622,plain,
% 0.83/0.82 (c1_1(a1862)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[621, 569])).
% 0.83/0.82 tff(623,plain,
% 0.83/0.82 (((~hskp16) | c3_1(a1872)) <=> ((~hskp16) | c3_1(a1872))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(624,axiom,((~hskp16) | c3_1(a1872)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.83/0.82 tff(625,plain,
% 0.83/0.82 ((~hskp16) | c3_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.83/0.82 tff(626,plain,
% 0.83/0.82 ((~hskp16) | c3_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[625, 623])).
% 0.83/0.82 tff(627,plain,
% 0.83/0.82 ((~hskp16) | c3_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[626, 623])).
% 0.83/0.82 tff(628,plain,
% 0.83/0.82 ((~hskp16) | c3_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[627, 623])).
% 0.83/0.82 tff(629,plain,
% 0.83/0.82 ((~hskp16) | c3_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[628, 623])).
% 0.83/0.82 tff(630,plain,
% 0.83/0.82 ((~hskp16) | c3_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[629, 623])).
% 0.83/0.82 tff(631,plain,
% 0.83/0.82 ((~hskp16) | c3_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[630, 623])).
% 0.83/0.82 tff(632,plain,
% 0.83/0.82 ((~hskp16) | c3_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[631, 623])).
% 0.83/0.82 tff(633,plain,
% 0.83/0.82 (c3_1(a1872)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[632, 605])).
% 0.83/0.82 tff(634,plain,
% 0.83/0.82 (((~hskp16) | c2_1(a1872)) <=> ((~hskp16) | c2_1(a1872))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(635,axiom,((~hskp16) | c2_1(a1872)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.83/0.82 tff(636,plain,
% 0.83/0.82 ((~hskp16) | c2_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.83/0.82 tff(637,plain,
% 0.83/0.82 ((~hskp16) | c2_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[636, 634])).
% 0.83/0.82 tff(638,plain,
% 0.83/0.82 ((~hskp16) | c2_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[637, 634])).
% 0.83/0.82 tff(639,plain,
% 0.83/0.82 ((~hskp16) | c2_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[638, 634])).
% 0.83/0.82 tff(640,plain,
% 0.83/0.82 ((~hskp16) | c2_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[639, 634])).
% 0.83/0.82 tff(641,plain,
% 0.83/0.82 ((~hskp16) | c2_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[640, 634])).
% 0.83/0.82 tff(642,plain,
% 0.83/0.82 ((~hskp16) | c2_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[641, 634])).
% 0.83/0.82 tff(643,plain,
% 0.83/0.82 ((~hskp16) | c2_1(a1872)),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[642, 634])).
% 0.83/0.82 tff(644,plain,
% 0.83/0.82 (c2_1(a1872)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[643, 605])).
% 0.83/0.82 tff(645,plain,
% 0.83/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1919) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1919) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(646,plain,
% 0.83/0.82 (((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872))) <=> (c1_1(a1919) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(647,plain,
% 0.83/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1919) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1919)) | (~c0_1(a1919))))),
% 0.83/0.82 inference(monotonicity,[status(thm)],[646])).
% 0.83/0.82 tff(648,plain,
% 0.83/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1919) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.83/0.82 inference(transitivity,[status(thm)],[647, 645])).
% 0.83/0.82 tff(649,plain,
% 0.83/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.83/0.82 inference(quant_inst,[status(thm)],[])).
% 0.83/0.82 tff(650,plain,
% 0.83/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1919) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1919)) | (~c0_1(a1919))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[649, 648])).
% 0.83/0.82 tff(651,plain,
% 0.83/0.82 (~c3_1(a1862)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[650, 140, 461, 644, 633, 622, 473, 611, 575, 10, 448])).
% 0.83/0.82 tff(652,plain,
% 0.83/0.82 (^[U: $i] : refl((hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.83/0.82 inference(bind,[status(th)],[])).
% 0.83/0.82 tff(653,plain,
% 0.83/0.82 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.83/0.82 inference(quant_intro,[status(thm)],[652])).
% 0.83/0.82 tff(654,plain,
% 0.83/0.82 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(655,plain,
% 0.83/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp27) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp27))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp27) <=> (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp27) <=> (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.83/0.82 inference(bind,[status(th)],[])).
% 0.83/0.82 tff(656,plain,
% 0.83/0.82 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp27) <=> ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.83/0.82 inference(quant_intro,[status(thm)],[655])).
% 0.83/0.82 tff(657,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.83/0.82 tff(658,plain,
% 0.83/0.82 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[657, 656])).
% 0.83/0.82 tff(659,plain,
% 0.83/0.82 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[658, 654])).
% 0.83/0.82 tff(660,plain,(
% 0.83/0.82 ![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.83/0.82 inference(skolemize,[status(sab)],[659])).
% 0.83/0.82 tff(661,plain,
% 0.83/0.82 (![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[660, 653])).
% 0.83/0.82 tff(662,plain,
% 0.83/0.82 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp26 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp26 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(663,plain,
% 0.83/0.82 ((hskp27 | hskp26 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919))) <=> (hskp27 | hskp26 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(664,plain,
% 0.83/0.82 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp26 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919))))),
% 0.83/0.82 inference(monotonicity,[status(thm)],[663])).
% 0.83/0.82 tff(665,plain,
% 0.83/0.82 (((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)))) <=> ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp26 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)))),
% 0.83/0.82 inference(transitivity,[status(thm)],[664, 662])).
% 0.83/0.82 tff(666,plain,
% 0.83/0.82 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp27 | hskp26 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)))),
% 0.83/0.82 inference(quant_inst,[status(thm)],[])).
% 0.83/0.82 tff(667,plain,
% 0.83/0.82 ((~![U: $i] : (hskp27 | hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp27 | hskp26 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[666, 665])).
% 0.83/0.82 tff(668,plain,
% 0.83/0.82 (hskp27 | hskp26),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[667, 140, 473, 460, 661, 448])).
% 0.83/0.82 tff(669,plain,
% 0.83/0.82 (hskp27),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[668, 544])).
% 0.83/0.82 tff(670,plain,
% 0.83/0.82 (c2_1(a1877)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[171, 669])).
% 0.83/0.82 tff(671,plain,
% 0.83/0.82 (c0_1(a1877)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[182, 669])).
% 0.83/0.82 tff(672,plain,
% 0.83/0.82 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(673,plain,
% 0.83/0.82 ((hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877))) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.83/0.82 inference(rewrite,[status(thm)],[])).
% 0.83/0.82 tff(674,plain,
% 0.83/0.82 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))))),
% 0.83/0.82 inference(monotonicity,[status(thm)],[673])).
% 0.83/0.82 tff(675,plain,
% 0.83/0.82 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.83/0.82 inference(transitivity,[status(thm)],[674, 672])).
% 0.83/0.82 tff(676,plain,
% 0.83/0.82 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a1877)) | (~c1_1(a1877)) | (~c0_1(a1877)))),
% 0.83/0.82 inference(quant_inst,[status(thm)],[])).
% 0.83/0.82 tff(677,plain,
% 0.83/0.82 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))),
% 0.83/0.82 inference(modus_ponens,[status(thm)],[676, 675])).
% 0.83/0.82 tff(678,plain,
% 0.83/0.82 (hskp3 | (~c1_1(a1877))),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[677, 140, 544, 671, 670, 542])).
% 0.83/0.82 tff(679,plain,
% 0.83/0.82 (~c1_1(a1877)),
% 0.83/0.82 inference(unit_resolution,[status(thm)],[678, 531])).
% 0.83/0.82 tff(680,plain,
% 0.83/0.82 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 0.83/0.82 inference(bind,[status(th)],[])).
% 0.83/0.82 tff(681,plain,
% 0.83/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.82 inference(quant_intro,[status(thm)],[680])).
% 0.83/0.82 tff(682,plain,
% 0.83/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.83 inference(rewrite,[status(thm)],[])).
% 0.83/0.83 tff(683,plain,
% 0.83/0.83 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 0.83/0.83 inference(bind,[status(th)],[])).
% 0.83/0.83 tff(684,plain,
% 0.83/0.83 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.83 inference(quant_intro,[status(thm)],[683])).
% 0.83/0.83 tff(685,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.83/0.83 tff(686,plain,
% 0.83/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[685, 684])).
% 0.83/0.83 tff(687,plain,
% 0.83/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[686, 682])).
% 0.83/0.83 tff(688,plain,(
% 0.83/0.83 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.83 inference(skolemize,[status(sab)],[687])).
% 0.83/0.83 tff(689,plain,
% 0.83/0.83 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 0.83/0.83 inference(modus_ponens,[status(thm)],[688, 681])).
% 0.90/0.83 tff(690,plain,
% 0.90/0.83 (c3_1(a1877)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[160, 669])).
% 0.90/0.83 tff(691,plain,
% 0.90/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c2_1(a1877)) | c1_1(a1877))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c2_1(a1877)) | c1_1(a1877))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(692,plain,
% 0.90/0.83 (((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1877) | (~c2_1(a1877)) | (~c3_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872))) <=> (c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c2_1(a1877)) | c1_1(a1877))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(693,plain,
% 0.90/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1877) | (~c2_1(a1877)) | (~c3_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c2_1(a1877)) | c1_1(a1877)))),
% 0.90/0.83 inference(monotonicity,[status(thm)],[692])).
% 0.90/0.83 tff(694,plain,
% 0.90/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1877) | (~c2_1(a1877)) | (~c3_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c2_1(a1877)) | c1_1(a1877))),
% 0.90/0.83 inference(transitivity,[status(thm)],[693, 691])).
% 0.90/0.83 tff(695,plain,
% 0.90/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1877) | (~c2_1(a1877)) | (~c3_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.90/0.83 inference(quant_inst,[status(thm)],[])).
% 0.90/0.83 tff(696,plain,
% 0.90/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c2_1(a1877)) | c1_1(a1877)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.90/0.83 tff(697,plain,
% 0.90/0.83 ($false),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[696, 140, 670, 690, 644, 633, 622, 611, 575, 689, 679, 651])).
% 0.90/0.83 tff(698,plain,(hskp3 | (~c3_1(a1919)) | c1_1(a1919) | (~c0_1(a1919)) | hskp22 | (~c1_1(a1878)) | (~c2_1(a1878)) | c2_1(a1919) | (~c3_1(a1878)) | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.90/0.83 tff(699,plain,
% 0.90/0.83 (hskp26),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[698, 532, 473, 448, 461, 531, 449, 460, 530, 529])).
% 0.90/0.83 tff(700,plain,
% 0.90/0.83 (c3_1(a1858)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[360, 699])).
% 0.90/0.83 tff(701,plain,
% 0.90/0.83 (c1_1(a1858)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[331, 699])).
% 0.90/0.83 tff(702,plain,
% 0.90/0.83 (c0_1(a1858)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[342, 699])).
% 0.90/0.83 tff(703,plain,
% 0.90/0.83 (^[U: $i] : refl((hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.90/0.83 inference(bind,[status(th)],[])).
% 0.90/0.83 tff(704,plain,
% 0.90/0.83 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.83 inference(quant_intro,[status(thm)],[703])).
% 0.90/0.83 tff(705,plain,
% 0.90/0.83 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(706,plain,
% 0.90/0.83 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp16) | hskp13) <=> ((hskp16 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp13))), rewrite(((hskp16 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp13) <=> (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp16) | hskp13) <=> (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.90/0.83 inference(bind,[status(th)],[])).
% 0.90/0.83 tff(707,plain,
% 0.90/0.83 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp16) | hskp13) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.83 inference(quant_intro,[status(thm)],[706])).
% 0.90/0.83 tff(708,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp16) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.90/0.83 tff(709,plain,
% 0.90/0.83 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.90/0.83 tff(710,plain,
% 0.90/0.83 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[709, 705])).
% 0.90/0.83 tff(711,plain,(
% 0.90/0.83 ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.83 inference(skolemize,[status(sab)],[710])).
% 0.90/0.83 tff(712,plain,
% 0.90/0.83 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[711, 704])).
% 0.90/0.83 tff(713,assumption,(~hskp16), introduced(assumption)).
% 0.90/0.83 tff(714,plain,
% 0.90/0.83 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.90/0.83 inference(bind,[status(th)],[])).
% 0.90/0.83 tff(715,plain,
% 0.90/0.83 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/0.83 inference(quant_intro,[status(thm)],[714])).
% 0.90/0.83 tff(716,plain,
% 0.90/0.83 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(717,plain,
% 0.90/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_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) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_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)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.90/0.83 inference(bind,[status(th)],[])).
% 0.90/0.83 tff(718,plain,
% 0.90/0.83 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/0.83 inference(quant_intro,[status(thm)],[717])).
% 0.90/0.83 tff(719,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)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 0.90/0.83 tff(720,plain,
% 0.90/0.83 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[719, 718])).
% 0.90/0.83 tff(721,plain,
% 0.90/0.83 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[720, 716])).
% 0.90/0.83 tff(722,plain,(
% 0.90/0.83 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/0.83 inference(skolemize,[status(sab)],[721])).
% 0.90/0.83 tff(723,plain,
% 0.90/0.83 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[722, 715])).
% 0.90/0.83 tff(724,assumption,(hskp8), introduced(assumption)).
% 0.90/0.83 tff(725,plain,
% 0.90/0.83 (~c2_1(a1862)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[574, 724])).
% 0.90/0.83 tff(726,plain,
% 0.90/0.83 (c1_1(a1862)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[621, 724])).
% 0.90/0.83 tff(727,plain,
% 0.90/0.83 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(728,plain,
% 0.90/0.83 ((hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862))) <=> (hskp16 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(729,plain,
% 0.90/0.83 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.90/0.83 inference(monotonicity,[status(thm)],[728])).
% 0.90/0.83 tff(730,plain,
% 0.90/0.83 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.90/0.83 inference(transitivity,[status(thm)],[729, 727])).
% 0.90/0.83 tff(731,plain,
% 0.90/0.83 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)))),
% 0.90/0.83 inference(quant_inst,[status(thm)],[])).
% 0.90/0.83 tff(732,plain,
% 0.90/0.83 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[731, 730])).
% 0.90/0.83 tff(733,plain,
% 0.90/0.83 (~c3_1(a1862)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[732, 140, 713, 287, 286, 285, 726, 725, 723])).
% 0.90/0.83 tff(734,plain,
% 0.90/0.83 (((~hskp8) | c0_1(a1862)) <=> ((~hskp8) | c0_1(a1862))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(735,axiom,((~hskp8) | c0_1(a1862)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.90/0.83 tff(736,plain,
% 0.90/0.83 ((~hskp8) | c0_1(a1862)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[735, 734])).
% 0.90/0.83 tff(737,plain,
% 0.90/0.83 ((~hskp8) | c0_1(a1862)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[736, 734])).
% 0.90/0.83 tff(738,plain,
% 0.90/0.83 ((~hskp8) | c0_1(a1862)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[737, 734])).
% 0.90/0.83 tff(739,plain,
% 0.90/0.83 ((~hskp8) | c0_1(a1862)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[738, 734])).
% 0.90/0.83 tff(740,plain,
% 0.90/0.83 ((~hskp8) | c0_1(a1862)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[739, 734])).
% 0.90/0.83 tff(741,plain,
% 0.90/0.83 ((~hskp8) | c0_1(a1862)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[740, 734])).
% 0.90/0.83 tff(742,plain,
% 0.90/0.83 ((~hskp8) | c0_1(a1862)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[741, 734])).
% 0.90/0.83 tff(743,plain,
% 0.90/0.83 ((~hskp8) | c0_1(a1862)),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[742, 734])).
% 0.90/0.83 tff(744,plain,
% 0.90/0.83 (c0_1(a1862)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[743, 724])).
% 0.90/0.83 tff(745,plain,
% 0.90/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(746,plain,
% 0.90/0.83 (((~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c3_1(a1862) | c2_1(a1862) | (~c1_1(a1862))) <=> (c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(747,plain,
% 0.90/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c3_1(a1862) | c2_1(a1862) | (~c1_1(a1862)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862))))),
% 0.90/0.83 inference(monotonicity,[status(thm)],[746])).
% 0.90/0.83 tff(748,plain,
% 0.90/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c3_1(a1862) | c2_1(a1862) | (~c1_1(a1862)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.90/0.83 inference(transitivity,[status(thm)],[747, 745])).
% 0.90/0.83 tff(749,plain,
% 0.90/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c3_1(a1862) | c2_1(a1862) | (~c1_1(a1862)))),
% 0.90/0.83 inference(quant_inst,[status(thm)],[])).
% 0.90/0.83 tff(750,plain,
% 0.90/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[749, 748])).
% 0.90/0.83 tff(751,plain,
% 0.90/0.83 ($false),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[750, 140, 744, 726, 725, 410, 733])).
% 0.90/0.83 tff(752,plain,((~hskp8) | hskp16 | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c3_1(a1877))), inference(lemma,lemma(discharge,[]))).
% 0.90/0.83 tff(753,plain,
% 0.90/0.83 (~hskp8),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[752, 713, 287, 286, 285])).
% 0.90/0.83 tff(754,assumption,(hskp13), introduced(assumption)).
% 0.90/0.83 tff(755,plain,
% 0.90/0.83 (((~hskp13) | (~c3_1(a1867))) <=> ((~hskp13) | (~c3_1(a1867)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(756,plain,
% 0.90/0.83 (((~c3_1(a1867)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a1867)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(757,axiom,((~c3_1(a1867)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 0.90/0.83 tff(758,plain,
% 0.90/0.83 ((~hskp13) | (~c3_1(a1867))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[757, 756])).
% 0.90/0.83 tff(759,plain,
% 0.90/0.83 ((~hskp13) | (~c3_1(a1867))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[758, 755])).
% 0.90/0.83 tff(760,plain,
% 0.90/0.83 (~c3_1(a1867)),
% 0.90/0.83 inference(unit_resolution,[status(thm)],[759, 754])).
% 0.90/0.83 tff(761,plain,
% 0.90/0.83 (((~hskp13) | (~c2_1(a1867))) <=> ((~hskp13) | (~c2_1(a1867)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(762,plain,
% 0.90/0.83 (((~c2_1(a1867)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a1867)))),
% 0.90/0.83 inference(rewrite,[status(thm)],[])).
% 0.90/0.83 tff(763,axiom,((~c2_1(a1867)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.90/0.83 tff(764,plain,
% 0.90/0.83 ((~hskp13) | (~c2_1(a1867))),
% 0.90/0.83 inference(modus_ponens,[status(thm)],[763, 762])).
% 0.90/0.84 tff(765,plain,
% 0.90/0.84 ((~hskp13) | (~c2_1(a1867))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[764, 761])).
% 0.90/0.84 tff(766,plain,
% 0.90/0.84 (~c2_1(a1867)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[765, 754])).
% 0.90/0.84 tff(767,plain,
% 0.90/0.84 (((~hskp13) | (~c1_1(a1867))) <=> ((~hskp13) | (~c1_1(a1867)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(768,plain,
% 0.90/0.84 (((~c1_1(a1867)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a1867)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(769,axiom,((~c1_1(a1867)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.90/0.84 tff(770,plain,
% 0.90/0.84 ((~hskp13) | (~c1_1(a1867))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[769, 768])).
% 0.90/0.84 tff(771,plain,
% 0.90/0.84 ((~hskp13) | (~c1_1(a1867))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[770, 767])).
% 0.90/0.84 tff(772,plain,
% 0.90/0.84 (~c1_1(a1867)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[771, 754])).
% 0.90/0.84 tff(773,plain,
% 0.90/0.84 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | c1_1(a1867) | c2_1(a1867) | c3_1(a1867) | (~ndr1_0))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp22 | hskp16 | c1_1(a1867) | c2_1(a1867) | c3_1(a1867) | (~ndr1_0))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(774,plain,
% 0.90/0.84 ((hskp22 | hskp16 | (~ndr1_0) | c2_1(a1867) | c1_1(a1867) | c3_1(a1867)) <=> (hskp22 | hskp16 | c1_1(a1867) | c2_1(a1867) | c3_1(a1867) | (~ndr1_0))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(775,plain,
% 0.90/0.84 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | (~ndr1_0) | c2_1(a1867) | c1_1(a1867) | c3_1(a1867))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | c1_1(a1867) | c2_1(a1867) | c3_1(a1867) | (~ndr1_0)))),
% 0.90/0.84 inference(monotonicity,[status(thm)],[774])).
% 0.90/0.84 tff(776,plain,
% 0.90/0.84 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | (~ndr1_0) | c2_1(a1867) | c1_1(a1867) | c3_1(a1867))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp22 | hskp16 | c1_1(a1867) | c2_1(a1867) | c3_1(a1867) | (~ndr1_0))),
% 0.90/0.84 inference(transitivity,[status(thm)],[775, 773])).
% 0.90/0.84 tff(777,plain,
% 0.90/0.84 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp22 | hskp16 | (~ndr1_0) | c2_1(a1867) | c1_1(a1867) | c3_1(a1867))),
% 0.90/0.84 inference(quant_inst,[status(thm)],[])).
% 0.90/0.84 tff(778,plain,
% 0.90/0.84 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp22 | hskp16 | c1_1(a1867) | c2_1(a1867) | c3_1(a1867) | (~ndr1_0)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[777, 776])).
% 0.90/0.84 tff(779,plain,
% 0.90/0.84 ($false),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[778, 140, 449, 713, 772, 766, 760, 597])).
% 0.90/0.84 tff(780,plain,((~hskp13) | hskp22 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.90/0.84 tff(781,plain,
% 0.90/0.84 (~hskp13),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[780, 713, 449])).
% 0.90/0.84 tff(782,plain,
% 0.90/0.84 (^[U: $i] : refl((hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.90/0.84 inference(bind,[status(th)],[])).
% 0.90/0.84 tff(783,plain,
% 0.90/0.84 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.90/0.84 inference(quant_intro,[status(thm)],[782])).
% 0.90/0.84 tff(784,plain,
% 0.90/0.84 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(785,plain,
% 0.90/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp13) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp13))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp13) <=> (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp13) <=> (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.90/0.84 inference(bind,[status(th)],[])).
% 0.90/0.84 tff(786,plain,
% 0.90/0.84 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp13) <=> ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.90/0.84 inference(quant_intro,[status(thm)],[785])).
% 0.90/0.84 tff(787,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 0.90/0.84 tff(788,plain,
% 0.90/0.84 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[787, 786])).
% 0.90/0.84 tff(789,plain,
% 0.90/0.84 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[788, 784])).
% 0.90/0.84 tff(790,plain,(
% 0.90/0.84 ![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.90/0.84 inference(skolemize,[status(sab)],[789])).
% 0.90/0.84 tff(791,plain,
% 0.90/0.84 (![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[790, 783])).
% 0.90/0.84 tff(792,plain,
% 0.90/0.84 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp13 | hskp9 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp13 | hskp9 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(793,plain,
% 0.90/0.84 ((hskp13 | hskp9 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919))) <=> (hskp13 | hskp9 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(794,plain,
% 0.90/0.84 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp13 | hskp9 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919))))),
% 0.90/0.84 inference(monotonicity,[status(thm)],[793])).
% 0.90/0.84 tff(795,plain,
% 0.90/0.84 (((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)))) <=> ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp13 | hskp9 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919)))),
% 0.90/0.84 inference(transitivity,[status(thm)],[794, 792])).
% 0.90/0.84 tff(796,plain,
% 0.90/0.84 ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp13 | hskp9 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)))),
% 0.90/0.84 inference(quant_inst,[status(thm)],[])).
% 0.90/0.84 tff(797,plain,
% 0.90/0.84 ((~![U: $i] : (hskp13 | hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp13 | hskp9 | c1_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c3_1(a1919))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[796, 795])).
% 0.90/0.84 tff(798,plain,
% 0.90/0.84 (hskp13 | hskp9),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[797, 140, 461, 473, 460, 791])).
% 0.90/0.84 tff(799,plain,
% 0.90/0.84 (hskp9),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[798, 781])).
% 0.90/0.84 tff(800,plain,
% 0.90/0.84 (^[U: $i] : refl((hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))),
% 0.90/0.84 inference(bind,[status(th)],[])).
% 0.90/0.84 tff(801,plain,
% 0.90/0.84 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(quant_intro,[status(thm)],[800])).
% 0.90/0.84 tff(802,plain,
% 0.90/0.84 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(803,plain,
% 0.90/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp23))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | hskp23) <=> (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))))),
% 0.90/0.84 inference(bind,[status(th)],[])).
% 0.90/0.84 tff(804,plain,
% 0.90/0.84 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(quant_intro,[status(thm)],[803])).
% 0.90/0.84 tff(805,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 0.90/0.84 tff(806,plain,
% 0.90/0.84 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[805, 804])).
% 0.90/0.84 tff(807,plain,
% 0.90/0.84 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[806, 802])).
% 0.90/0.84 tff(808,plain,(
% 0.90/0.84 ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(skolemize,[status(sab)],[807])).
% 0.90/0.84 tff(809,plain,
% 0.90/0.84 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[808, 801])).
% 0.90/0.84 tff(810,assumption,(hskp9), introduced(assumption)).
% 0.90/0.84 tff(811,plain,
% 0.90/0.84 (((~hskp9) | (~c3_1(a1863))) <=> ((~hskp9) | (~c3_1(a1863)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(812,plain,
% 0.90/0.84 (((~c3_1(a1863)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a1863)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(813,axiom,((~c3_1(a1863)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 0.90/0.84 tff(814,plain,
% 0.90/0.84 ((~hskp9) | (~c3_1(a1863))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[813, 812])).
% 0.90/0.84 tff(815,plain,
% 0.90/0.84 ((~hskp9) | (~c3_1(a1863))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[814, 811])).
% 0.90/0.84 tff(816,plain,
% 0.90/0.84 (~c3_1(a1863)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[815, 810])).
% 0.90/0.84 tff(817,plain,
% 0.90/0.84 (((~hskp9) | (~c1_1(a1863))) <=> ((~hskp9) | (~c1_1(a1863)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(818,plain,
% 0.90/0.84 (((~c1_1(a1863)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a1863)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(819,axiom,((~c1_1(a1863)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.90/0.84 tff(820,plain,
% 0.90/0.84 ((~hskp9) | (~c1_1(a1863))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[819, 818])).
% 0.90/0.84 tff(821,plain,
% 0.90/0.84 ((~hskp9) | (~c1_1(a1863))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[820, 817])).
% 0.90/0.84 tff(822,plain,
% 0.90/0.84 (~c1_1(a1863)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[821, 810])).
% 0.90/0.84 tff(823,plain,
% 0.90/0.84 (((~hskp9) | c2_1(a1863)) <=> ((~hskp9) | c2_1(a1863))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(824,axiom,((~hskp9) | c2_1(a1863)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 0.90/0.84 tff(825,plain,
% 0.90/0.84 ((~hskp9) | c2_1(a1863)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[824, 823])).
% 0.90/0.84 tff(826,plain,
% 0.90/0.84 ((~hskp9) | c2_1(a1863)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[825, 823])).
% 0.90/0.84 tff(827,plain,
% 0.90/0.84 ((~hskp9) | c2_1(a1863)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[826, 823])).
% 0.90/0.84 tff(828,plain,
% 0.90/0.84 ((~hskp9) | c2_1(a1863)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[827, 823])).
% 0.90/0.84 tff(829,plain,
% 0.90/0.84 ((~hskp9) | c2_1(a1863)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[828, 823])).
% 0.90/0.84 tff(830,plain,
% 0.90/0.84 ((~hskp9) | c2_1(a1863)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[829, 823])).
% 0.90/0.84 tff(831,plain,
% 0.90/0.84 ((~hskp9) | c2_1(a1863)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[830, 823])).
% 0.90/0.84 tff(832,plain,
% 0.90/0.84 ((~hskp9) | c2_1(a1863)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[831, 823])).
% 0.90/0.84 tff(833,plain,
% 0.90/0.84 (c2_1(a1863)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[832, 810])).
% 0.90/0.84 tff(834,assumption,(~hskp23), introduced(assumption)).
% 0.90/0.84 tff(835,plain,
% 0.90/0.84 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(836,plain,
% 0.90/0.84 ((hskp23 | hskp8 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863))) <=> (hskp23 | hskp8 | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(837,plain,
% 0.90/0.84 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863))))),
% 0.90/0.84 inference(monotonicity,[status(thm)],[836])).
% 0.90/0.84 tff(838,plain,
% 0.90/0.84 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)))),
% 0.90/0.84 inference(transitivity,[status(thm)],[837, 835])).
% 0.90/0.84 tff(839,plain,
% 0.90/0.84 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)))),
% 0.90/0.84 inference(quant_inst,[status(thm)],[])).
% 0.90/0.84 tff(840,plain,
% 0.90/0.84 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[839, 838])).
% 0.90/0.84 tff(841,plain,
% 0.90/0.84 ($false),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[840, 140, 834, 21, 833, 822, 816, 809])).
% 0.90/0.84 tff(842,plain,((~hskp9) | hskp23 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.90/0.84 tff(843,plain,
% 0.90/0.84 (hskp23),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[842, 799, 753])).
% 0.90/0.84 tff(844,plain,
% 0.90/0.84 (~c3_1(a1911)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[247, 843])).
% 0.90/0.84 tff(845,plain,
% 0.90/0.84 (~c1_1(a1911)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[253, 843])).
% 0.90/0.84 tff(846,plain,
% 0.90/0.84 (c2_1(a1911)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[603, 140, 449, 713, 845, 844, 597])).
% 0.90/0.84 tff(847,plain,
% 0.90/0.84 (c0_1(a1911)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[264, 843])).
% 0.90/0.84 tff(848,assumption,(hskp20), introduced(assumption)).
% 0.90/0.84 tff(849,plain,
% 0.90/0.84 (((~hskp20) | (~c1_1(a1890))) <=> ((~hskp20) | (~c1_1(a1890)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(850,plain,
% 0.90/0.84 (((~c1_1(a1890)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a1890)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(851,axiom,((~c1_1(a1890)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.90/0.84 tff(852,plain,
% 0.90/0.84 ((~hskp20) | (~c1_1(a1890))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[851, 850])).
% 0.90/0.84 tff(853,plain,
% 0.90/0.84 ((~hskp20) | (~c1_1(a1890))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[852, 849])).
% 0.90/0.84 tff(854,plain,
% 0.90/0.84 (~c1_1(a1890)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[853, 848])).
% 0.90/0.84 tff(855,plain,
% 0.90/0.84 (((~hskp20) | (~c0_1(a1890))) <=> ((~hskp20) | (~c0_1(a1890)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(856,plain,
% 0.90/0.84 (((~c0_1(a1890)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a1890)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(857,axiom,((~c0_1(a1890)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.90/0.84 tff(858,plain,
% 0.90/0.84 ((~hskp20) | (~c0_1(a1890))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[857, 856])).
% 0.90/0.84 tff(859,plain,
% 0.90/0.84 ((~hskp20) | (~c0_1(a1890))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[858, 855])).
% 0.90/0.84 tff(860,plain,
% 0.90/0.84 (~c0_1(a1890)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[859, 848])).
% 0.90/0.84 tff(861,assumption,(~hskp13), introduced(assumption)).
% 0.90/0.84 tff(862,plain,
% 0.90/0.84 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c3_1(a1890)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c3_1(a1890)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(863,plain,
% 0.90/0.84 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c3_1(a1890))) <=> (hskp16 | hskp13 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c3_1(a1890)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(864,plain,
% 0.90/0.84 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c3_1(a1890)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c3_1(a1890))))),
% 0.90/0.84 inference(monotonicity,[status(thm)],[863])).
% 0.90/0.84 tff(865,plain,
% 0.90/0.84 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c3_1(a1890)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c3_1(a1890)))),
% 0.90/0.84 inference(transitivity,[status(thm)],[864, 862])).
% 0.90/0.84 tff(866,plain,
% 0.90/0.84 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c3_1(a1890)))),
% 0.90/0.84 inference(quant_inst,[status(thm)],[])).
% 0.90/0.84 tff(867,plain,
% 0.90/0.84 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c3_1(a1890))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[866, 865])).
% 0.90/0.84 tff(868,plain,
% 0.90/0.84 (~c3_1(a1890)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[867, 140, 713, 861, 860, 854, 712])).
% 0.90/0.84 tff(869,assumption,(c2_1(a1911)), introduced(assumption)).
% 0.90/0.84 tff(870,plain,
% 0.90/0.84 (^[U: $i] : refl((hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.90/0.84 inference(bind,[status(th)],[])).
% 0.90/0.84 tff(871,plain,
% 0.90/0.84 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(quant_intro,[status(thm)],[870])).
% 0.90/0.84 tff(872,plain,
% 0.90/0.84 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(873,plain,
% 0.90/0.84 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) | hskp13) <=> ((hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp13))), rewrite(((hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) | hskp13) <=> (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.90/0.84 inference(bind,[status(th)],[])).
% 0.90/0.84 tff(874,plain,
% 0.90/0.84 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) | hskp13) <=> ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(quant_intro,[status(thm)],[873])).
% 0.90/0.84 tff(875,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 0.90/0.84 tff(876,plain,
% 0.90/0.84 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[875, 874])).
% 0.90/0.84 tff(877,plain,
% 0.90/0.84 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[876, 872])).
% 0.90/0.84 tff(878,plain,(
% 0.90/0.84 ![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(skolemize,[status(sab)],[877])).
% 0.90/0.84 tff(879,plain,
% 0.90/0.84 (![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[878, 871])).
% 0.90/0.84 tff(880,plain,
% 0.90/0.84 (((~hskp20) | c2_1(a1890)) <=> ((~hskp20) | c2_1(a1890))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(881,axiom,((~hskp20) | c2_1(a1890)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 0.90/0.84 tff(882,plain,
% 0.90/0.84 ((~hskp20) | c2_1(a1890)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[881, 880])).
% 0.90/0.84 tff(883,plain,
% 0.90/0.84 ((~hskp20) | c2_1(a1890)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[882, 880])).
% 0.90/0.84 tff(884,plain,
% 0.90/0.84 ((~hskp20) | c2_1(a1890)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[883, 880])).
% 0.90/0.84 tff(885,plain,
% 0.90/0.84 ((~hskp20) | c2_1(a1890)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[884, 880])).
% 0.90/0.84 tff(886,plain,
% 0.90/0.84 ((~hskp20) | c2_1(a1890)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[885, 880])).
% 0.90/0.84 tff(887,plain,
% 0.90/0.84 ((~hskp20) | c2_1(a1890)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[886, 880])).
% 0.90/0.84 tff(888,plain,
% 0.90/0.84 ((~hskp20) | c2_1(a1890)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[887, 880])).
% 0.90/0.84 tff(889,plain,
% 0.90/0.84 ((~hskp20) | c2_1(a1890)),
% 0.90/0.84 inference(modus_ponens,[status(thm)],[888, 880])).
% 0.90/0.84 tff(890,plain,
% 0.90/0.84 (c2_1(a1890)),
% 0.90/0.84 inference(unit_resolution,[status(thm)],[889, 848])).
% 0.90/0.84 tff(891,plain,
% 0.90/0.84 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp13 | hskp12 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp13 | hskp12 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))),
% 0.90/0.84 inference(rewrite,[status(thm)],[])).
% 0.90/0.84 tff(892,plain,
% 0.90/0.84 ((hskp13 | hskp12 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890))) <=> (hskp13 | hskp12 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(893,plain,
% 0.90/0.85 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp13 | hskp12 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890))))),
% 0.90/0.85 inference(monotonicity,[status(thm)],[892])).
% 0.90/0.85 tff(894,plain,
% 0.90/0.85 (((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)))) <=> ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp13 | hskp12 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))),
% 0.90/0.85 inference(transitivity,[status(thm)],[893, 891])).
% 0.90/0.85 tff(895,plain,
% 0.90/0.85 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp13 | hskp12 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)))),
% 0.90/0.85 inference(quant_inst,[status(thm)],[])).
% 0.90/0.85 tff(896,plain,
% 0.90/0.85 ((~![U: $i] : (hskp13 | hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp13 | hskp12 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[895, 894])).
% 0.90/0.85 tff(897,plain,
% 0.90/0.85 (hskp12),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[896, 140, 861, 890, 860, 854, 879])).
% 0.90/0.85 tff(898,plain,
% 0.90/0.85 (((~hskp12) | (~c0_1(a1866))) <=> ((~hskp12) | (~c0_1(a1866)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(899,plain,
% 0.90/0.85 (((~c0_1(a1866)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a1866)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(900,axiom,((~c0_1(a1866)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 0.90/0.85 tff(901,plain,
% 0.90/0.85 ((~hskp12) | (~c0_1(a1866))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[900, 899])).
% 0.90/0.85 tff(902,plain,
% 0.90/0.85 ((~hskp12) | (~c0_1(a1866))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[901, 898])).
% 0.90/0.85 tff(903,plain,
% 0.90/0.85 (~c0_1(a1866)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[902, 897])).
% 0.90/0.85 tff(904,assumption,(~c3_1(a1911)), introduced(assumption)).
% 0.90/0.85 tff(905,plain,
% 0.90/0.85 (((~hskp12) | c3_1(a1866)) <=> ((~hskp12) | c3_1(a1866))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(906,axiom,((~hskp12) | c3_1(a1866)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.90/0.85 tff(907,plain,
% 0.90/0.85 ((~hskp12) | c3_1(a1866)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[906, 905])).
% 0.90/0.85 tff(908,plain,
% 0.90/0.85 ((~hskp12) | c3_1(a1866)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[907, 905])).
% 0.90/0.85 tff(909,plain,
% 0.90/0.85 ((~hskp12) | c3_1(a1866)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[908, 905])).
% 0.90/0.85 tff(910,plain,
% 0.90/0.85 ((~hskp12) | c3_1(a1866)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[909, 905])).
% 0.90/0.85 tff(911,plain,
% 0.90/0.85 ((~hskp12) | c3_1(a1866)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[910, 905])).
% 0.90/0.85 tff(912,plain,
% 0.90/0.85 ((~hskp12) | c3_1(a1866)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[911, 905])).
% 0.90/0.85 tff(913,plain,
% 0.90/0.85 ((~hskp12) | c3_1(a1866)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[912, 905])).
% 0.90/0.85 tff(914,plain,
% 0.90/0.85 ((~hskp12) | c3_1(a1866)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[913, 905])).
% 0.90/0.85 tff(915,plain,
% 0.90/0.85 (c3_1(a1866)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[914, 897])).
% 0.90/0.85 tff(916,assumption,(c0_1(a1911)), introduced(assumption)).
% 0.90/0.85 tff(917,plain,
% 0.90/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a1911) | c1_1(a1890) | c0_1(a1866) | (~ndr1_0) | (~c2_1(a1890)) | c3_1(a1890) | (~c3_1(a1866)) | (~c1_1(a1866)) | (~c0_1(a1911)) | (~c2_1(a1911)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1911) | c1_1(a1890) | c0_1(a1866) | (~ndr1_0) | (~c2_1(a1890)) | c3_1(a1890) | (~c3_1(a1866)) | (~c1_1(a1866)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(918,plain,
% 0.90/0.85 (((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1890) | c1_1(a1890) | (~c2_1(a1890)) | c0_1(a1866) | (~c3_1(a1866)) | (~c1_1(a1866))) <=> (c3_1(a1911) | c1_1(a1890) | c0_1(a1866) | (~ndr1_0) | (~c2_1(a1890)) | c3_1(a1890) | (~c3_1(a1866)) | (~c1_1(a1866)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(919,plain,
% 0.90/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1890) | c1_1(a1890) | (~c2_1(a1890)) | c0_1(a1866) | (~c3_1(a1866)) | (~c1_1(a1866)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a1911) | c1_1(a1890) | c0_1(a1866) | (~ndr1_0) | (~c2_1(a1890)) | c3_1(a1890) | (~c3_1(a1866)) | (~c1_1(a1866)) | (~c0_1(a1911)) | (~c2_1(a1911))))),
% 0.90/0.85 inference(monotonicity,[status(thm)],[918])).
% 0.90/0.85 tff(920,plain,
% 0.90/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1890) | c1_1(a1890) | (~c2_1(a1890)) | c0_1(a1866) | (~c3_1(a1866)) | (~c1_1(a1866)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1911) | c1_1(a1890) | c0_1(a1866) | (~ndr1_0) | (~c2_1(a1890)) | c3_1(a1890) | (~c3_1(a1866)) | (~c1_1(a1866)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 0.90/0.85 inference(transitivity,[status(thm)],[919, 917])).
% 0.90/0.85 tff(921,plain,
% 0.90/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1890) | c1_1(a1890) | (~c2_1(a1890)) | c0_1(a1866) | (~c3_1(a1866)) | (~c1_1(a1866)))),
% 0.90/0.85 inference(quant_inst,[status(thm)],[])).
% 0.90/0.85 tff(922,plain,
% 0.90/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1911) | c1_1(a1890) | c0_1(a1866) | (~ndr1_0) | (~c2_1(a1890)) | c3_1(a1890) | (~c3_1(a1866)) | (~c1_1(a1866)) | (~c0_1(a1911)) | (~c2_1(a1911))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[921, 920])).
% 0.90/0.85 tff(923,plain,
% 0.90/0.85 (~c1_1(a1866)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[922, 140, 916, 890, 915, 904, 854, 903, 241, 869, 868])).
% 0.90/0.85 tff(924,plain,
% 0.90/0.85 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | c0_1(a1866) | (~ndr1_0) | (~c3_1(a1866)) | c1_1(a1866))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1866) | (~ndr1_0) | (~c3_1(a1866)) | c1_1(a1866))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(925,plain,
% 0.90/0.85 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a1866) | c0_1(a1866) | (~c3_1(a1866))) <=> (hskp16 | hskp13 | c0_1(a1866) | (~ndr1_0) | (~c3_1(a1866)) | c1_1(a1866))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(926,plain,
% 0.90/0.85 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1866) | c0_1(a1866) | (~c3_1(a1866)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | c0_1(a1866) | (~ndr1_0) | (~c3_1(a1866)) | c1_1(a1866)))),
% 0.90/0.85 inference(monotonicity,[status(thm)],[925])).
% 0.90/0.85 tff(927,plain,
% 0.90/0.85 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1866) | c0_1(a1866) | (~c3_1(a1866)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1866) | (~ndr1_0) | (~c3_1(a1866)) | c1_1(a1866))),
% 0.90/0.85 inference(transitivity,[status(thm)],[926, 924])).
% 0.90/0.85 tff(928,plain,
% 0.90/0.85 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1866) | c0_1(a1866) | (~c3_1(a1866)))),
% 0.90/0.85 inference(quant_inst,[status(thm)],[])).
% 0.90/0.85 tff(929,plain,
% 0.90/0.85 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1866) | (~ndr1_0) | (~c3_1(a1866)) | c1_1(a1866)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[928, 927])).
% 0.90/0.85 tff(930,plain,
% 0.90/0.85 ($false),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[929, 140, 713, 861, 915, 903, 712, 923])).
% 0.90/0.85 tff(931,plain,((~hskp20) | hskp16 | hskp13 | (~c0_1(a1911)) | c3_1(a1911) | (~c2_1(a1911))), inference(lemma,lemma(discharge,[]))).
% 0.90/0.85 tff(932,plain,
% 0.90/0.85 (~hskp20),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[931, 713, 781, 847, 844, 846])).
% 0.90/0.85 tff(933,plain,
% 0.90/0.85 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(934,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[933])).
% 0.90/0.85 tff(935,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(936,plain,
% 0.90/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp20) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(937,plain,
% 0.90/0.85 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[936])).
% 0.90/0.85 tff(938,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(V)) | c3_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 0.90/0.85 tff(939,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[938, 937])).
% 0.90/0.85 tff(940,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[939, 935])).
% 0.90/0.85 tff(941,plain,(
% 0.90/0.85 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(skolemize,[status(sab)],[940])).
% 0.90/0.85 tff(942,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[941, 934])).
% 0.90/0.85 tff(943,plain,
% 0.90/0.85 (^[U: $i] : refl((hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(944,plain,
% 0.90/0.85 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[943])).
% 0.90/0.85 tff(945,plain,
% 0.90/0.85 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(946,plain,
% 0.90/0.85 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp18) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp18))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp18) <=> (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(947,plain,
% 0.90/0.85 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp18) <=> ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[946])).
% 0.90/0.85 tff(948,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp8) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 0.90/0.85 tff(949,plain,
% 0.90/0.85 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[948, 947])).
% 0.90/0.85 tff(950,plain,
% 0.90/0.85 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[949, 945])).
% 0.90/0.85 tff(951,plain,(
% 0.90/0.85 ![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.90/0.85 inference(skolemize,[status(sab)],[950])).
% 0.90/0.85 tff(952,plain,
% 0.90/0.85 (![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[951, 944])).
% 0.90/0.85 tff(953,plain,
% 0.90/0.85 ((hskp17 | hskp16 | hskp8) <=> (hskp17 | hskp16 | hskp8)),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(954,plain,
% 0.90/0.85 (((hskp17 | hskp8) | hskp16) <=> (hskp17 | hskp16 | hskp8)),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(955,plain,
% 0.90/0.85 ((hskp8 | hskp17) <=> (hskp17 | hskp8)),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(956,plain,
% 0.90/0.85 (((hskp8 | hskp17) | hskp16) <=> ((hskp17 | hskp8) | hskp16)),
% 0.90/0.85 inference(monotonicity,[status(thm)],[955])).
% 0.90/0.85 tff(957,plain,
% 0.90/0.85 (((hskp8 | hskp17) | hskp16) <=> (hskp17 | hskp16 | hskp8)),
% 0.90/0.85 inference(transitivity,[status(thm)],[956, 954])).
% 0.90/0.85 tff(958,axiom,((hskp8 | hskp17) | hskp16), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 0.90/0.85 tff(959,plain,
% 0.90/0.85 (hskp17 | hskp16 | hskp8),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[958, 957])).
% 0.90/0.85 tff(960,plain,
% 0.90/0.85 (hskp17 | hskp16 | hskp8),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[959, 953])).
% 0.90/0.85 tff(961,plain,
% 0.90/0.85 (hskp17 | hskp16 | hskp8),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[960, 953])).
% 0.90/0.85 tff(962,plain,
% 0.90/0.85 (hskp17 | hskp16 | hskp8),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[961, 953])).
% 0.90/0.85 tff(963,plain,
% 0.90/0.85 (hskp17 | hskp16 | hskp8),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[962, 953])).
% 0.90/0.85 tff(964,plain,
% 0.90/0.85 (hskp17 | hskp16 | hskp8),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[963, 953])).
% 0.90/0.85 tff(965,plain,
% 0.90/0.85 (hskp17 | hskp16 | hskp8),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[964, 953])).
% 0.90/0.85 tff(966,plain,
% 0.90/0.85 (hskp17 | hskp16 | hskp8),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[965, 953])).
% 0.90/0.85 tff(967,plain,
% 0.90/0.85 (hskp17),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[966, 753, 713])).
% 0.90/0.85 tff(968,plain,
% 0.90/0.85 (((~hskp17) | (~c1_1(a1874))) <=> ((~hskp17) | (~c1_1(a1874)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(969,plain,
% 0.90/0.85 (((~c1_1(a1874)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1874)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(970,axiom,((~c1_1(a1874)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.90/0.85 tff(971,plain,
% 0.90/0.85 ((~hskp17) | (~c1_1(a1874))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[970, 969])).
% 0.90/0.85 tff(972,plain,
% 0.90/0.85 ((~hskp17) | (~c1_1(a1874))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[971, 968])).
% 0.90/0.85 tff(973,plain,
% 0.90/0.85 (~c1_1(a1874)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[972, 967])).
% 0.90/0.85 tff(974,plain,
% 0.90/0.85 (((~hskp17) | c2_1(a1874)) <=> ((~hskp17) | c2_1(a1874))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(975,axiom,((~hskp17) | c2_1(a1874)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.90/0.85 tff(976,plain,
% 0.90/0.85 ((~hskp17) | c2_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[975, 974])).
% 0.90/0.85 tff(977,plain,
% 0.90/0.85 ((~hskp17) | c2_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[976, 974])).
% 0.90/0.85 tff(978,plain,
% 0.90/0.85 ((~hskp17) | c2_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[977, 974])).
% 0.90/0.85 tff(979,plain,
% 0.90/0.85 ((~hskp17) | c2_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[978, 974])).
% 0.90/0.85 tff(980,plain,
% 0.90/0.85 ((~hskp17) | c2_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[979, 974])).
% 0.90/0.85 tff(981,plain,
% 0.90/0.85 ((~hskp17) | c2_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[980, 974])).
% 0.90/0.85 tff(982,plain,
% 0.90/0.85 ((~hskp17) | c2_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[981, 974])).
% 0.90/0.85 tff(983,plain,
% 0.90/0.85 ((~hskp17) | c2_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[982, 974])).
% 0.90/0.85 tff(984,plain,
% 0.90/0.85 (c2_1(a1874)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[983, 967])).
% 0.90/0.85 tff(985,plain,
% 0.90/0.85 (((~hskp17) | c0_1(a1874)) <=> ((~hskp17) | c0_1(a1874))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(986,axiom,((~hskp17) | c0_1(a1874)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.90/0.85 tff(987,plain,
% 0.90/0.85 ((~hskp17) | c0_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[986, 985])).
% 0.90/0.85 tff(988,plain,
% 0.90/0.85 ((~hskp17) | c0_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[987, 985])).
% 0.90/0.85 tff(989,plain,
% 0.90/0.85 ((~hskp17) | c0_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[988, 985])).
% 0.90/0.85 tff(990,plain,
% 0.90/0.85 ((~hskp17) | c0_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[989, 985])).
% 0.90/0.85 tff(991,plain,
% 0.90/0.85 ((~hskp17) | c0_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[990, 985])).
% 0.90/0.85 tff(992,plain,
% 0.90/0.85 ((~hskp17) | c0_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[991, 985])).
% 0.90/0.85 tff(993,plain,
% 0.90/0.85 ((~hskp17) | c0_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[992, 985])).
% 0.90/0.85 tff(994,plain,
% 0.90/0.85 ((~hskp17) | c0_1(a1874)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[993, 985])).
% 0.90/0.85 tff(995,plain,
% 0.90/0.85 (c0_1(a1874)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[994, 967])).
% 0.90/0.85 tff(996,plain,
% 0.90/0.85 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | c1_1(a1874) | (~ndr1_0) | (~c0_1(a1874)) | (~c2_1(a1874)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp8 | c1_1(a1874) | (~ndr1_0) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(997,plain,
% 0.90/0.85 ((hskp18 | hskp8 | (~ndr1_0) | c1_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874))) <=> (hskp18 | hskp8 | c1_1(a1874) | (~ndr1_0) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(998,plain,
% 0.90/0.85 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c1_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | c1_1(a1874) | (~ndr1_0) | (~c0_1(a1874)) | (~c2_1(a1874))))),
% 0.90/0.85 inference(monotonicity,[status(thm)],[997])).
% 0.90/0.85 tff(999,plain,
% 0.90/0.85 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c1_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp8 | c1_1(a1874) | (~ndr1_0) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.90/0.85 inference(transitivity,[status(thm)],[998, 996])).
% 0.90/0.85 tff(1000,plain,
% 0.90/0.85 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c1_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)))),
% 0.90/0.85 inference(quant_inst,[status(thm)],[])).
% 0.90/0.85 tff(1001,plain,
% 0.90/0.85 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp8 | c1_1(a1874) | (~ndr1_0) | (~c0_1(a1874)) | (~c2_1(a1874))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1000, 999])).
% 0.90/0.85 tff(1002,plain,
% 0.90/0.85 (hskp18),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[1001, 140, 753, 995, 984, 973, 952])).
% 0.90/0.85 tff(1003,plain,
% 0.90/0.85 (((~hskp18) | (~c3_1(a1875))) <=> ((~hskp18) | (~c3_1(a1875)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1004,plain,
% 0.90/0.85 (((~c3_1(a1875)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a1875)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1005,axiom,((~c3_1(a1875)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.90/0.85 tff(1006,plain,
% 0.90/0.85 ((~hskp18) | (~c3_1(a1875))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 0.90/0.85 tff(1007,plain,
% 0.90/0.85 ((~hskp18) | (~c3_1(a1875))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1006, 1003])).
% 0.90/0.85 tff(1008,plain,
% 0.90/0.85 (~c3_1(a1875)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[1007, 1002])).
% 0.90/0.85 tff(1009,plain,
% 0.90/0.85 (((~hskp18) | c1_1(a1875)) <=> ((~hskp18) | c1_1(a1875))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(1010,axiom,((~hskp18) | c1_1(a1875)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.90/0.85 tff(1011,plain,
% 0.90/0.85 ((~hskp18) | c1_1(a1875)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 0.90/0.85 tff(1012,plain,
% 0.90/0.85 ((~hskp18) | c1_1(a1875)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1011, 1009])).
% 0.90/0.85 tff(1013,plain,
% 0.90/0.85 ((~hskp18) | c1_1(a1875)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[1012, 1009])).
% 0.90/0.85 tff(1014,plain,
% 0.90/0.85 ((~hskp18) | c1_1(a1875)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1013, 1009])).
% 0.90/0.86 tff(1015,plain,
% 0.90/0.86 ((~hskp18) | c1_1(a1875)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1014, 1009])).
% 0.90/0.86 tff(1016,plain,
% 0.90/0.86 ((~hskp18) | c1_1(a1875)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1015, 1009])).
% 0.90/0.86 tff(1017,plain,
% 0.90/0.86 ((~hskp18) | c1_1(a1875)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1016, 1009])).
% 0.90/0.86 tff(1018,plain,
% 0.90/0.86 ((~hskp18) | c1_1(a1875)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1017, 1009])).
% 0.90/0.86 tff(1019,plain,
% 0.90/0.86 (c1_1(a1875)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1018, 1002])).
% 0.90/0.86 tff(1020,assumption,(c3_1(a1858)), introduced(assumption)).
% 0.90/0.86 tff(1021,assumption,(c1_1(a1858)), introduced(assumption)).
% 0.90/0.86 tff(1022,assumption,(c0_1(a1858)), introduced(assumption)).
% 0.90/0.86 tff(1023,plain,
% 0.90/0.86 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp20 | c3_1(a1875) | (~ndr1_0) | (~c1_1(a1875)) | c2_1(a1875) | (~c3_1(a1858)) | (~c0_1(a1858)) | (~c1_1(a1858)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp20 | c3_1(a1875) | (~ndr1_0) | (~c1_1(a1875)) | c2_1(a1875) | (~c3_1(a1858)) | (~c0_1(a1858)) | (~c1_1(a1858)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1024,plain,
% 0.90/0.86 ((hskp20 | (~ndr1_0) | (~c3_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)) | c3_1(a1875) | c2_1(a1875) | (~c1_1(a1875))) <=> (hskp20 | c3_1(a1875) | (~ndr1_0) | (~c1_1(a1875)) | c2_1(a1875) | (~c3_1(a1858)) | (~c0_1(a1858)) | (~c1_1(a1858)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1025,plain,
% 0.90/0.86 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)) | c3_1(a1875) | c2_1(a1875) | (~c1_1(a1875)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp20 | c3_1(a1875) | (~ndr1_0) | (~c1_1(a1875)) | c2_1(a1875) | (~c3_1(a1858)) | (~c0_1(a1858)) | (~c1_1(a1858))))),
% 0.90/0.86 inference(monotonicity,[status(thm)],[1024])).
% 0.90/0.86 tff(1026,plain,
% 0.90/0.86 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)) | c3_1(a1875) | c2_1(a1875) | (~c1_1(a1875)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp20 | c3_1(a1875) | (~ndr1_0) | (~c1_1(a1875)) | c2_1(a1875) | (~c3_1(a1858)) | (~c0_1(a1858)) | (~c1_1(a1858)))),
% 0.90/0.86 inference(transitivity,[status(thm)],[1025, 1023])).
% 0.90/0.86 tff(1027,plain,
% 0.90/0.86 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a1858)) | (~c1_1(a1858)) | (~c0_1(a1858)) | c3_1(a1875) | c2_1(a1875) | (~c1_1(a1875)))),
% 0.90/0.86 inference(quant_inst,[status(thm)],[])).
% 0.90/0.86 tff(1028,plain,
% 0.90/0.86 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp20 | c3_1(a1875) | (~ndr1_0) | (~c1_1(a1875)) | c2_1(a1875) | (~c3_1(a1858)) | (~c0_1(a1858)) | (~c1_1(a1858))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1027, 1026])).
% 0.90/0.86 tff(1029,plain,
% 0.90/0.86 (hskp20 | c2_1(a1875)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1028, 140, 1022, 1021, 1020, 1019, 1008, 942])).
% 0.90/0.86 tff(1030,plain,
% 0.90/0.86 (c2_1(a1875)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1029, 932])).
% 0.90/0.86 tff(1031,plain,
% 0.90/0.86 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.90/0.86 inference(bind,[status(th)],[])).
% 0.90/0.86 tff(1032,plain,
% 0.90/0.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.86 inference(quant_intro,[status(thm)],[1031])).
% 0.90/0.86 tff(1033,plain,
% 0.90/0.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1034,plain,
% 0.90/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_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) | (~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))) | (~c2_1(U))) | (~ndr1_0)) | (~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))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_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)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_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)) | c3_1(V)) | hskp21) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_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)) | c3_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.90/0.86 inference(bind,[status(th)],[])).
% 0.90/0.86 tff(1035,plain,
% 0.90/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.86 inference(quant_intro,[status(thm)],[1034])).
% 0.90/0.86 tff(1036,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 0.90/0.86 tff(1037,plain,
% 0.90/0.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 0.90/0.86 tff(1038,plain,
% 0.90/0.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1037, 1033])).
% 0.90/0.86 tff(1039,plain,(
% 0.90/0.86 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.86 inference(skolemize,[status(sab)],[1038])).
% 0.90/0.86 tff(1040,plain,
% 0.90/0.86 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1039, 1032])).
% 0.90/0.86 tff(1041,plain,
% 0.90/0.86 (((~hskp18) | c0_1(a1875)) <=> ((~hskp18) | c0_1(a1875))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1042,axiom,((~hskp18) | c0_1(a1875)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 0.90/0.86 tff(1043,plain,
% 0.90/0.86 ((~hskp18) | c0_1(a1875)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1042, 1041])).
% 0.90/0.86 tff(1044,plain,
% 0.90/0.86 ((~hskp18) | c0_1(a1875)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1043, 1041])).
% 0.90/0.86 tff(1045,plain,
% 0.90/0.86 ((~hskp18) | c0_1(a1875)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1044, 1041])).
% 0.90/0.86 tff(1046,plain,
% 0.90/0.86 ((~hskp18) | c0_1(a1875)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1045, 1041])).
% 0.90/0.86 tff(1047,plain,
% 0.90/0.86 ((~hskp18) | c0_1(a1875)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1046, 1041])).
% 0.90/0.86 tff(1048,plain,
% 0.90/0.86 ((~hskp18) | c0_1(a1875)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1047, 1041])).
% 0.90/0.86 tff(1049,plain,
% 0.90/0.86 ((~hskp18) | c0_1(a1875)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1048, 1041])).
% 0.90/0.86 tff(1050,plain,
% 0.90/0.86 ((~hskp18) | c0_1(a1875)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1049, 1041])).
% 0.90/0.86 tff(1051,plain,
% 0.90/0.86 (c0_1(a1875)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1050, 1002])).
% 0.90/0.86 tff(1052,plain,
% 0.90/0.86 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)) | (~c0_1(a1911)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)) | (~c0_1(a1911)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1053,plain,
% 0.90/0.86 ((hskp21 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)) | c3_1(a1911) | c1_1(a1911) | (~c0_1(a1911))) <=> (hskp21 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)) | (~c0_1(a1911)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1054,plain,
% 0.90/0.86 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)) | c3_1(a1911) | c1_1(a1911) | (~c0_1(a1911)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)) | (~c0_1(a1911))))),
% 0.90/0.86 inference(monotonicity,[status(thm)],[1053])).
% 0.90/0.86 tff(1055,plain,
% 0.90/0.86 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)) | c3_1(a1911) | c1_1(a1911) | (~c0_1(a1911)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)) | (~c0_1(a1911)))),
% 0.90/0.86 inference(transitivity,[status(thm)],[1054, 1052])).
% 0.90/0.86 tff(1056,plain,
% 0.90/0.86 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)) | c3_1(a1911) | c1_1(a1911) | (~c0_1(a1911)))),
% 0.90/0.86 inference(quant_inst,[status(thm)],[])).
% 0.90/0.86 tff(1057,plain,
% 0.90/0.86 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c1_1(a1911) | c3_1(a1911) | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)) | (~c0_1(a1911))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 0.90/0.86 tff(1058,plain,
% 0.90/0.86 (hskp21),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1057, 140, 847, 1051, 1019, 845, 844, 1040, 1030])).
% 0.90/0.86 tff(1059,plain,
% 0.90/0.86 (((~hskp21) | (~c1_1(a1898))) <=> ((~hskp21) | (~c1_1(a1898)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1060,plain,
% 0.90/0.86 (((~c1_1(a1898)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a1898)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1061,axiom,((~c1_1(a1898)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.90/0.86 tff(1062,plain,
% 0.90/0.86 ((~hskp21) | (~c1_1(a1898))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 0.90/0.86 tff(1063,plain,
% 0.90/0.86 ((~hskp21) | (~c1_1(a1898))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1062, 1059])).
% 0.90/0.86 tff(1064,plain,
% 0.90/0.86 (~c1_1(a1898)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1063, 1058])).
% 0.90/0.86 tff(1065,plain,
% 0.90/0.86 (((~hskp21) | (~c0_1(a1898))) <=> ((~hskp21) | (~c0_1(a1898)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1066,plain,
% 0.90/0.86 (((~c0_1(a1898)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a1898)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1067,axiom,((~c0_1(a1898)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.90/0.86 tff(1068,plain,
% 0.90/0.86 ((~hskp21) | (~c0_1(a1898))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 0.90/0.86 tff(1069,plain,
% 0.90/0.86 ((~hskp21) | (~c0_1(a1898))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1068, 1065])).
% 0.90/0.86 tff(1070,plain,
% 0.90/0.86 (~c0_1(a1898)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1069, 1058])).
% 0.90/0.86 tff(1071,plain,
% 0.90/0.86 (((~hskp21) | c3_1(a1898)) <=> ((~hskp21) | c3_1(a1898))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1072,axiom,((~hskp21) | c3_1(a1898)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.90/0.86 tff(1073,plain,
% 0.90/0.86 ((~hskp21) | c3_1(a1898)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 0.90/0.86 tff(1074,plain,
% 0.90/0.86 ((~hskp21) | c3_1(a1898)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1073, 1071])).
% 0.90/0.86 tff(1075,plain,
% 0.90/0.86 ((~hskp21) | c3_1(a1898)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1074, 1071])).
% 0.90/0.86 tff(1076,plain,
% 0.90/0.86 ((~hskp21) | c3_1(a1898)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1075, 1071])).
% 0.90/0.86 tff(1077,plain,
% 0.90/0.86 ((~hskp21) | c3_1(a1898)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1076, 1071])).
% 0.90/0.86 tff(1078,plain,
% 0.90/0.86 ((~hskp21) | c3_1(a1898)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1077, 1071])).
% 0.90/0.86 tff(1079,plain,
% 0.90/0.86 ((~hskp21) | c3_1(a1898)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1078, 1071])).
% 0.90/0.86 tff(1080,plain,
% 0.90/0.86 ((~hskp21) | c3_1(a1898)),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1079, 1071])).
% 0.90/0.86 tff(1081,plain,
% 0.90/0.86 (c3_1(a1898)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1080, 1058])).
% 0.90/0.86 tff(1082,plain,
% 0.90/0.86 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1083,plain,
% 0.90/0.86 ((hskp16 | hskp13 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898))) <=> (hskp16 | hskp13 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1084,plain,
% 0.90/0.86 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898))))),
% 0.90/0.86 inference(monotonicity,[status(thm)],[1083])).
% 0.90/0.86 tff(1085,plain,
% 0.90/0.86 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))),
% 0.90/0.86 inference(transitivity,[status(thm)],[1084, 1082])).
% 0.90/0.86 tff(1086,plain,
% 0.90/0.86 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898)))),
% 0.90/0.86 inference(quant_inst,[status(thm)],[])).
% 0.90/0.86 tff(1087,plain,
% 0.90/0.86 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp16 | hskp13 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 0.90/0.86 tff(1088,plain,
% 0.90/0.86 ($false),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1087, 140, 713, 781, 1081, 1070, 1064, 712])).
% 0.90/0.86 tff(1089,plain,(hskp16 | (~c0_1(a1858)) | (~c1_1(a1858)) | (~c3_1(a1858)) | hskp22 | (~c3_1(a1919)) | c1_1(a1919) | c2_1(a1919) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c3_1(a1877))), inference(lemma,lemma(discharge,[]))).
% 0.90/0.86 tff(1090,plain,
% 0.90/0.86 (hskp16),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1089, 702, 701, 700, 449, 461, 473, 460, 472, 471, 470])).
% 0.90/0.86 tff(1091,plain,
% 0.90/0.86 (c2_1(a1872)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[643, 1090])).
% 0.90/0.86 tff(1092,plain,
% 0.90/0.86 (~c0_1(a1872)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[610, 1090])).
% 0.90/0.86 tff(1093,plain,
% 0.90/0.86 (c3_1(a1872)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[632, 1090])).
% 0.90/0.86 tff(1094,assumption,(~c0_1(a1872)), introduced(assumption)).
% 0.90/0.86 tff(1095,assumption,(c2_1(a1872)), introduced(assumption)).
% 0.90/0.86 tff(1096,plain,
% 0.90/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | (~c1_1(a1872)) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | (~c1_1(a1872)) | (~c3_1(a1919)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1097,plain,
% 0.90/0.86 ((hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872))) <=> (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | (~c1_1(a1872)) | (~c3_1(a1919)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1098,plain,
% 0.90/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | (~c1_1(a1872)) | (~c3_1(a1919))))),
% 0.90/0.86 inference(monotonicity,[status(thm)],[1097])).
% 0.90/0.86 tff(1099,plain,
% 0.90/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | (~c1_1(a1872)) | (~c3_1(a1919)))),
% 0.90/0.86 inference(transitivity,[status(thm)],[1098, 1096])).
% 0.90/0.86 tff(1100,plain,
% 0.90/0.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872)))),
% 0.90/0.86 inference(quant_inst,[status(thm)],[])).
% 0.90/0.86 tff(1101,plain,
% 0.90/0.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | (~c1_1(a1872)) | (~c3_1(a1919))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1100, 1099])).
% 0.90/0.86 tff(1102,plain,
% 0.90/0.86 (hskp8 | (~c1_1(a1872))),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1101, 140, 461, 1095, 473, 460, 1094, 562])).
% 0.90/0.86 tff(1103,plain,
% 0.90/0.86 (~c1_1(a1872)),
% 0.90/0.86 inference(unit_resolution,[status(thm)],[1102, 21])).
% 0.90/0.86 tff(1104,plain,
% 0.90/0.86 (^[U: $i] : refl((hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.90/0.86 inference(bind,[status(th)],[])).
% 0.90/0.86 tff(1105,plain,
% 0.90/0.86 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.86 inference(quant_intro,[status(thm)],[1104])).
% 0.90/0.86 tff(1106,plain,
% 0.90/0.86 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1107,plain,
% 0.90/0.86 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp15) | hskp3) <=> ((hskp15 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp3))), rewrite(((hskp15 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp3) <=> (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp15) | hskp3) <=> (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.90/0.86 inference(bind,[status(th)],[])).
% 0.90/0.86 tff(1108,plain,
% 0.90/0.86 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp15) | hskp3) <=> ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.86 inference(quant_intro,[status(thm)],[1107])).
% 0.90/0.86 tff(1109,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp15) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.90/0.86 tff(1110,plain,
% 0.90/0.86 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 0.90/0.86 tff(1111,plain,
% 0.90/0.86 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1110, 1106])).
% 0.90/0.86 tff(1112,plain,(
% 0.90/0.86 ![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.86 inference(skolemize,[status(sab)],[1111])).
% 0.90/0.86 tff(1113,plain,
% 0.90/0.86 (![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.90/0.86 inference(modus_ponens,[status(thm)],[1112, 1105])).
% 0.90/0.86 tff(1114,assumption,(c3_1(a1872)), introduced(assumption)).
% 0.90/0.86 tff(1115,plain,
% 0.90/0.86 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | c0_1(a1872) | (~ndr1_0) | (~c3_1(a1872)) | c1_1(a1872))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp3 | c0_1(a1872) | (~ndr1_0) | (~c3_1(a1872)) | c1_1(a1872))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1116,plain,
% 0.90/0.86 ((hskp15 | hskp3 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c3_1(a1872))) <=> (hskp15 | hskp3 | c0_1(a1872) | (~ndr1_0) | (~c3_1(a1872)) | c1_1(a1872))),
% 0.90/0.86 inference(rewrite,[status(thm)],[])).
% 0.90/0.86 tff(1117,plain,
% 0.90/0.86 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c3_1(a1872)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | c0_1(a1872) | (~ndr1_0) | (~c3_1(a1872)) | c1_1(a1872)))),
% 0.90/0.86 inference(monotonicity,[status(thm)],[1116])).
% 0.90/0.86 tff(1118,plain,
% 0.90/0.86 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c3_1(a1872)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp3 | c0_1(a1872) | (~ndr1_0) | (~c3_1(a1872)) | c1_1(a1872))),
% 0.94/0.87 inference(transitivity,[status(thm)],[1117, 1115])).
% 0.94/0.87 tff(1119,plain,
% 0.94/0.87 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c3_1(a1872)))),
% 0.94/0.87 inference(quant_inst,[status(thm)],[])).
% 0.94/0.87 tff(1120,plain,
% 0.94/0.87 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp3 | c0_1(a1872) | (~ndr1_0) | (~c3_1(a1872)) | c1_1(a1872)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1119, 1118])).
% 0.94/0.87 tff(1121,plain,
% 0.94/0.87 (hskp15 | c1_1(a1872)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1120, 140, 531, 1114, 1094, 1113])).
% 0.94/0.87 tff(1122,plain,
% 0.94/0.87 (hskp15),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1121, 1103])).
% 0.94/0.87 tff(1123,plain,
% 0.94/0.87 (((~hskp15) | (~c0_1(a1870))) <=> ((~hskp15) | (~c0_1(a1870)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1124,plain,
% 0.94/0.87 (((~c0_1(a1870)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a1870)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1125,axiom,((~c0_1(a1870)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.94/0.87 tff(1126,plain,
% 0.94/0.87 ((~hskp15) | (~c0_1(a1870))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1125, 1124])).
% 0.94/0.87 tff(1127,plain,
% 0.94/0.87 ((~hskp15) | (~c0_1(a1870))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1126, 1123])).
% 0.94/0.87 tff(1128,plain,
% 0.94/0.87 (~c0_1(a1870)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1127, 1122])).
% 0.94/0.87 tff(1129,plain,
% 0.94/0.87 (((~hskp15) | c1_1(a1870)) <=> ((~hskp15) | c1_1(a1870))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1130,axiom,((~hskp15) | c1_1(a1870)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.94/0.87 tff(1131,plain,
% 0.94/0.87 ((~hskp15) | c1_1(a1870)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 0.94/0.87 tff(1132,plain,
% 0.94/0.87 ((~hskp15) | c1_1(a1870)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1131, 1129])).
% 0.94/0.87 tff(1133,plain,
% 0.94/0.87 ((~hskp15) | c1_1(a1870)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1132, 1129])).
% 0.94/0.87 tff(1134,plain,
% 0.94/0.87 ((~hskp15) | c1_1(a1870)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1133, 1129])).
% 0.94/0.87 tff(1135,plain,
% 0.94/0.87 ((~hskp15) | c1_1(a1870)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1134, 1129])).
% 0.94/0.87 tff(1136,plain,
% 0.94/0.87 ((~hskp15) | c1_1(a1870)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1135, 1129])).
% 0.94/0.87 tff(1137,plain,
% 0.94/0.87 ((~hskp15) | c1_1(a1870)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1136, 1129])).
% 0.94/0.87 tff(1138,plain,
% 0.94/0.87 ((~hskp15) | c1_1(a1870)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1137, 1129])).
% 0.94/0.87 tff(1139,plain,
% 0.94/0.87 (c1_1(a1870)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1138, 1122])).
% 0.94/0.87 tff(1140,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | c2_1(a1870) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | c2_1(a1870) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1141,plain,
% 0.94/0.87 ((hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1870) | c2_1(a1870) | (~c1_1(a1870))) <=> (hskp8 | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | c2_1(a1870) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1142,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1870) | c2_1(a1870) | (~c1_1(a1870)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | c2_1(a1870) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[1141])).
% 0.94/0.87 tff(1143,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1870) | c2_1(a1870) | (~c1_1(a1870)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | c2_1(a1870) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.87 inference(transitivity,[status(thm)],[1142, 1140])).
% 0.94/0.87 tff(1144,plain,
% 0.94/0.87 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1870) | c2_1(a1870) | (~c1_1(a1870)))),
% 0.94/0.87 inference(quant_inst,[status(thm)],[])).
% 0.94/0.87 tff(1145,plain,
% 0.94/0.87 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | c2_1(a1870) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 0.94/0.87 tff(1146,plain,
% 0.94/0.87 (c2_1(a1870)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1145, 140, 21, 287, 286, 285, 1139, 1128, 31])).
% 0.94/0.87 tff(1147,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | (~c2_1(a1870)) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | (~c2_1(a1870)) | (~c3_1(a1919)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1148,plain,
% 0.94/0.87 ((hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1870) | (~c2_1(a1870)) | (~c1_1(a1870))) <=> (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | (~c2_1(a1870)) | (~c3_1(a1919)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1149,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1870) | (~c2_1(a1870)) | (~c1_1(a1870)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | (~c2_1(a1870)) | (~c3_1(a1919))))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[1148])).
% 0.94/0.87 tff(1150,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1870) | (~c2_1(a1870)) | (~c1_1(a1870)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | (~c2_1(a1870)) | (~c3_1(a1919)))),
% 0.94/0.87 inference(transitivity,[status(thm)],[1149, 1147])).
% 0.94/0.87 tff(1151,plain,
% 0.94/0.87 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1870) | (~c2_1(a1870)) | (~c1_1(a1870)))),
% 0.94/0.87 inference(quant_inst,[status(thm)],[])).
% 0.94/0.87 tff(1152,plain,
% 0.94/0.87 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1870) | (~ndr1_0) | (~c1_1(a1870)) | (~c2_1(a1870)) | (~c3_1(a1919))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 0.94/0.87 tff(1153,plain,
% 0.94/0.87 ($false),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1152, 140, 21, 461, 1139, 473, 460, 1128, 562, 1146])).
% 0.94/0.87 tff(1154,plain,(hskp8 | (~c3_1(a1919)) | c1_1(a1919) | c2_1(a1919) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c3_1(a1877)) | hskp3 | (~c3_1(a1872)) | c0_1(a1872) | (~c2_1(a1872))), inference(lemma,lemma(discharge,[]))).
% 0.94/0.87 tff(1155,plain,
% 0.94/0.87 (hskp8),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1154, 472, 473, 460, 461, 471, 470, 531, 1093, 1092, 1091])).
% 0.94/0.87 tff(1156,plain,
% 0.94/0.87 (~c2_1(a1862)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[574, 1155])).
% 0.94/0.87 tff(1157,plain,
% 0.94/0.87 (c1_1(a1862)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[621, 1155])).
% 0.94/0.87 tff(1158,plain,
% 0.94/0.87 (~c3_1(a1862)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[650, 140, 461, 1091, 1093, 1157, 473, 1092, 1156, 10, 448])).
% 0.94/0.87 tff(1159,plain,
% 0.94/0.87 (c0_1(a1862)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[743, 1155])).
% 0.94/0.87 tff(1160,plain,
% 0.94/0.87 ($false),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[750, 140, 1159, 1157, 1156, 410, 1158])).
% 0.94/0.87 tff(1161,plain,(hskp22 | (~c3_1(a1919)) | c1_1(a1919) | (~c0_1(a1919)) | c2_1(a1919) | hskp3 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.94/0.87 tff(1162,plain,
% 0.94/0.87 (hskp22),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1161, 393, 382, 400, 376, 447, 43])).
% 0.94/0.87 tff(1163,plain,
% 0.94/0.87 (((~hskp22) | (~c3_1(a1899))) <=> ((~hskp22) | (~c3_1(a1899)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1164,plain,
% 0.94/0.87 (((~c3_1(a1899)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a1899)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1165,axiom,((~c3_1(a1899)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 0.94/0.87 tff(1166,plain,
% 0.94/0.87 ((~hskp22) | (~c3_1(a1899))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 0.94/0.87 tff(1167,plain,
% 0.94/0.87 ((~hskp22) | (~c3_1(a1899))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1166, 1163])).
% 0.94/0.87 tff(1168,plain,
% 0.94/0.87 (~c3_1(a1899)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1167, 1162])).
% 0.94/0.87 tff(1169,plain,
% 0.94/0.87 (((~hskp22) | (~c2_1(a1899))) <=> ((~hskp22) | (~c2_1(a1899)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1170,plain,
% 0.94/0.87 (((~c2_1(a1899)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a1899)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1171,axiom,((~c2_1(a1899)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.94/0.87 tff(1172,plain,
% 0.94/0.87 ((~hskp22) | (~c2_1(a1899))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 0.94/0.87 tff(1173,plain,
% 0.94/0.87 ((~hskp22) | (~c2_1(a1899))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1172, 1169])).
% 0.94/0.87 tff(1174,plain,
% 0.94/0.87 (~c2_1(a1899)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1173, 1162])).
% 0.94/0.87 tff(1175,plain,
% 0.94/0.87 (((~hskp22) | c0_1(a1899)) <=> ((~hskp22) | c0_1(a1899))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1176,axiom,((~hskp22) | c0_1(a1899)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.94/0.87 tff(1177,plain,
% 0.94/0.87 ((~hskp22) | c0_1(a1899)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 0.94/0.87 tff(1178,plain,
% 0.94/0.87 ((~hskp22) | c0_1(a1899)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1177, 1175])).
% 0.94/0.87 tff(1179,plain,
% 0.94/0.87 ((~hskp22) | c0_1(a1899)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1178, 1175])).
% 0.94/0.87 tff(1180,plain,
% 0.94/0.87 ((~hskp22) | c0_1(a1899)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1179, 1175])).
% 0.94/0.87 tff(1181,plain,
% 0.94/0.87 ((~hskp22) | c0_1(a1899)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1180, 1175])).
% 0.94/0.87 tff(1182,plain,
% 0.94/0.87 ((~hskp22) | c0_1(a1899)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1181, 1175])).
% 0.94/0.87 tff(1183,plain,
% 0.94/0.87 ((~hskp22) | c0_1(a1899)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1182, 1175])).
% 0.94/0.87 tff(1184,plain,
% 0.94/0.87 ((~hskp22) | c0_1(a1899)),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1183, 1175])).
% 0.94/0.87 tff(1185,plain,
% 0.94/0.87 (c0_1(a1899)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1184, 1162])).
% 0.94/0.87 tff(1186,plain,
% 0.94/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1899)) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1899)) | (~c0_1(a1899)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1187,plain,
% 0.94/0.87 (((~ndr1_0) | c3_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c2_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c3_1(a1899) | c2_1(a1899) | (~c1_1(a1899))) <=> (c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1899)) | (~c0_1(a1899)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1188,plain,
% 0.94/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c2_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c3_1(a1899) | c2_1(a1899) | (~c1_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | (c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1899)) | (~c0_1(a1899))))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[1187])).
% 0.94/0.87 tff(1189,plain,
% 0.94/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c2_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c3_1(a1899) | c2_1(a1899) | (~c1_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1899)) | (~c0_1(a1899)))),
% 0.94/0.87 inference(transitivity,[status(thm)],[1188, 1186])).
% 0.94/0.87 tff(1190,plain,
% 0.94/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c2_1(a1899) | (~c1_1(a1899)) | (~c0_1(a1899)) | c3_1(a1899) | c2_1(a1899) | (~c1_1(a1899)))),
% 0.94/0.87 inference(quant_inst,[status(thm)],[])).
% 0.94/0.87 tff(1191,plain,
% 0.94/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | (~c1_1(W)))) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1899)) | (~c0_1(a1899))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 0.94/0.87 tff(1192,plain,
% 0.94/0.87 (~c1_1(a1899)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1191, 140, 1185, 1174, 1168, 410])).
% 0.94/0.87 tff(1193,plain,
% 0.94/0.87 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.94/0.87 inference(bind,[status(th)],[])).
% 0.94/0.87 tff(1194,plain,
% 0.94/0.87 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.94/0.87 inference(quant_intro,[status(thm)],[1193])).
% 0.94/0.87 tff(1195,plain,
% 0.94/0.87 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1196,plain,
% 0.94/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | 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) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.94/0.87 inference(bind,[status(th)],[])).
% 0.94/0.87 tff(1197,plain,
% 0.94/0.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.94/0.87 inference(quant_intro,[status(thm)],[1196])).
% 0.94/0.87 tff(1198,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.94/0.87 tff(1199,plain,
% 0.94/0.87 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 0.94/0.87 tff(1200,plain,
% 0.94/0.87 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1199, 1195])).
% 0.94/0.87 tff(1201,plain,(
% 0.94/0.87 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.94/0.87 inference(skolemize,[status(sab)],[1200])).
% 0.94/0.87 tff(1202,plain,
% 0.94/0.87 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1201, 1194])).
% 0.94/0.87 tff(1203,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a1919) | c2_1(a1919) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c0_1(a1899)) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a1919) | c2_1(a1919) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c0_1(a1899)) | (~c3_1(a1919)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1204,plain,
% 0.94/0.87 ((hskp9 | (~ndr1_0) | c2_1(a1899) | c3_1(a1899) | (~c0_1(a1899)) | c1_1(a1919) | c2_1(a1919) | (~c3_1(a1919))) <=> (hskp9 | c1_1(a1919) | c2_1(a1919) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c0_1(a1899)) | (~c3_1(a1919)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1205,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a1899) | c3_1(a1899) | (~c0_1(a1899)) | c1_1(a1919) | c2_1(a1919) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | c1_1(a1919) | c2_1(a1919) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c0_1(a1899)) | (~c3_1(a1919))))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[1204])).
% 0.94/0.87 tff(1206,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a1899) | c3_1(a1899) | (~c0_1(a1899)) | c1_1(a1919) | c2_1(a1919) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a1919) | c2_1(a1919) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c0_1(a1899)) | (~c3_1(a1919)))),
% 0.94/0.87 inference(transitivity,[status(thm)],[1205, 1203])).
% 0.94/0.87 tff(1207,plain,
% 0.94/0.87 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a1899) | c3_1(a1899) | (~c0_1(a1899)) | c1_1(a1919) | c2_1(a1919) | (~c3_1(a1919)))),
% 0.94/0.87 inference(quant_inst,[status(thm)],[])).
% 0.94/0.87 tff(1208,plain,
% 0.94/0.87 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp9 | c1_1(a1919) | c2_1(a1919) | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | (~c0_1(a1899)) | (~c3_1(a1919))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 0.94/0.87 tff(1209,plain,
% 0.94/0.87 (hskp9),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1208, 140, 393, 1185, 382, 376, 1174, 1168, 1202])).
% 0.94/0.87 tff(1210,plain,
% 0.94/0.87 (~c3_1(a1863)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[815, 1209])).
% 0.94/0.87 tff(1211,plain,
% 0.94/0.87 (~c1_1(a1863)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[821, 1209])).
% 0.94/0.87 tff(1212,plain,
% 0.94/0.87 (c2_1(a1863)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[832, 1209])).
% 0.94/0.87 tff(1213,plain,
% 0.94/0.87 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 0.94/0.87 inference(bind,[status(th)],[])).
% 0.94/0.87 tff(1214,plain,
% 0.94/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.87 inference(quant_intro,[status(thm)],[1213])).
% 0.94/0.87 tff(1215,plain,
% 0.94/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1216,plain,
% 0.94/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp27) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp27))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 0.94/0.87 inference(bind,[status(th)],[])).
% 0.94/0.87 tff(1217,plain,
% 0.94/0.87 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.87 inference(quant_intro,[status(thm)],[1216])).
% 0.94/0.87 tff(1218,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.94/0.87 tff(1219,plain,
% 0.94/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 0.94/0.87 tff(1220,plain,
% 0.94/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1219, 1215])).
% 0.94/0.87 tff(1221,plain,(
% 0.94/0.87 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.87 inference(skolemize,[status(sab)],[1220])).
% 0.94/0.87 tff(1222,plain,
% 0.94/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1221, 1214])).
% 0.94/0.87 tff(1223,assumption,(~c3_1(a1863)), introduced(assumption)).
% 0.94/0.87 tff(1224,assumption,(~c1_1(a1863)), introduced(assumption)).
% 0.94/0.87 tff(1225,assumption,(~c1_1(a1899)), introduced(assumption)).
% 0.94/0.87 tff(1226,assumption,(~c3_1(a1899)), introduced(assumption)).
% 0.94/0.87 tff(1227,assumption,(c0_1(a1899)), introduced(assumption)).
% 0.94/0.87 tff(1228,assumption,(~hskp27), introduced(assumption)).
% 0.94/0.87 tff(1229,plain,
% 0.94/0.87 (hskp29),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[136, 1228, 32])).
% 0.94/0.87 tff(1230,plain,
% 0.94/0.87 (c2_1(a1885)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[75, 1229])).
% 0.94/0.87 tff(1231,plain,
% 0.94/0.87 (c1_1(a1885)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[86, 1229])).
% 0.94/0.87 tff(1232,plain,
% 0.94/0.87 (c0_1(a1885)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[97, 1229])).
% 0.94/0.87 tff(1233,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)) | c1_1(a1899) | (~c0_1(a1899)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)) | c1_1(a1899) | (~c0_1(a1899)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1234,plain,
% 0.94/0.87 ((hskp21 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)) | c3_1(a1899) | c1_1(a1899) | (~c0_1(a1899))) <=> (hskp21 | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)) | c1_1(a1899) | (~c0_1(a1899)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1235,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)) | c3_1(a1899) | c1_1(a1899) | (~c0_1(a1899)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)) | c1_1(a1899) | (~c0_1(a1899))))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[1234])).
% 0.94/0.87 tff(1236,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)) | c3_1(a1899) | c1_1(a1899) | (~c0_1(a1899)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)) | c1_1(a1899) | (~c0_1(a1899)))),
% 0.94/0.87 inference(transitivity,[status(thm)],[1235, 1233])).
% 0.94/0.87 tff(1237,plain,
% 0.94/0.87 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a1885)) | (~c1_1(a1885)) | (~c0_1(a1885)) | c3_1(a1899) | c1_1(a1899) | (~c0_1(a1899)))),
% 0.94/0.87 inference(quant_inst,[status(thm)],[])).
% 0.94/0.87 tff(1238,plain,
% 0.94/0.87 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp21 | c3_1(a1899) | (~ndr1_0) | (~c1_1(a1885)) | (~c0_1(a1885)) | (~c2_1(a1885)) | c1_1(a1899) | (~c0_1(a1899))),
% 0.94/0.87 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 0.94/0.87 tff(1239,plain,
% 0.94/0.87 (hskp21),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1238, 140, 1232, 1231, 1230, 1227, 1226, 1040, 1225])).
% 0.94/0.87 tff(1240,plain,
% 0.94/0.87 (~c0_1(a1898)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1069, 1239])).
% 0.94/0.87 tff(1241,assumption,(c2_1(a1863)), introduced(assumption)).
% 0.94/0.87 tff(1242,plain,
% 0.94/0.87 (c3_1(a1898)),
% 0.94/0.87 inference(unit_resolution,[status(thm)],[1080, 1239])).
% 0.94/0.87 tff(1243,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c0_1(a1898) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1898)) | (~c2_1(a1898)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c0_1(a1898) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1898)) | (~c2_1(a1898)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1244,plain,
% 0.94/0.87 ((hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1898) | (~c2_1(a1898)) | (~c3_1(a1898))) <=> (hskp27 | c0_1(a1898) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1898)) | (~c2_1(a1898)))),
% 0.94/0.87 inference(rewrite,[status(thm)],[])).
% 0.94/0.87 tff(1245,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1898) | (~c2_1(a1898)) | (~c3_1(a1898)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c0_1(a1898) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1898)) | (~c2_1(a1898))))),
% 0.94/0.87 inference(monotonicity,[status(thm)],[1244])).
% 0.94/0.87 tff(1246,plain,
% 0.94/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1898) | (~c2_1(a1898)) | (~c3_1(a1898)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c0_1(a1898) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1898)) | (~c2_1(a1898)))),
% 0.94/0.87 inference(transitivity,[status(thm)],[1245, 1243])).
% 0.94/0.88 tff(1247,plain,
% 0.94/0.88 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1898) | (~c2_1(a1898)) | (~c3_1(a1898)))),
% 0.94/0.88 inference(quant_inst,[status(thm)],[])).
% 0.94/0.88 tff(1248,plain,
% 0.94/0.88 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c0_1(a1898) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1898)) | (~c2_1(a1898))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 0.94/0.88 tff(1249,plain,
% 0.94/0.88 (~c2_1(a1898)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1248, 140, 1228, 1242, 1241, 1240, 1224, 1223, 1222])).
% 0.94/0.88 tff(1250,plain,
% 0.94/0.88 (~c1_1(a1898)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1063, 1239])).
% 0.94/0.88 tff(1251,plain,
% 0.94/0.88 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | c2_1(a1898) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | c2_1(a1898) | (~c3_1(a1919)))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1252,plain,
% 0.94/0.88 ((hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898)) <=> (hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | c2_1(a1898) | (~c3_1(a1919)))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1253,plain,
% 0.94/0.88 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | c2_1(a1898) | (~c3_1(a1919))))),
% 0.94/0.88 inference(monotonicity,[status(thm)],[1252])).
% 0.94/0.88 tff(1254,plain,
% 0.94/0.88 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | c2_1(a1898) | (~c3_1(a1919)))),
% 0.94/0.88 inference(transitivity,[status(thm)],[1253, 1251])).
% 0.94/0.88 tff(1255,plain,
% 0.94/0.88 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))),
% 0.94/0.88 inference(quant_inst,[status(thm)],[])).
% 0.94/0.88 tff(1256,plain,
% 0.94/0.88 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp1 | c1_1(a1919) | c2_1(a1919) | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | c2_1(a1898) | (~c3_1(a1919))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 0.94/0.88 tff(1257,plain,
% 0.94/0.88 ($false),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1256, 140, 32, 461, 473, 460, 1240, 1250, 42, 1249])).
% 0.94/0.88 tff(1258,plain,(hskp27 | hskp1 | (~c3_1(a1919)) | c1_1(a1919) | c2_1(a1919) | (~c2_1(a1863)) | c1_1(a1863) | c3_1(a1863) | (~c0_1(a1899)) | c3_1(a1899) | c1_1(a1899)), inference(lemma,lemma(discharge,[]))).
% 0.94/0.88 tff(1259,plain,
% 0.94/0.88 (hskp27),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1258, 393, 32, 382, 376, 1212, 1211, 1210, 1185, 1168, 1192])).
% 0.94/0.88 tff(1260,plain,
% 0.94/0.88 (c3_1(a1877)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[160, 1259])).
% 0.94/0.88 tff(1261,plain,
% 0.94/0.88 (c2_1(a1877)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[171, 1259])).
% 0.94/0.88 tff(1262,plain,
% 0.94/0.88 (c0_1(a1877)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[182, 1259])).
% 0.94/0.88 tff(1263,plain,
% 0.94/0.88 (^[U: $i] : refl((hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(1264,plain,
% 0.94/0.88 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[1263])).
% 0.94/0.88 tff(1265,plain,
% 0.94/0.88 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) <=> ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1266,plain,
% 0.94/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp21) <=> ((hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp21))), rewrite(((hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U)) | hskp21) <=> (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp21) <=> (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(1267,plain,
% 0.94/0.88 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp21) <=> ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[1266])).
% 0.94/0.88 tff(1268,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp8) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 0.94/0.88 tff(1269,plain,
% 0.94/0.88 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 0.94/0.88 tff(1270,plain,
% 0.94/0.88 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1269, 1265])).
% 0.94/0.88 tff(1271,plain,(
% 0.94/0.88 ![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.94/0.88 inference(skolemize,[status(sab)],[1270])).
% 0.94/0.88 tff(1272,plain,
% 0.94/0.88 (![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1271, 1264])).
% 0.94/0.88 tff(1273,assumption,(~c2_1(a1899)), introduced(assumption)).
% 0.94/0.88 tff(1274,plain,
% 0.94/0.88 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | c1_1(a1899))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp21 | hskp8 | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | c1_1(a1899))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1275,plain,
% 0.94/0.88 ((hskp21 | hskp8 | (~ndr1_0) | c2_1(a1899) | c1_1(a1899) | c3_1(a1899)) <=> (hskp21 | hskp8 | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | c1_1(a1899))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1276,plain,
% 0.94/0.88 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | (~ndr1_0) | c2_1(a1899) | c1_1(a1899) | c3_1(a1899))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | c1_1(a1899)))),
% 0.94/0.88 inference(monotonicity,[status(thm)],[1275])).
% 0.94/0.88 tff(1277,plain,
% 0.94/0.88 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | (~ndr1_0) | c2_1(a1899) | c1_1(a1899) | c3_1(a1899))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp21 | hskp8 | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | c1_1(a1899))),
% 0.94/0.88 inference(transitivity,[status(thm)],[1276, 1274])).
% 0.94/0.88 tff(1278,plain,
% 0.94/0.88 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | (~ndr1_0) | c2_1(a1899) | c1_1(a1899) | c3_1(a1899))),
% 0.94/0.88 inference(quant_inst,[status(thm)],[])).
% 0.94/0.88 tff(1279,plain,
% 0.94/0.88 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp21 | hskp8 | c2_1(a1899) | c3_1(a1899) | (~ndr1_0) | c1_1(a1899)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 0.94/0.88 tff(1280,plain,
% 0.94/0.88 (hskp21 | hskp8),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1279, 140, 1273, 1226, 1272, 1225])).
% 0.94/0.88 tff(1281,plain,
% 0.94/0.88 (hskp21),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1280, 21])).
% 0.94/0.88 tff(1282,plain,
% 0.94/0.88 (~c1_1(a1898)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1063, 1281])).
% 0.94/0.88 tff(1283,plain,
% 0.94/0.88 (~c0_1(a1898)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1069, 1281])).
% 0.94/0.88 tff(1284,plain,
% 0.94/0.88 (c3_1(a1898)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1080, 1281])).
% 0.94/0.88 tff(1285,plain,
% 0.94/0.88 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp3 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1286,plain,
% 0.94/0.88 ((hskp15 | hskp3 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898))) <=> (hskp15 | hskp3 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1287,plain,
% 0.94/0.88 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898))))),
% 0.94/0.88 inference(monotonicity,[status(thm)],[1286])).
% 0.94/0.88 tff(1288,plain,
% 0.94/0.88 (((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898)))) <=> ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp3 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898)))),
% 0.94/0.88 inference(transitivity,[status(thm)],[1287, 1285])).
% 0.94/0.88 tff(1289,plain,
% 0.94/0.88 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp15 | hskp3 | (~ndr1_0) | c1_1(a1898) | c0_1(a1898) | (~c3_1(a1898)))),
% 0.94/0.88 inference(quant_inst,[status(thm)],[])).
% 0.94/0.88 tff(1290,plain,
% 0.94/0.88 ((~![U: $i] : (hskp15 | hskp3 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp15 | hskp3 | c0_1(a1898) | c1_1(a1898) | (~ndr1_0) | (~c3_1(a1898))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 0.94/0.88 tff(1291,plain,
% 0.94/0.88 (hskp15),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1290, 140, 531, 1284, 1283, 1282, 1113])).
% 0.94/0.88 tff(1292,plain,
% 0.94/0.88 (~c0_1(a1870)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1127, 1291])).
% 0.94/0.88 tff(1293,plain,
% 0.94/0.88 (c1_1(a1870)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1138, 1291])).
% 0.94/0.88 tff(1294,plain,
% 0.94/0.88 (c2_1(a1870)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1145, 140, 21, 287, 286, 285, 1293, 1292, 31])).
% 0.94/0.88 tff(1295,plain,
% 0.94/0.88 ($false),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1152, 140, 21, 461, 1293, 473, 460, 1292, 562, 1294])).
% 0.94/0.88 tff(1296,plain,(hskp8 | (~c3_1(a1919)) | c1_1(a1919) | c2_1(a1919) | (~c0_1(a1877)) | (~c2_1(a1877)) | (~c3_1(a1877)) | hskp3 | c2_1(a1899) | c3_1(a1899) | c1_1(a1899)), inference(lemma,lemma(discharge,[]))).
% 0.94/0.88 tff(1297,plain,
% 0.94/0.88 (hskp8),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1296, 393, 382, 376, 1262, 1261, 1260, 447, 1174, 1168, 1192])).
% 0.94/0.88 tff(1298,plain,
% 0.94/0.88 (~c2_1(a1862)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[574, 1297])).
% 0.94/0.88 tff(1299,plain,
% 0.94/0.88 (hskp16),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[752, 1297, 1262, 1261, 1260])).
% 0.94/0.88 tff(1300,plain,
% 0.94/0.88 (~c0_1(a1872)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[610, 1299])).
% 0.94/0.88 tff(1301,plain,
% 0.94/0.88 (c1_1(a1862)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[621, 1297])).
% 0.94/0.88 tff(1302,plain,
% 0.94/0.88 (c3_1(a1872)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[632, 1299])).
% 0.94/0.88 tff(1303,plain,
% 0.94/0.88 (c2_1(a1872)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[643, 1299])).
% 0.94/0.88 tff(1304,plain,
% 0.94/0.88 (~c3_1(a1862)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[650, 140, 393, 1303, 1302, 1301, 382, 1300, 1298, 10, 400])).
% 0.94/0.88 tff(1305,plain,
% 0.94/0.88 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(1306,plain,
% 0.94/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[1305])).
% 0.94/0.88 tff(1307,plain,
% 0.94/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1308,plain,
% 0.94/0.88 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(1309,plain,
% 0.94/0.88 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[1308])).
% 0.94/0.88 tff(1310,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.94/0.88 tff(1311,plain,
% 0.94/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 0.94/0.88 tff(1312,plain,
% 0.94/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1311, 1307])).
% 0.94/0.88 tff(1313,plain,(
% 0.94/0.88 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.94/0.88 inference(skolemize,[status(sab)],[1312])).
% 0.94/0.88 tff(1314,plain,
% 0.94/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1313, 1306])).
% 0.94/0.88 tff(1315,plain,
% 0.94/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a1919) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1899) | (~c3_1(a1919)) | (~c0_1(a1919)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a1919) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1899) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1316,plain,
% 0.94/0.88 (((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c3_1(a1899) | c2_1(a1899) | c1_1(a1899)) <=> (c1_1(a1919) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1899) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1317,plain,
% 0.94/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c3_1(a1899) | c2_1(a1899) | c1_1(a1899))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a1919) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1899) | (~c3_1(a1919)) | (~c0_1(a1919))))),
% 0.94/0.88 inference(monotonicity,[status(thm)],[1316])).
% 0.94/0.88 tff(1318,plain,
% 0.94/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c3_1(a1899) | c2_1(a1899) | c1_1(a1899))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a1919) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1899) | (~c3_1(a1919)) | (~c0_1(a1919)))),
% 0.94/0.88 inference(transitivity,[status(thm)],[1317, 1315])).
% 0.94/0.88 tff(1319,plain,
% 0.94/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | c2_1(a1862) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1919) | (~c3_1(a1919)) | (~c0_1(a1919)) | c3_1(a1899) | c2_1(a1899) | c1_1(a1899))),
% 0.94/0.88 inference(quant_inst,[status(thm)],[])).
% 0.94/0.88 tff(1320,plain,
% 0.94/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a1919) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | c3_1(a1862) | (~c1_1(a1862)) | c1_1(a1899) | (~c3_1(a1919)) | (~c0_1(a1919))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 0.94/0.88 tff(1321,plain,
% 0.94/0.88 ($false),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1320, 140, 393, 1301, 382, 1174, 1168, 1298, 1314, 400, 1192, 1304])).
% 0.94/0.88 tff(1322,plain,(hskp0 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.94/0.88 tff(1323,plain,
% 0.94/0.88 (hskp0),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1322, 32])).
% 0.94/0.88 tff(1324,plain,
% 0.94/0.88 (((~hskp0) | (~c2_1(a1852))) <=> ((~hskp0) | (~c2_1(a1852)))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1325,plain,
% 0.94/0.88 (((~c2_1(a1852)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a1852)))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1326,axiom,((~c2_1(a1852)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.94/0.88 tff(1327,plain,
% 0.94/0.88 ((~hskp0) | (~c2_1(a1852))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1326, 1325])).
% 0.94/0.88 tff(1328,plain,
% 0.94/0.88 ((~hskp0) | (~c2_1(a1852))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1327, 1324])).
% 0.94/0.88 tff(1329,plain,
% 0.94/0.88 (~c2_1(a1852)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1328, 1323])).
% 0.94/0.88 tff(1330,plain,
% 0.94/0.88 (((~hskp0) | c3_1(a1852)) <=> ((~hskp0) | c3_1(a1852))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1331,axiom,((~hskp0) | c3_1(a1852)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.94/0.88 tff(1332,plain,
% 0.94/0.88 ((~hskp0) | c3_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 0.94/0.88 tff(1333,plain,
% 0.94/0.88 ((~hskp0) | c3_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1332, 1330])).
% 0.94/0.88 tff(1334,plain,
% 0.94/0.88 ((~hskp0) | c3_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1333, 1330])).
% 0.94/0.88 tff(1335,plain,
% 0.94/0.88 ((~hskp0) | c3_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1334, 1330])).
% 0.94/0.88 tff(1336,plain,
% 0.94/0.88 ((~hskp0) | c3_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1335, 1330])).
% 0.94/0.88 tff(1337,plain,
% 0.94/0.88 ((~hskp0) | c3_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1336, 1330])).
% 0.94/0.88 tff(1338,plain,
% 0.94/0.88 ((~hskp0) | c3_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1337, 1330])).
% 0.94/0.88 tff(1339,plain,
% 0.94/0.88 ((~hskp0) | c3_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1338, 1330])).
% 0.94/0.88 tff(1340,plain,
% 0.94/0.88 (c3_1(a1852)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1339, 1323])).
% 0.94/0.88 tff(1341,plain,
% 0.94/0.88 (((~hskp0) | c1_1(a1852)) <=> ((~hskp0) | c1_1(a1852))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1342,axiom,((~hskp0) | c1_1(a1852)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.94/0.88 tff(1343,plain,
% 0.94/0.88 ((~hskp0) | c1_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 0.94/0.88 tff(1344,plain,
% 0.94/0.88 ((~hskp0) | c1_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1343, 1341])).
% 0.94/0.88 tff(1345,plain,
% 0.94/0.88 ((~hskp0) | c1_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1344, 1341])).
% 0.94/0.88 tff(1346,plain,
% 0.94/0.88 ((~hskp0) | c1_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1345, 1341])).
% 0.94/0.88 tff(1347,plain,
% 0.94/0.88 ((~hskp0) | c1_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1346, 1341])).
% 0.94/0.88 tff(1348,plain,
% 0.94/0.88 ((~hskp0) | c1_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1347, 1341])).
% 0.94/0.88 tff(1349,plain,
% 0.94/0.88 ((~hskp0) | c1_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1348, 1341])).
% 0.94/0.88 tff(1350,plain,
% 0.94/0.88 ((~hskp0) | c1_1(a1852)),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1349, 1341])).
% 0.94/0.88 tff(1351,plain,
% 0.94/0.88 (c1_1(a1852)),
% 0.94/0.88 inference(unit_resolution,[status(thm)],[1350, 1323])).
% 0.94/0.88 tff(1352,assumption,(c0_1(a1852)), introduced(assumption)).
% 0.94/0.88 tff(1353,plain,
% 0.94/0.88 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W))))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(1354,plain,
% 0.94/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[1353])).
% 0.94/0.88 tff(1355,plain,
% 0.94/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.94/0.88 inference(rewrite,[status(thm)],[])).
% 0.94/0.88 tff(1356,plain,
% 0.94/0.88 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c2_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))))),
% 0.94/0.88 inference(bind,[status(th)],[])).
% 0.94/0.88 tff(1357,plain,
% 0.94/0.88 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.94/0.88 inference(quant_intro,[status(thm)],[1356])).
% 0.94/0.88 tff(1358,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.94/0.88 tff(1359,plain,
% 0.94/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 0.94/0.88 tff(1360,plain,
% 0.94/0.88 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.94/0.88 inference(modus_ponens,[status(thm)],[1359, 1355])).
% 0.94/0.88 tff(1361,plain,(
% 0.94/0.88 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.94/0.88 inference(skolemize,[status(sab)],[1360])).
% 0.94/0.89 tff(1362,plain,
% 0.94/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))),
% 0.94/0.89 inference(modus_ponens,[status(thm)],[1361, 1354])).
% 0.94/0.89 tff(1363,assumption,(~c2_1(a1852)), introduced(assumption)).
% 0.94/0.89 tff(1364,assumption,(c3_1(a1852)), introduced(assumption)).
% 0.94/0.89 tff(1365,plain,
% 0.94/0.89 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c0_1(a1852)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c0_1(a1852)))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1366,plain,
% 0.94/0.89 ((hskp27 | hskp22 | (~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c0_1(a1852))) <=> (hskp27 | hskp22 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c0_1(a1852)))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1367,plain,
% 0.94/0.89 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c0_1(a1852)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c0_1(a1852))))),
% 0.94/0.89 inference(monotonicity,[status(thm)],[1366])).
% 0.94/0.89 tff(1368,plain,
% 0.94/0.89 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c0_1(a1852)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c0_1(a1852)))),
% 0.94/0.89 inference(transitivity,[status(thm)],[1367, 1365])).
% 0.94/0.89 tff(1369,plain,
% 0.94/0.89 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c0_1(a1852)))),
% 0.94/0.89 inference(quant_inst,[status(thm)],[])).
% 0.94/0.89 tff(1370,plain,
% 0.94/0.89 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c0_1(a1852))),
% 0.94/0.89 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 0.94/0.89 tff(1371,plain,
% 0.94/0.89 (hskp27 | hskp22 | (~c0_1(a1852))),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1370, 140, 1364, 1363, 459])).
% 0.94/0.89 tff(1372,plain,
% 0.94/0.89 (hskp22),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1371, 1352, 1228])).
% 0.94/0.89 tff(1373,plain,
% 0.94/0.89 (~c3_1(a1899)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1167, 1372])).
% 0.94/0.89 tff(1374,plain,
% 0.94/0.89 (~c2_1(a1899)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1173, 1372])).
% 0.94/0.89 tff(1375,assumption,(c1_1(a1852)), introduced(assumption)).
% 0.94/0.89 tff(1376,plain,
% 0.94/0.89 (c0_1(a1899)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1184, 1372])).
% 0.94/0.89 tff(1377,plain,
% 0.94/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a1899) | c3_1(a1899) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1899) | c3_1(a1899) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c0_1(a1899)))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1378,plain,
% 0.94/0.89 (((~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899))) <=> (c2_1(a1899) | c3_1(a1899) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c0_1(a1899)))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1379,plain,
% 0.94/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a1899) | c3_1(a1899) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c0_1(a1899))))),
% 0.94/0.89 inference(monotonicity,[status(thm)],[1378])).
% 0.94/0.89 tff(1380,plain,
% 0.94/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1899) | c3_1(a1899) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c0_1(a1899)))),
% 0.94/0.89 inference(transitivity,[status(thm)],[1379, 1377])).
% 0.94/0.89 tff(1381,plain,
% 0.94/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899)))),
% 0.94/0.89 inference(quant_inst,[status(thm)],[])).
% 0.94/0.89 tff(1382,plain,
% 0.94/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1899) | c3_1(a1899) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c0_1(a1899))),
% 0.94/0.89 inference(modus_ponens,[status(thm)],[1381, 1380])).
% 0.94/0.89 tff(1383,plain,
% 0.94/0.89 ($false),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1382, 140, 1376, 1375, 1364, 1374, 1373, 1363, 1362, 1352])).
% 0.94/0.89 tff(1384,plain,((~c0_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1852)) | c2_1(a1852) | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.94/0.89 tff(1385,plain,
% 0.94/0.89 (~c0_1(a1852)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1384, 1228, 1340, 1329, 1351])).
% 0.94/0.89 tff(1386,plain,
% 0.94/0.89 (^[U: $i] : refl((hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.94/0.89 inference(bind,[status(th)],[])).
% 0.94/0.89 tff(1387,plain,
% 0.94/0.89 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.94/0.89 inference(quant_intro,[status(thm)],[1386])).
% 0.94/0.89 tff(1388,plain,
% 0.94/0.89 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1389,plain,
% 0.94/0.89 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp9) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp9) <=> (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp9) <=> (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.94/0.89 inference(bind,[status(th)],[])).
% 0.94/0.89 tff(1390,plain,
% 0.94/0.89 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp9) <=> ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.94/0.89 inference(quant_intro,[status(thm)],[1389])).
% 0.94/0.89 tff(1391,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp1) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.94/0.89 tff(1392,plain,
% 0.94/0.89 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.94/0.89 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 0.94/0.89 tff(1393,plain,
% 0.94/0.89 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.94/0.89 inference(modus_ponens,[status(thm)],[1392, 1388])).
% 0.94/0.89 tff(1394,plain,(
% 0.94/0.89 ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.94/0.89 inference(skolemize,[status(sab)],[1393])).
% 0.94/0.89 tff(1395,plain,
% 0.94/0.89 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.94/0.89 inference(modus_ponens,[status(thm)],[1394, 1387])).
% 0.94/0.89 tff(1396,plain,
% 0.94/0.89 (((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp1 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852))) <=> ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp1 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1397,plain,
% 0.94/0.89 ((hskp9 | hskp1 | (~ndr1_0) | c2_1(a1852) | c0_1(a1852) | (~c1_1(a1852))) <=> (hskp9 | hskp1 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1398,plain,
% 0.94/0.89 (((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp1 | (~ndr1_0) | c2_1(a1852) | c0_1(a1852) | (~c1_1(a1852)))) <=> ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp1 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852)))),
% 0.94/0.89 inference(monotonicity,[status(thm)],[1397])).
% 0.94/0.89 tff(1399,plain,
% 0.94/0.89 (((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp1 | (~ndr1_0) | c2_1(a1852) | c0_1(a1852) | (~c1_1(a1852)))) <=> ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp1 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852))),
% 0.94/0.89 inference(transitivity,[status(thm)],[1398, 1396])).
% 0.94/0.89 tff(1400,plain,
% 0.94/0.89 ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp9 | hskp1 | (~ndr1_0) | c2_1(a1852) | c0_1(a1852) | (~c1_1(a1852)))),
% 0.94/0.89 inference(quant_inst,[status(thm)],[])).
% 0.94/0.89 tff(1401,plain,
% 0.94/0.89 ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp9 | hskp1 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852)),
% 0.94/0.89 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 0.94/0.89 tff(1402,plain,
% 0.94/0.89 (hskp9 | c0_1(a1852)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1401, 140, 32, 1351, 1329, 1395])).
% 0.94/0.89 tff(1403,plain,
% 0.94/0.89 (hskp9),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1402, 1385])).
% 0.94/0.89 tff(1404,plain,
% 0.94/0.89 (~c3_1(a1863)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[815, 1403])).
% 0.94/0.89 tff(1405,plain,
% 0.94/0.89 (~c1_1(a1863)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[821, 1403])).
% 0.94/0.89 tff(1406,assumption,(~c3_1(a1885)), introduced(assumption)).
% 0.94/0.89 tff(1407,assumption,(~c0_1(a1852)), introduced(assumption)).
% 0.94/0.89 tff(1408,plain,
% 0.94/0.89 (hskp9),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1402, 1407])).
% 0.94/0.89 tff(1409,plain,
% 0.94/0.89 (~c3_1(a1863)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[815, 1408])).
% 0.94/0.89 tff(1410,plain,
% 0.94/0.89 (~c1_1(a1863)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[821, 1408])).
% 0.94/0.89 tff(1411,plain,
% 0.94/0.89 (c2_1(a1863)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[832, 1408])).
% 0.94/0.89 tff(1412,assumption,(c2_1(a1885)), introduced(assumption)).
% 0.94/0.89 tff(1413,assumption,(c0_1(a1885)), introduced(assumption)).
% 0.94/0.89 tff(1414,plain,
% 0.94/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | (~c2_1(a1863)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | (~c2_1(a1863)))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1415,plain,
% 0.94/0.89 (((~ndr1_0) | c3_1(a1885) | (~c2_1(a1885)) | (~c0_1(a1885)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852))) <=> (c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | (~c2_1(a1863)))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1416,plain,
% 0.94/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1885) | (~c2_1(a1885)) | (~c0_1(a1885)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | (~c2_1(a1863))))),
% 0.94/0.89 inference(monotonicity,[status(thm)],[1415])).
% 0.94/0.89 tff(1417,plain,
% 0.94/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1885) | (~c2_1(a1885)) | (~c0_1(a1885)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | (~c2_1(a1863)))),
% 0.94/0.89 inference(transitivity,[status(thm)],[1416, 1414])).
% 0.94/0.89 tff(1418,plain,
% 0.94/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1885) | (~c2_1(a1885)) | (~c0_1(a1885)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))),
% 0.94/0.89 inference(quant_inst,[status(thm)],[])).
% 0.94/0.89 tff(1419,plain,
% 0.94/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | (~c2_1(a1863))),
% 0.94/0.89 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 0.94/0.89 tff(1420,plain,
% 0.94/0.89 ($false),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1419, 140, 1413, 1412, 1411, 1351, 1340, 1410, 1409, 241, 1407, 1406])).
% 0.94/0.89 tff(1421,plain,(c0_1(a1852) | (~c0_1(a1885)) | (~c2_1(a1885)) | c3_1(a1885) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.94/0.89 tff(1422,plain,
% 0.94/0.89 (c3_1(a1885)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1421, 1385, 1230, 1232, 32])).
% 0.94/0.89 tff(1423,plain,
% 0.94/0.89 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1885)) | (~c2_1(a1885)) | (~c3_1(a1885)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1885)) | (~c2_1(a1885)) | (~c3_1(a1885)))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1424,plain,
% 0.94/0.89 ((hskp16 | (~ndr1_0) | (~c2_1(a1885)) | (~c3_1(a1885)) | (~c0_1(a1885)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852))) <=> (hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1885)) | (~c2_1(a1885)) | (~c3_1(a1885)))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1425,plain,
% 0.94/0.89 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1885)) | (~c3_1(a1885)) | (~c0_1(a1885)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1885)) | (~c2_1(a1885)) | (~c3_1(a1885))))),
% 0.94/0.89 inference(monotonicity,[status(thm)],[1424])).
% 0.94/0.89 tff(1426,plain,
% 0.94/0.89 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1885)) | (~c3_1(a1885)) | (~c0_1(a1885)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1885)) | (~c2_1(a1885)) | (~c3_1(a1885)))),
% 0.94/0.89 inference(transitivity,[status(thm)],[1425, 1423])).
% 0.94/0.89 tff(1427,plain,
% 0.94/0.89 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1885)) | (~c3_1(a1885)) | (~c0_1(a1885)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))),
% 0.94/0.89 inference(quant_inst,[status(thm)],[])).
% 0.94/0.89 tff(1428,plain,
% 0.94/0.89 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c0_1(a1885)) | (~c2_1(a1885)) | (~c3_1(a1885))),
% 0.94/0.89 inference(modus_ponens,[status(thm)],[1427, 1426])).
% 0.94/0.89 tff(1429,plain,
% 0.94/0.89 (hskp16 | (~c3_1(a1885))),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1428, 140, 1232, 1230, 1351, 1340, 1329, 723])).
% 0.94/0.89 tff(1430,plain,
% 0.94/0.89 (hskp16),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1429, 1422])).
% 0.94/0.89 tff(1431,plain,
% 0.94/0.89 (~c0_1(a1872)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[610, 1430])).
% 0.94/0.89 tff(1432,plain,
% 0.94/0.89 (c2_1(a1863)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[832, 1403])).
% 0.94/0.89 tff(1433,plain,
% 0.94/0.89 (c3_1(a1872)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[632, 1430])).
% 0.94/0.89 tff(1434,plain,
% 0.94/0.89 (c2_1(a1872)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[643, 1430])).
% 0.94/0.89 tff(1435,plain,
% 0.94/0.89 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c0_1(a1872) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c0_1(a1872) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1436,plain,
% 0.94/0.89 ((hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1872) | (~c2_1(a1872)) | (~c3_1(a1872))) <=> (hskp27 | c0_1(a1872) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1437,plain,
% 0.94/0.89 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1872) | (~c2_1(a1872)) | (~c3_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c0_1(a1872) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1872)) | (~c2_1(a1872))))),
% 0.94/0.89 inference(monotonicity,[status(thm)],[1436])).
% 0.94/0.89 tff(1438,plain,
% 0.94/0.89 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1872) | (~c2_1(a1872)) | (~c3_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c0_1(a1872) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.94/0.89 inference(transitivity,[status(thm)],[1437, 1435])).
% 0.94/0.89 tff(1439,plain,
% 0.94/0.89 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a1863) | c3_1(a1863) | (~c2_1(a1863)) | c0_1(a1872) | (~c2_1(a1872)) | (~c3_1(a1872)))),
% 0.94/0.89 inference(quant_inst,[status(thm)],[])).
% 0.94/0.89 tff(1440,plain,
% 0.94/0.89 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c0_1(a1872) | c1_1(a1863) | c3_1(a1863) | (~ndr1_0) | (~c2_1(a1863)) | (~c3_1(a1872)) | (~c2_1(a1872))),
% 0.94/0.89 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 0.94/0.89 tff(1441,plain,
% 0.94/0.89 ($false),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1440, 140, 1228, 1434, 1433, 1432, 1431, 1405, 1404, 1222])).
% 0.94/0.89 tff(1442,plain,(hskp27 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.94/0.89 tff(1443,plain,
% 0.94/0.89 (hskp27),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1442, 32])).
% 0.94/0.89 tff(1444,plain,
% 0.94/0.89 (c3_1(a1877)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[160, 1443])).
% 0.94/0.89 tff(1445,plain,
% 0.94/0.89 (c2_1(a1877)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[171, 1443])).
% 0.94/0.89 tff(1446,plain,
% 0.94/0.89 (c0_1(a1877)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[182, 1443])).
% 0.94/0.89 tff(1447,plain,
% 0.94/0.89 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1448,plain,
% 0.94/0.89 ((hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852))) <=> (hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1449,plain,
% 0.94/0.89 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.94/0.89 inference(monotonicity,[status(thm)],[1448])).
% 0.94/0.89 tff(1450,plain,
% 0.94/0.89 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.89 inference(transitivity,[status(thm)],[1449, 1447])).
% 0.94/0.89 tff(1451,plain,
% 0.94/0.89 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)))),
% 0.94/0.89 inference(quant_inst,[status(thm)],[])).
% 0.94/0.89 tff(1452,plain,
% 0.94/0.89 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.94/0.89 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 0.94/0.89 tff(1453,plain,
% 0.94/0.89 (hskp16),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1452, 140, 1446, 1445, 1444, 1351, 1340, 1329, 723])).
% 0.94/0.89 tff(1454,plain,
% 0.94/0.89 (~c0_1(a1872)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[610, 1453])).
% 0.94/0.89 tff(1455,plain,
% 0.94/0.89 (c3_1(a1872)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[632, 1453])).
% 0.94/0.89 tff(1456,plain,
% 0.94/0.89 (c2_1(a1872)),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[643, 1453])).
% 0.94/0.89 tff(1457,assumption,(~c1_1(a1877)), introduced(assumption)).
% 0.94/0.89 tff(1458,plain,
% 0.94/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1459,plain,
% 0.94/0.89 (((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872))) <=> (c0_1(a1872) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.94/0.89 inference(rewrite,[status(thm)],[])).
% 0.94/0.89 tff(1460,plain,
% 0.94/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877)))),
% 0.94/0.89 inference(monotonicity,[status(thm)],[1459])).
% 0.94/0.89 tff(1461,plain,
% 0.94/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877))),
% 0.94/0.89 inference(transitivity,[status(thm)],[1460, 1458])).
% 0.94/0.89 tff(1462,plain,
% 0.94/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1877) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.94/0.89 inference(quant_inst,[status(thm)],[])).
% 0.94/0.89 tff(1463,plain,
% 0.94/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1872)) | (~c2_1(a1872)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c1_1(a1877)),
% 0.94/0.89 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 0.94/0.89 tff(1464,plain,
% 0.94/0.89 ($false),
% 0.94/0.89 inference(unit_resolution,[status(thm)],[1463, 140, 287, 285, 1095, 1114, 1375, 1364, 1094, 1363, 10, 1457])).
% 0.94/0.89 tff(1465,plain,(c1_1(a1877) | (~c0_1(a1877)) | (~c3_1(a1877)) | (~c2_1(a1872)) | (~c3_1(a1872)) | (~c1_1(a1852)) | (~c3_1(a1852)) | c0_1(a1872) | c2_1(a1852)), inference(lemma,lemma(discharge,[]))).
% 0.94/0.90 tff(1466,plain,
% 0.94/0.90 (c1_1(a1877)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1465, 1446, 1444, 1456, 1455, 1351, 1340, 1454, 1329])).
% 0.94/0.90 tff(1467,plain,
% 0.94/0.90 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.94/0.90 inference(bind,[status(th)],[])).
% 0.94/0.90 tff(1468,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.94/0.90 inference(quant_intro,[status(thm)],[1467])).
% 0.94/0.90 tff(1469,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1470,plain,
% 0.94/0.90 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.94/0.90 inference(bind,[status(th)],[])).
% 0.94/0.90 tff(1471,plain,
% 0.94/0.90 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.94/0.90 inference(quant_intro,[status(thm)],[1470])).
% 0.94/0.90 tff(1472,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.94/0.90 tff(1473,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 0.94/0.90 tff(1474,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1473, 1469])).
% 0.94/0.90 tff(1475,plain,(
% 0.94/0.90 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.94/0.90 inference(skolemize,[status(sab)],[1474])).
% 0.94/0.90 tff(1476,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1475, 1468])).
% 0.94/0.90 tff(1477,assumption,(hskp10), introduced(assumption)).
% 0.94/0.90 tff(1478,plain,
% 0.94/0.90 (((~hskp10) | (~c1_1(a1864))) <=> ((~hskp10) | (~c1_1(a1864)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1479,plain,
% 0.94/0.90 (((~c1_1(a1864)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1864)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1480,axiom,((~c1_1(a1864)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.94/0.90 tff(1481,plain,
% 0.94/0.90 ((~hskp10) | (~c1_1(a1864))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 0.94/0.90 tff(1482,plain,
% 0.94/0.90 ((~hskp10) | (~c1_1(a1864))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1481, 1478])).
% 0.94/0.90 tff(1483,plain,
% 0.94/0.90 (~c1_1(a1864)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1482, 1477])).
% 0.94/0.90 tff(1484,plain,
% 0.94/0.90 (c3_1(a1864)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[496, 1477])).
% 0.94/0.90 tff(1485,plain,
% 0.94/0.90 (c0_1(a1864)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[507, 1477])).
% 0.94/0.90 tff(1486,plain,
% 0.94/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c1_1(a1864) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c1_1(a1864) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1487,plain,
% 0.94/0.90 (((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872))) <=> (c0_1(a1872) | c1_1(a1864) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1488,plain,
% 0.94/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c1_1(a1864) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872))))),
% 0.94/0.90 inference(monotonicity,[status(thm)],[1487])).
% 0.94/0.90 tff(1489,plain,
% 0.94/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c1_1(a1864) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.94/0.90 inference(transitivity,[status(thm)],[1488, 1486])).
% 0.94/0.90 tff(1490,plain,
% 0.94/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 0.94/0.90 inference(quant_inst,[status(thm)],[])).
% 0.94/0.90 tff(1491,plain,
% 0.94/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c1_1(a1864) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1490, 1489])).
% 0.94/0.90 tff(1492,plain,
% 0.94/0.90 ($false),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1491, 140, 1095, 1114, 1485, 1484, 1375, 1364, 1094, 1483, 1363, 10])).
% 0.94/0.90 tff(1493,plain,((~hskp10) | (~c2_1(a1872)) | (~c3_1(a1872)) | (~c1_1(a1852)) | (~c3_1(a1852)) | c0_1(a1872) | c2_1(a1852)), inference(lemma,lemma(discharge,[]))).
% 0.94/0.90 tff(1494,plain,
% 0.94/0.90 (~hskp10),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1493, 1456, 1455, 1351, 1340, 1454, 1329])).
% 0.94/0.90 tff(1495,plain,
% 0.94/0.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1496,plain,
% 0.94/0.90 ((hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1852) | (~c1_1(a1852)) | (~c0_1(a1852))) <=> (hskp10 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1497,plain,
% 0.94/0.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1852) | (~c1_1(a1852)) | (~c0_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))))),
% 0.94/0.90 inference(monotonicity,[status(thm)],[1496])).
% 0.94/0.90 tff(1498,plain,
% 0.94/0.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1852) | (~c1_1(a1852)) | (~c0_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.94/0.90 inference(transitivity,[status(thm)],[1497, 1495])).
% 0.94/0.90 tff(1499,plain,
% 0.94/0.90 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1852) | (~c1_1(a1852)) | (~c0_1(a1852)))),
% 0.94/0.90 inference(quant_inst,[status(thm)],[])).
% 0.94/0.90 tff(1500,plain,
% 0.94/0.90 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | (~c0_1(a1852)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1499, 1498])).
% 0.94/0.90 tff(1501,plain,
% 0.94/0.90 (hskp10 | (~c0_1(a1852)) | (~c1_1(a1877))),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1500, 140, 1445, 1444, 1351, 1329, 1476])).
% 0.94/0.90 tff(1502,plain,
% 0.94/0.90 (~c0_1(a1852)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1501, 1466, 1494])).
% 0.94/0.90 tff(1503,plain,
% 0.94/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1504,plain,
% 0.94/0.90 ((hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1852) | c2_1(a1852) | (~c1_1(a1852))) <=> (hskp8 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1505,plain,
% 0.94/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1852) | c2_1(a1852) | (~c1_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.94/0.90 inference(monotonicity,[status(thm)],[1504])).
% 0.94/0.90 tff(1506,plain,
% 0.94/0.90 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1852) | c2_1(a1852) | (~c1_1(a1852)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.90 inference(transitivity,[status(thm)],[1505, 1503])).
% 0.94/0.90 tff(1507,plain,
% 0.94/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1852) | c2_1(a1852) | (~c1_1(a1852)))),
% 0.94/0.90 inference(quant_inst,[status(thm)],[])).
% 0.94/0.90 tff(1508,plain,
% 0.94/0.90 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c2_1(a1852) | (~ndr1_0) | (~c1_1(a1852)) | c0_1(a1852) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1507, 1506])).
% 0.94/0.90 tff(1509,plain,
% 0.94/0.90 (hskp8),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1508, 140, 1446, 1445, 1444, 1351, 1329, 31, 1502])).
% 0.94/0.90 tff(1510,plain,
% 0.94/0.90 (~c2_1(a1862)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[574, 1509])).
% 0.94/0.90 tff(1511,plain,
% 0.94/0.90 (c1_1(a1862)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[621, 1509])).
% 0.94/0.90 tff(1512,plain,
% 0.94/0.90 (c0_1(a1862)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[743, 1509])).
% 0.94/0.90 tff(1513,plain,
% 0.94/0.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1862) | (~ndr1_0) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1862) | (~ndr1_0) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1514,plain,
% 0.94/0.90 ((hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862))) <=> (hskp10 | c2_1(a1862) | (~ndr1_0) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1515,plain,
% 0.94/0.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1862) | (~ndr1_0) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))))),
% 0.94/0.90 inference(monotonicity,[status(thm)],[1514])).
% 0.94/0.90 tff(1516,plain,
% 0.94/0.90 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1862) | (~ndr1_0) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877)))),
% 0.94/0.90 inference(transitivity,[status(thm)],[1515, 1513])).
% 0.94/0.90 tff(1517,plain,
% 0.94/0.90 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c1_1(a1877)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.94/0.90 inference(quant_inst,[status(thm)],[])).
% 0.94/0.90 tff(1518,plain,
% 0.94/0.90 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1862) | (~ndr1_0) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c3_1(a1877)) | (~c2_1(a1877)) | (~c1_1(a1877))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 0.94/0.90 tff(1519,plain,
% 0.94/0.90 ($false),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1518, 140, 1494, 1445, 1444, 1512, 1511, 1510, 1476, 1466])).
% 0.94/0.90 tff(1520,plain,(hskp1), inference(lemma,lemma(discharge,[]))).
% 0.94/0.90 tff(1521,plain,
% 0.94/0.90 (((~hskp1) | (~c0_1(a1853))) <=> ((~hskp1) | (~c0_1(a1853)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1522,plain,
% 0.94/0.90 (((~c0_1(a1853)) | (~hskp1)) <=> ((~hskp1) | (~c0_1(a1853)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1523,axiom,((~c0_1(a1853)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.94/0.90 tff(1524,plain,
% 0.94/0.90 ((~hskp1) | (~c0_1(a1853))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 0.94/0.90 tff(1525,plain,
% 0.94/0.90 ((~hskp1) | (~c0_1(a1853))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1524, 1521])).
% 0.94/0.90 tff(1526,plain,
% 0.94/0.90 (~c0_1(a1853)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1525, 1520])).
% 0.94/0.90 tff(1527,plain,
% 0.94/0.90 (((~hskp1) | c1_1(a1853)) <=> ((~hskp1) | c1_1(a1853))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1528,axiom,((~hskp1) | c1_1(a1853)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.94/0.90 tff(1529,plain,
% 0.94/0.90 ((~hskp1) | c1_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1528, 1527])).
% 0.94/0.90 tff(1530,plain,
% 0.94/0.90 ((~hskp1) | c1_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1529, 1527])).
% 0.94/0.90 tff(1531,plain,
% 0.94/0.90 ((~hskp1) | c1_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1530, 1527])).
% 0.94/0.90 tff(1532,plain,
% 0.94/0.90 ((~hskp1) | c1_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1531, 1527])).
% 0.94/0.90 tff(1533,plain,
% 0.94/0.90 ((~hskp1) | c1_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1532, 1527])).
% 0.94/0.90 tff(1534,plain,
% 0.94/0.90 ((~hskp1) | c1_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1533, 1527])).
% 0.94/0.90 tff(1535,plain,
% 0.94/0.90 ((~hskp1) | c1_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1534, 1527])).
% 0.94/0.90 tff(1536,plain,
% 0.94/0.90 ((~hskp1) | c1_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1535, 1527])).
% 0.94/0.90 tff(1537,plain,
% 0.94/0.90 (c1_1(a1853)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1536, 1520])).
% 0.94/0.90 tff(1538,assumption,(c3_1(a1862)), introduced(assumption)).
% 0.94/0.90 tff(1539,plain,
% 0.94/0.90 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.94/0.90 inference(bind,[status(th)],[])).
% 0.94/0.90 tff(1540,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.94/0.90 inference(quant_intro,[status(thm)],[1539])).
% 0.94/0.90 tff(1541,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1542,plain,
% 0.94/0.90 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.94/0.90 inference(bind,[status(th)],[])).
% 0.94/0.90 tff(1543,plain,
% 0.94/0.90 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.94/0.90 inference(quant_intro,[status(thm)],[1542])).
% 0.94/0.90 tff(1544,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 0.94/0.90 tff(1545,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1544, 1543])).
% 0.94/0.90 tff(1546,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1545, 1541])).
% 0.94/0.90 tff(1547,plain,(
% 0.94/0.90 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.94/0.90 inference(skolemize,[status(sab)],[1546])).
% 0.94/0.90 tff(1548,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1547, 1540])).
% 0.94/0.90 tff(1549,plain,
% 0.94/0.90 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 0.94/0.90 inference(bind,[status(th)],[])).
% 0.94/0.90 tff(1550,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.90 inference(quant_intro,[status(thm)],[1549])).
% 0.94/0.90 tff(1551,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1552,plain,
% 0.94/0.90 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 0.94/0.90 inference(bind,[status(th)],[])).
% 0.94/0.90 tff(1553,plain,
% 0.94/0.90 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.90 inference(quant_intro,[status(thm)],[1552])).
% 0.94/0.90 tff(1554,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 0.94/0.90 tff(1555,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 0.94/0.90 tff(1556,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1555, 1551])).
% 0.94/0.90 tff(1557,plain,(
% 0.94/0.90 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.90 inference(skolemize,[status(sab)],[1556])).
% 0.94/0.90 tff(1558,plain,
% 0.94/0.90 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1557, 1550])).
% 0.94/0.90 tff(1559,plain,
% 0.94/0.90 (hskp17),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[966, 21, 713])).
% 0.94/0.90 tff(1560,plain,
% 0.94/0.90 (~c1_1(a1874)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[972, 1559])).
% 0.94/0.90 tff(1561,plain,
% 0.94/0.90 (c2_1(a1874)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[983, 1559])).
% 0.94/0.90 tff(1562,plain,
% 0.94/0.90 (c0_1(a1874)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[994, 1559])).
% 0.94/0.90 tff(1563,plain,
% 0.94/0.90 (hskp18),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1001, 140, 21, 1562, 1561, 1560, 952])).
% 0.94/0.90 tff(1564,plain,
% 0.94/0.90 (~c3_1(a1875)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1007, 1563])).
% 0.94/0.90 tff(1565,plain,
% 0.94/0.90 (((~hskp1) | c3_1(a1853)) <=> ((~hskp1) | c3_1(a1853))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1566,axiom,((~hskp1) | c3_1(a1853)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.94/0.90 tff(1567,plain,
% 0.94/0.90 ((~hskp1) | c3_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 0.94/0.90 tff(1568,plain,
% 0.94/0.90 ((~hskp1) | c3_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1567, 1565])).
% 0.94/0.90 tff(1569,plain,
% 0.94/0.90 ((~hskp1) | c3_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1568, 1565])).
% 0.94/0.90 tff(1570,plain,
% 0.94/0.90 ((~hskp1) | c3_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1569, 1565])).
% 0.94/0.90 tff(1571,plain,
% 0.94/0.90 ((~hskp1) | c3_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1570, 1565])).
% 0.94/0.90 tff(1572,plain,
% 0.94/0.90 ((~hskp1) | c3_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1571, 1565])).
% 0.94/0.90 tff(1573,plain,
% 0.94/0.90 ((~hskp1) | c3_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1572, 1565])).
% 0.94/0.90 tff(1574,plain,
% 0.94/0.90 ((~hskp1) | c3_1(a1853)),
% 0.94/0.90 inference(modus_ponens,[status(thm)],[1573, 1565])).
% 0.94/0.90 tff(1575,plain,
% 0.94/0.90 (c3_1(a1853)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1574, 1520])).
% 0.94/0.90 tff(1576,plain,
% 0.94/0.90 (c1_1(a1875)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1018, 1563])).
% 0.94/0.90 tff(1577,plain,
% 0.94/0.90 (c0_1(a1875)),
% 0.94/0.90 inference(unit_resolution,[status(thm)],[1050, 1563])).
% 0.94/0.90 tff(1578,plain,
% 0.94/0.90 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c3_1(a1875) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1875)) | (~c0_1(a1875)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c3_1(a1875) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1875)) | (~c0_1(a1875)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1579,plain,
% 0.94/0.90 ((hskp27 | (~ndr1_0) | c3_1(a1875) | (~c1_1(a1875)) | (~c0_1(a1875)) | c0_1(a1853) | (~c2_1(a1853)) | (~c3_1(a1853))) <=> (hskp27 | c3_1(a1875) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1875)) | (~c0_1(a1875)))),
% 0.94/0.90 inference(rewrite,[status(thm)],[])).
% 0.94/0.90 tff(1580,plain,
% 0.94/0.90 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1875) | (~c1_1(a1875)) | (~c0_1(a1875)) | c0_1(a1853) | (~c2_1(a1853)) | (~c3_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | c3_1(a1875) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1875)) | (~c0_1(a1875))))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[1579])).
% 0.94/0.91 tff(1581,plain,
% 0.94/0.91 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1875) | (~c1_1(a1875)) | (~c0_1(a1875)) | c0_1(a1853) | (~c2_1(a1853)) | (~c3_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c3_1(a1875) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1875)) | (~c0_1(a1875)))),
% 0.94/0.91 inference(transitivity,[status(thm)],[1580, 1578])).
% 0.94/0.91 tff(1582,plain,
% 0.94/0.91 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c3_1(a1875) | (~c1_1(a1875)) | (~c0_1(a1875)) | c0_1(a1853) | (~c2_1(a1853)) | (~c3_1(a1853)))),
% 0.94/0.91 inference(quant_inst,[status(thm)],[])).
% 0.94/0.91 tff(1583,plain,
% 0.94/0.91 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp27 | c3_1(a1875) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1875)) | (~c0_1(a1875))),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1582, 1581])).
% 0.94/0.91 tff(1584,plain,
% 0.94/0.91 (~c2_1(a1853)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1583, 140, 1228, 1577, 1576, 1575, 1564, 1526, 1558])).
% 0.94/0.91 tff(1585,plain,
% 0.94/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1874)) | (~c0_1(a1874)) | (~c2_1(a1874)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1874)) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1586,plain,
% 0.94/0.91 ((hskp8 | (~ndr1_0) | (~c2_1(a1874)) | (~c3_1(a1874)) | (~c0_1(a1874)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853))) <=> (hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1874)) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1587,plain,
% 0.94/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1874)) | (~c3_1(a1874)) | (~c0_1(a1874)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1874)) | (~c0_1(a1874)) | (~c2_1(a1874))))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[1586])).
% 0.94/0.91 tff(1588,plain,
% 0.94/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1874)) | (~c3_1(a1874)) | (~c0_1(a1874)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1874)) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.94/0.91 inference(transitivity,[status(thm)],[1587, 1585])).
% 0.94/0.91 tff(1589,plain,
% 0.94/0.91 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1874)) | (~c3_1(a1874)) | (~c0_1(a1874)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853)))),
% 0.94/0.91 inference(quant_inst,[status(thm)],[])).
% 0.94/0.91 tff(1590,plain,
% 0.94/0.91 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1874)) | (~c0_1(a1874)) | (~c2_1(a1874))),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1589, 1588])).
% 0.94/0.91 tff(1591,plain,
% 0.94/0.91 (c2_1(a1853) | (~c3_1(a1874))),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1590, 140, 21, 1562, 1561, 1537, 1526, 31])).
% 0.94/0.91 tff(1592,plain,
% 0.94/0.91 (~c3_1(a1874)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1591, 1584])).
% 0.94/0.91 tff(1593,plain,
% 0.94/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1874) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | c3_1(a1874) | (~c0_1(a1874)) | (~c2_1(a1874)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1874) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | c3_1(a1874) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1594,plain,
% 0.94/0.91 (((~ndr1_0) | c3_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)) | c3_1(a1874) | c1_1(a1874) | (~c2_1(a1874)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853))) <=> (c1_1(a1874) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | c3_1(a1874) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1595,plain,
% 0.94/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)) | c3_1(a1874) | c1_1(a1874) | (~c2_1(a1874)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1874) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | c3_1(a1874) | (~c0_1(a1874)) | (~c2_1(a1874))))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[1594])).
% 0.94/0.91 tff(1596,plain,
% 0.94/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)) | c3_1(a1874) | c1_1(a1874) | (~c2_1(a1874)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1874) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | c3_1(a1874) | (~c0_1(a1874)) | (~c2_1(a1874)))),
% 0.94/0.91 inference(transitivity,[status(thm)],[1595, 1593])).
% 0.94/0.91 tff(1597,plain,
% 0.94/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1874) | (~c2_1(a1874)) | (~c0_1(a1874)) | c3_1(a1874) | c1_1(a1874) | (~c2_1(a1874)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))),
% 0.94/0.91 inference(quant_inst,[status(thm)],[])).
% 0.94/0.91 tff(1598,plain,
% 0.94/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1874) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | c3_1(a1874) | (~c0_1(a1874)) | (~c2_1(a1874))),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1597, 1596])).
% 0.94/0.91 tff(1599,plain,
% 0.94/0.91 ($false),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1598, 140, 1562, 1561, 1537, 1575, 1560, 1526, 241, 1592])).
% 0.94/0.91 tff(1600,plain,(hskp8 | hskp27 | hskp16), inference(lemma,lemma(discharge,[]))).
% 0.94/0.91 tff(1601,plain,
% 0.94/0.91 (hskp8),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1600, 713, 1228])).
% 0.94/0.91 tff(1602,plain,
% 0.94/0.91 (~c2_1(a1862)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[574, 1601])).
% 0.94/0.91 tff(1603,plain,
% 0.94/0.91 (c1_1(a1862)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[621, 1601])).
% 0.94/0.91 tff(1604,plain,
% 0.94/0.91 (c0_1(a1862)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[743, 1601])).
% 0.94/0.91 tff(1605,plain,
% 0.94/0.91 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1862) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1862) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1606,plain,
% 0.94/0.91 ((hskp16 | (~ndr1_0) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853))) <=> (hskp16 | c2_1(a1862) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1607,plain,
% 0.94/0.91 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c2_1(a1862) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1862)) | (~c0_1(a1862))))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[1606])).
% 0.94/0.91 tff(1608,plain,
% 0.94/0.91 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1862) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 0.94/0.91 inference(transitivity,[status(thm)],[1607, 1605])).
% 0.94/0.91 tff(1609,plain,
% 0.94/0.91 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))),
% 0.94/0.91 inference(quant_inst,[status(thm)],[])).
% 0.94/0.91 tff(1610,plain,
% 0.94/0.91 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c2_1(a1862) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c1_1(a1862)) | (~c0_1(a1862))),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 0.94/0.91 tff(1611,plain,
% 0.94/0.91 ($false),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1610, 140, 713, 1604, 1603, 1537, 1575, 1602, 1526, 1548])).
% 0.94/0.91 tff(1612,plain,(hskp16 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.94/0.91 tff(1613,plain,
% 0.94/0.91 (hskp16),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1612, 1228])).
% 0.94/0.91 tff(1614,plain,
% 0.94/0.91 (~c0_1(a1872)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[610, 1613])).
% 0.94/0.91 tff(1615,plain,
% 0.94/0.91 (c3_1(a1872)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[632, 1613])).
% 0.94/0.91 tff(1616,plain,
% 0.94/0.91 (c2_1(a1872)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[643, 1613])).
% 0.94/0.91 tff(1617,plain,
% 0.94/0.91 ($false),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1440, 140, 1228, 1616, 1615, 833, 1614, 822, 816, 1222])).
% 0.94/0.91 tff(1618,plain,((~hskp9) | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.94/0.91 tff(1619,plain,
% 0.94/0.91 (~hskp9),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1618, 1228])).
% 0.94/0.91 tff(1620,plain,
% 0.94/0.91 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1621,plain,
% 0.94/0.91 ((hskp9 | hskp8 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872))) <=> (hskp9 | hskp8 | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1622,plain,
% 0.94/0.91 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872)))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[1621])).
% 0.94/0.91 tff(1623,plain,
% 0.94/0.91 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872))),
% 0.94/0.91 inference(transitivity,[status(thm)],[1622, 1620])).
% 0.94/0.91 tff(1624,plain,
% 0.94/0.91 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)))),
% 0.94/0.91 inference(quant_inst,[status(thm)],[])).
% 0.94/0.91 tff(1625,plain,
% 0.94/0.91 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872)),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1624, 1623])).
% 0.94/0.91 tff(1626,plain,
% 0.94/0.91 (hskp9 | hskp8 | c1_1(a1872)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1625, 140, 1616, 1614, 20])).
% 0.94/0.91 tff(1627,plain,
% 0.94/0.91 (c1_1(a1872)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1626, 21, 1619])).
% 0.94/0.91 tff(1628,assumption,(c2_1(a1864)), introduced(assumption)).
% 0.94/0.91 tff(1629,plain,
% 0.94/0.91 ((hskp24 | hskp10 | hskp8) <=> (hskp24 | hskp10 | hskp8)),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1630,plain,
% 0.94/0.91 (((hskp10 | hskp8) | hskp24) <=> (hskp24 | hskp10 | hskp8)),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1631,plain,
% 0.94/0.91 ((hskp8 | hskp10) <=> (hskp10 | hskp8)),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1632,plain,
% 0.94/0.91 (((hskp8 | hskp10) | hskp24) <=> ((hskp10 | hskp8) | hskp24)),
% 0.94/0.91 inference(monotonicity,[status(thm)],[1631])).
% 0.94/0.91 tff(1633,plain,
% 0.94/0.91 (((hskp8 | hskp10) | hskp24) <=> (hskp24 | hskp10 | hskp8)),
% 0.94/0.91 inference(transitivity,[status(thm)],[1632, 1630])).
% 0.94/0.91 tff(1634,axiom,((hskp8 | hskp10) | hskp24), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 0.94/0.91 tff(1635,plain,
% 0.94/0.91 (hskp24 | hskp10 | hskp8),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 0.94/0.91 tff(1636,plain,
% 0.94/0.91 (hskp24 | hskp10 | hskp8),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1635, 1629])).
% 0.94/0.91 tff(1637,plain,
% 0.94/0.91 (hskp24 | hskp10 | hskp8),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1636, 1629])).
% 0.94/0.91 tff(1638,plain,
% 0.94/0.91 (hskp24 | hskp10 | hskp8),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1637, 1629])).
% 0.94/0.91 tff(1639,plain,
% 0.94/0.91 (hskp24 | hskp10 | hskp8),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1638, 1629])).
% 0.94/0.91 tff(1640,plain,
% 0.94/0.91 (hskp24 | hskp10 | hskp8),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1639, 1629])).
% 0.94/0.91 tff(1641,plain,
% 0.94/0.91 (hskp24 | hskp10 | hskp8),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1640, 1629])).
% 0.94/0.91 tff(1642,plain,
% 0.94/0.91 (hskp24 | hskp10 | hskp8),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1641, 1629])).
% 0.94/0.91 tff(1643,plain,
% 0.94/0.91 (hskp10),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1642, 64, 21])).
% 0.94/0.91 tff(1644,plain,
% 0.94/0.91 (~c1_1(a1864)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1482, 1643])).
% 0.94/0.91 tff(1645,plain,
% 0.94/0.91 (c0_1(a1864)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[507, 1643])).
% 0.94/0.91 tff(1646,plain,
% 0.94/0.91 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | c1_1(a1864) | (~ndr1_0) | (~c0_1(a1864)) | (~c2_1(a1864)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp8 | c1_1(a1864) | (~ndr1_0) | (~c0_1(a1864)) | (~c2_1(a1864)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1647,plain,
% 0.94/0.91 ((hskp18 | hskp8 | (~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864))) <=> (hskp18 | hskp8 | c1_1(a1864) | (~ndr1_0) | (~c0_1(a1864)) | (~c2_1(a1864)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1648,plain,
% 0.94/0.91 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | c1_1(a1864) | (~ndr1_0) | (~c0_1(a1864)) | (~c2_1(a1864))))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[1647])).
% 0.94/0.91 tff(1649,plain,
% 0.94/0.91 (((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)))) <=> ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp8 | c1_1(a1864) | (~ndr1_0) | (~c0_1(a1864)) | (~c2_1(a1864)))),
% 0.94/0.91 inference(transitivity,[status(thm)],[1648, 1646])).
% 0.94/0.91 tff(1650,plain,
% 0.94/0.91 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp18 | hskp8 | (~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)))),
% 0.94/0.91 inference(quant_inst,[status(thm)],[])).
% 0.94/0.91 tff(1651,plain,
% 0.94/0.91 ((~![U: $i] : (hskp18 | hskp8 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp18 | hskp8 | c1_1(a1864) | (~ndr1_0) | (~c0_1(a1864)) | (~c2_1(a1864))),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 0.94/0.91 tff(1652,plain,
% 0.94/0.91 (hskp18 | (~c2_1(a1864))),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1651, 140, 21, 1645, 1644, 952])).
% 0.94/0.91 tff(1653,plain,
% 0.94/0.91 (hskp18),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1652, 1628])).
% 0.94/0.91 tff(1654,plain,
% 0.94/0.91 (~c3_1(a1875)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1007, 1653])).
% 0.94/0.91 tff(1655,plain,
% 0.94/0.91 (c3_1(a1864)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[496, 1643])).
% 0.94/0.91 tff(1656,plain,
% 0.94/0.91 (c0_1(a1875)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1050, 1653])).
% 0.94/0.91 tff(1657,plain,
% 0.94/0.91 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c3_1(a1875) | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)) | (~c0_1(a1875)) | c2_1(a1875))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1875) | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)) | (~c0_1(a1875)) | c2_1(a1875))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1658,plain,
% 0.94/0.91 ((hskp24 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c3_1(a1875) | c2_1(a1875) | (~c0_1(a1875))) <=> (hskp24 | c3_1(a1875) | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)) | (~c0_1(a1875)) | c2_1(a1875))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1659,plain,
% 0.94/0.91 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c3_1(a1875) | c2_1(a1875) | (~c0_1(a1875)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c3_1(a1875) | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)) | (~c0_1(a1875)) | c2_1(a1875)))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[1658])).
% 0.94/0.91 tff(1660,plain,
% 0.94/0.91 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c3_1(a1875) | c2_1(a1875) | (~c0_1(a1875)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1875) | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)) | (~c0_1(a1875)) | c2_1(a1875))),
% 0.94/0.91 inference(transitivity,[status(thm)],[1659, 1657])).
% 0.94/0.91 tff(1661,plain,
% 0.94/0.91 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1864)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c3_1(a1875) | c2_1(a1875) | (~c0_1(a1875)))),
% 0.94/0.91 inference(quant_inst,[status(thm)],[])).
% 0.94/0.91 tff(1662,plain,
% 0.94/0.91 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1875) | (~ndr1_0) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c2_1(a1864)) | (~c0_1(a1875)) | c2_1(a1875)),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 0.94/0.91 tff(1663,plain,
% 0.94/0.91 (c2_1(a1875)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1662, 140, 64, 1656, 1645, 1655, 1654, 284, 1628])).
% 0.94/0.91 tff(1664,plain,
% 0.94/0.91 (c1_1(a1875)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1018, 1653])).
% 0.94/0.91 tff(1665,plain,
% 0.94/0.91 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1666,plain,
% 0.94/0.91 ((hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875))) <=> (hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1667,plain,
% 0.94/0.91 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875))))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[1666])).
% 0.94/0.91 tff(1668,plain,
% 0.94/0.91 (((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)))) <=> ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875)))),
% 0.94/0.91 inference(transitivity,[status(thm)],[1667, 1665])).
% 0.94/0.91 tff(1669,plain,
% 0.94/0.91 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(a1875)) | (~c1_1(a1875)) | (~c0_1(a1875)))),
% 0.94/0.91 inference(quant_inst,[status(thm)],[])).
% 0.94/0.91 tff(1670,plain,
% 0.94/0.91 ((~![U: $i] : (hskp24 | hskp0 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp0 | (~ndr1_0) | (~c1_1(a1875)) | (~c0_1(a1875)) | (~c2_1(a1875))),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1669, 1668])).
% 0.94/0.91 tff(1671,plain,
% 0.94/0.91 ($false),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1670, 140, 64, 43, 1656, 1664, 53, 1663])).
% 0.94/0.91 tff(1672,plain,((~c2_1(a1864)) | hskp24 | hskp0 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.94/0.91 tff(1673,plain,
% 0.94/0.91 (~c2_1(a1864)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1672, 64, 43, 21])).
% 0.94/0.91 tff(1674,plain,
% 0.94/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a1872) | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864) | (~c2_1(a1872)) | (~c1_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a1872) | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864) | (~c2_1(a1872)) | (~c1_1(a1872)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1675,plain,
% 0.94/0.91 ((hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872))) <=> (hskp8 | c0_1(a1872) | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864) | (~c2_1(a1872)) | (~c1_1(a1872)))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1676,plain,
% 0.94/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c0_1(a1872) | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864) | (~c2_1(a1872)) | (~c1_1(a1872))))),
% 0.94/0.91 inference(monotonicity,[status(thm)],[1675])).
% 0.94/0.91 tff(1677,plain,
% 0.94/0.91 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a1872) | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864) | (~c2_1(a1872)) | (~c1_1(a1872)))),
% 0.94/0.91 inference(transitivity,[status(thm)],[1676, 1674])).
% 0.94/0.91 tff(1678,plain,
% 0.94/0.91 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1872) | (~c2_1(a1872)) | (~c1_1(a1872)))),
% 0.94/0.91 inference(quant_inst,[status(thm)],[])).
% 0.94/0.91 tff(1679,plain,
% 0.94/0.91 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c0_1(a1872) | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864) | (~c2_1(a1872)) | (~c1_1(a1872))),
% 0.94/0.91 inference(modus_ponens,[status(thm)],[1678, 1677])).
% 0.94/0.91 tff(1680,plain,
% 0.94/0.91 (~c1_1(a1872)),
% 0.94/0.91 inference(unit_resolution,[status(thm)],[1679, 140, 21, 1616, 1655, 1614, 1644, 562, 1673])).
% 0.94/0.91 tff(1681,plain,
% 0.94/0.91 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 0.94/0.91 inference(bind,[status(th)],[])).
% 0.94/0.91 tff(1682,plain,
% 0.94/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.94/0.91 inference(quant_intro,[status(thm)],[1681])).
% 0.94/0.91 tff(1683,plain,
% 0.94/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.94/0.91 inference(rewrite,[status(thm)],[])).
% 0.94/0.91 tff(1684,plain,
% 0.94/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_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) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c2_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) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c2_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) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c2_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) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 0.94/0.92 inference(bind,[status(th)],[])).
% 0.94/0.92 tff(1685,plain,
% 0.94/0.92 (![V: $i, U: $i] : ((((((((~c2_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) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.94/0.92 inference(quant_intro,[status(thm)],[1684])).
% 0.94/0.92 tff(1686,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 0.94/0.92 tff(1687,plain,
% 0.94/0.92 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1686, 1685])).
% 0.94/0.92 tff(1688,plain,
% 0.94/0.92 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1687, 1683])).
% 0.94/0.92 tff(1689,plain,(
% 0.94/0.92 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.94/0.92 inference(skolemize,[status(sab)],[1688])).
% 0.94/0.92 tff(1690,plain,
% 0.94/0.92 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1689, 1682])).
% 0.94/0.92 tff(1691,plain,
% 0.94/0.92 (hskp22),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[521, 140, 1228, 1645, 1655, 459, 1673])).
% 0.94/0.92 tff(1692,plain,
% 0.94/0.92 (~c3_1(a1899)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1167, 1691])).
% 0.94/0.92 tff(1693,plain,
% 0.94/0.92 (~c2_1(a1899)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1173, 1691])).
% 0.94/0.92 tff(1694,plain,
% 0.94/0.92 (c0_1(a1899)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1184, 1691])).
% 0.94/0.92 tff(1695,plain,
% 0.94/0.92 (~c1_1(a1899)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1191, 140, 1694, 1693, 1692, 410])).
% 0.94/0.92 tff(1696,plain,
% 0.94/0.92 (hskp21),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1279, 140, 21, 1693, 1692, 1272, 1695])).
% 0.94/0.92 tff(1697,plain,
% 0.94/0.92 (~c1_1(a1898)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1063, 1696])).
% 0.94/0.92 tff(1698,plain,
% 0.94/0.92 (~c0_1(a1898)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1069, 1696])).
% 0.94/0.92 tff(1699,plain,
% 0.94/0.92 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c2_1(a1898))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1700,plain,
% 0.94/0.92 ((hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898)) <=> (hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c2_1(a1898))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1701,plain,
% 0.94/0.92 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c2_1(a1898)))),
% 0.94/0.92 inference(monotonicity,[status(thm)],[1700])).
% 0.94/0.92 tff(1702,plain,
% 0.94/0.92 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c2_1(a1898))),
% 0.94/0.92 inference(transitivity,[status(thm)],[1701, 1699])).
% 0.94/0.92 tff(1703,plain,
% 0.94/0.92 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))),
% 0.94/0.92 inference(quant_inst,[status(thm)],[])).
% 0.94/0.92 tff(1704,plain,
% 0.94/0.92 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c2_1(a1898)),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 0.94/0.92 tff(1705,plain,
% 0.94/0.92 (c2_1(a1898)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1704, 140, 43, 1616, 1698, 1697, 1614, 1690, 1680])).
% 0.94/0.92 tff(1706,plain,
% 0.94/0.92 (^[U: $i] : refl((hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.94/0.92 inference(bind,[status(th)],[])).
% 0.94/0.92 tff(1707,plain,
% 0.94/0.92 (![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.94/0.92 inference(quant_intro,[status(thm)],[1706])).
% 0.94/0.92 tff(1708,plain,
% 0.94/0.92 (![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1709,plain,
% 0.94/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp20) <=> ((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp20))), rewrite(((hskp29 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp20) <=> (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp20) <=> (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.94/0.92 inference(bind,[status(th)],[])).
% 0.94/0.92 tff(1710,plain,
% 0.94/0.92 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp20) <=> ![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.94/0.92 inference(quant_intro,[status(thm)],[1709])).
% 0.94/0.92 tff(1711,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp29) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.94/0.92 tff(1712,plain,
% 0.94/0.92 (![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 0.94/0.92 tff(1713,plain,
% 0.94/0.92 (![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1712, 1708])).
% 0.94/0.92 tff(1714,plain,(
% 0.94/0.92 ![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.94/0.92 inference(skolemize,[status(sab)],[1713])).
% 0.94/0.92 tff(1715,plain,
% 0.94/0.92 (![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1714, 1707])).
% 0.94/0.92 tff(1716,plain,
% 0.94/0.92 (((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp29 | hskp20 | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864))) <=> ((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp29 | hskp20 | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1717,plain,
% 0.94/0.92 ((hskp29 | hskp20 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864))) <=> (hskp29 | hskp20 | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1718,plain,
% 0.94/0.92 (((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp29 | hskp20 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)))) <=> ((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp29 | hskp20 | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864)))),
% 0.94/0.92 inference(monotonicity,[status(thm)],[1717])).
% 0.94/0.92 tff(1719,plain,
% 0.94/0.92 (((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp29 | hskp20 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)))) <=> ((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp29 | hskp20 | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864))),
% 0.94/0.92 inference(transitivity,[status(thm)],[1718, 1716])).
% 0.94/0.92 tff(1720,plain,
% 0.94/0.92 ((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp29 | hskp20 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)))),
% 0.94/0.92 inference(quant_inst,[status(thm)],[])).
% 0.94/0.92 tff(1721,plain,
% 0.94/0.92 ((~![U: $i] : (hskp29 | hskp20 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp29 | hskp20 | c1_1(a1864) | (~ndr1_0) | (~c3_1(a1864)) | c2_1(a1864)),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1720, 1719])).
% 0.94/0.92 tff(1722,plain,
% 0.94/0.92 (hskp20),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1721, 149, 140, 1655, 1644, 1715, 1673])).
% 0.94/0.92 tff(1723,plain,
% 0.94/0.92 (~c1_1(a1890)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[853, 1722])).
% 0.94/0.92 tff(1724,plain,
% 0.94/0.92 (~c0_1(a1890)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[859, 1722])).
% 0.94/0.92 tff(1725,plain,
% 0.94/0.92 (c2_1(a1890)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[889, 1722])).
% 0.94/0.92 tff(1726,plain,
% 0.94/0.92 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1727,plain,
% 0.94/0.92 ((hskp9 | hskp8 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890))) <=> (hskp9 | hskp8 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1728,plain,
% 0.94/0.92 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890))))),
% 0.94/0.92 inference(monotonicity,[status(thm)],[1727])).
% 0.94/0.92 tff(1729,plain,
% 0.94/0.92 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)))),
% 0.94/0.92 inference(transitivity,[status(thm)],[1728, 1726])).
% 0.94/0.92 tff(1730,plain,
% 0.94/0.92 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)))),
% 0.94/0.92 inference(quant_inst,[status(thm)],[])).
% 0.94/0.92 tff(1731,plain,
% 0.94/0.92 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890))),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1730, 1729])).
% 0.94/0.92 tff(1732,plain,
% 0.94/0.92 (hskp9),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1731, 140, 21, 1725, 1724, 1723, 20])).
% 0.94/0.92 tff(1733,plain,
% 0.94/0.92 (~c3_1(a1863)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[815, 1732])).
% 0.94/0.92 tff(1734,plain,
% 0.94/0.92 (~c1_1(a1863)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[821, 1732])).
% 0.94/0.92 tff(1735,plain,
% 0.94/0.92 (c2_1(a1863)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[832, 1732])).
% 0.94/0.92 tff(1736,plain,
% 0.94/0.92 (c3_1(a1898)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1080, 1696])).
% 0.94/0.92 tff(1737,plain,
% 0.94/0.92 ($false),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1248, 140, 1228, 1736, 1735, 1698, 1734, 1733, 1222, 1705])).
% 0.94/0.92 tff(1738,plain,(hskp24 | hskp27 | hskp0 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.94/0.92 tff(1739,plain,
% 0.94/0.92 (hskp24),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1738, 43, 1228, 21])).
% 0.94/0.92 tff(1740,plain,
% 0.94/0.92 (~c1_1(a1919)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[381, 1739])).
% 0.94/0.92 tff(1741,plain,
% 0.94/0.92 (~c2_1(a1919)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[375, 1739])).
% 0.94/0.92 tff(1742,assumption,(~c3_1(a1919)), introduced(assumption)).
% 0.94/0.92 tff(1743,plain,
% 0.94/0.92 (~hskp24),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[392, 1742])).
% 0.94/0.92 tff(1744,plain,
% 0.94/0.92 (~c2_1(a1864)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1672, 1743, 43, 21])).
% 0.94/0.92 tff(1745,plain,
% 0.94/0.92 (hskp10),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1642, 1743, 21])).
% 0.94/0.92 tff(1746,plain,
% 0.94/0.92 (~c1_1(a1864)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1482, 1745])).
% 0.94/0.92 tff(1747,plain,
% 0.94/0.92 (c3_1(a1864)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[496, 1745])).
% 0.94/0.92 tff(1748,plain,
% 0.94/0.92 (~hskp29),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[148, 1743, 43])).
% 0.94/0.92 tff(1749,plain,
% 0.94/0.92 (hskp20 | c2_1(a1864)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1721, 1748, 140, 1747, 1746, 1715])).
% 0.94/0.92 tff(1750,plain,
% 0.94/0.92 (hskp20),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1749, 1744])).
% 0.94/0.92 tff(1751,plain,
% 0.94/0.92 (~c1_1(a1890)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[853, 1750])).
% 0.94/0.92 tff(1752,plain,
% 0.94/0.92 (~c0_1(a1890)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[859, 1750])).
% 0.94/0.92 tff(1753,plain,
% 0.94/0.92 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | c3_1(a1919) | c1_1(a1919) | c2_1(a1919) | (~ndr1_0))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp21 | hskp8 | c3_1(a1919) | c1_1(a1919) | c2_1(a1919) | (~ndr1_0))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1754,plain,
% 0.94/0.92 ((hskp21 | hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | c3_1(a1919)) <=> (hskp21 | hskp8 | c3_1(a1919) | c1_1(a1919) | c2_1(a1919) | (~ndr1_0))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1755,plain,
% 0.94/0.92 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | c3_1(a1919))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | c3_1(a1919) | c1_1(a1919) | c2_1(a1919) | (~ndr1_0)))),
% 0.94/0.92 inference(monotonicity,[status(thm)],[1754])).
% 0.94/0.92 tff(1756,plain,
% 0.94/0.92 (((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | c3_1(a1919))) <=> ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp21 | hskp8 | c3_1(a1919) | c1_1(a1919) | c2_1(a1919) | (~ndr1_0))),
% 0.94/0.92 inference(transitivity,[status(thm)],[1755, 1753])).
% 0.94/0.92 tff(1757,plain,
% 0.94/0.92 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | (hskp21 | hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | c3_1(a1919))),
% 0.94/0.92 inference(quant_inst,[status(thm)],[])).
% 0.94/0.92 tff(1758,plain,
% 0.94/0.92 ((~![U: $i] : (hskp21 | hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | c3_1(U))) | hskp21 | hskp8 | c3_1(a1919) | c1_1(a1919) | c2_1(a1919) | (~ndr1_0)),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1757, 1756])).
% 0.94/0.92 tff(1759,plain,
% 0.94/0.92 (hskp21 | c3_1(a1919) | c2_1(a1919)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1758, 140, 21, 473, 1272])).
% 0.94/0.92 tff(1760,plain,
% 0.94/0.92 (hskp21),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1759, 1742, 460])).
% 0.94/0.92 tff(1761,plain,
% 0.94/0.92 (~c1_1(a1898)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1063, 1760])).
% 0.94/0.92 tff(1762,plain,
% 0.94/0.92 (~c0_1(a1898)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1069, 1760])).
% 0.94/0.92 tff(1763,plain,
% 0.94/0.92 (c2_1(a1890)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[889, 1750])).
% 0.94/0.92 tff(1764,plain,
% 0.94/0.92 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)) | c2_1(a1898))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1765,plain,
% 0.94/0.92 ((hskp0 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898)) <=> (hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)) | c2_1(a1898))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1766,plain,
% 0.94/0.92 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)) | c2_1(a1898)))),
% 0.94/0.92 inference(monotonicity,[status(thm)],[1765])).
% 0.94/0.92 tff(1767,plain,
% 0.94/0.92 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)) | c2_1(a1898))),
% 0.94/0.92 inference(transitivity,[status(thm)],[1766, 1764])).
% 0.94/0.92 tff(1768,plain,
% 0.94/0.92 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1890) | c0_1(a1890) | (~c2_1(a1890)) | c1_1(a1898) | c0_1(a1898) | c2_1(a1898))),
% 0.94/0.92 inference(quant_inst,[status(thm)],[])).
% 0.94/0.92 tff(1769,plain,
% 0.94/0.92 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a1898) | c1_1(a1898) | c0_1(a1890) | c1_1(a1890) | (~ndr1_0) | (~c2_1(a1890)) | c2_1(a1898)),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1768, 1767])).
% 0.94/0.92 tff(1770,plain,
% 0.94/0.92 (c2_1(a1898)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1769, 140, 43, 1763, 1762, 1761, 1752, 1751, 1690])).
% 0.94/0.92 tff(1771,plain,
% 0.94/0.92 (hskp9),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1731, 140, 21, 1763, 1752, 1751, 20])).
% 0.94/0.92 tff(1772,plain,
% 0.94/0.92 (~c3_1(a1863)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[815, 1771])).
% 0.94/0.92 tff(1773,plain,
% 0.94/0.92 (~c1_1(a1863)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[821, 1771])).
% 0.94/0.92 tff(1774,plain,
% 0.94/0.92 (c2_1(a1863)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[832, 1771])).
% 0.94/0.92 tff(1775,plain,
% 0.94/0.92 (c3_1(a1898)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1080, 1760])).
% 0.94/0.92 tff(1776,plain,
% 0.94/0.92 ($false),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1248, 140, 1228, 1775, 1774, 1762, 1773, 1772, 1222, 1770])).
% 0.94/0.92 tff(1777,plain,(c3_1(a1919) | hskp27 | hskp0 | hskp8 | c2_1(a1919) | c1_1(a1919)), inference(lemma,lemma(discharge,[]))).
% 0.94/0.92 tff(1778,plain,
% 0.94/0.92 (c3_1(a1919)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1777, 460, 43, 21, 1228, 473])).
% 0.94/0.92 tff(1779,plain,
% 0.94/0.92 ((~c1_1(a1872)) | (~c3_1(a1919))),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1101, 140, 21, 1616, 473, 460, 1614, 562])).
% 0.94/0.92 tff(1780,plain,
% 0.94/0.92 (~c1_1(a1872)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1779, 1778])).
% 0.94/0.92 tff(1781,plain,
% 0.94/0.92 (hskp9),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1626, 1780, 21])).
% 0.94/0.92 tff(1782,plain,
% 0.94/0.92 (~c3_1(a1863)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[815, 1781])).
% 0.94/0.92 tff(1783,plain,
% 0.94/0.92 (~c1_1(a1863)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[821, 1781])).
% 0.94/0.92 tff(1784,plain,
% 0.94/0.92 (c2_1(a1863)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[832, 1781])).
% 0.94/0.92 tff(1785,plain,
% 0.94/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c0_1(a1863)) | (~c2_1(a1863)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c0_1(a1863)) | (~c2_1(a1863)))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1786,plain,
% 0.94/0.92 (((~ndr1_0) | c3_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1863)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853))) <=> (c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c0_1(a1863)) | (~c2_1(a1863)))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1787,plain,
% 0.94/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1863)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c0_1(a1863)) | (~c2_1(a1863))))),
% 0.94/0.92 inference(monotonicity,[status(thm)],[1786])).
% 0.94/0.92 tff(1788,plain,
% 0.94/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1863)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c0_1(a1863)) | (~c2_1(a1863)))),
% 0.94/0.92 inference(transitivity,[status(thm)],[1787, 1785])).
% 0.94/0.92 tff(1789,plain,
% 0.94/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1863)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))),
% 0.94/0.92 inference(quant_inst,[status(thm)],[])).
% 0.94/0.92 tff(1790,plain,
% 0.94/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c0_1(a1863)) | (~c2_1(a1863))),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 0.94/0.92 tff(1791,plain,
% 0.94/0.92 (~c0_1(a1863)),
% 0.94/0.92 inference(unit_resolution,[status(thm)],[1790, 140, 1784, 1537, 1575, 1783, 1782, 1526, 241])).
% 0.94/0.92 tff(1792,plain,
% 0.94/0.92 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.94/0.92 inference(bind,[status(th)],[])).
% 0.94/0.92 tff(1793,plain,
% 0.94/0.92 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.94/0.92 inference(quant_intro,[status(thm)],[1792])).
% 0.94/0.92 tff(1794,plain,
% 0.94/0.92 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.94/0.92 inference(rewrite,[status(thm)],[])).
% 0.94/0.92 tff(1795,plain,
% 0.94/0.92 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.94/0.92 inference(bind,[status(th)],[])).
% 0.94/0.92 tff(1796,plain,
% 0.94/0.92 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.94/0.92 inference(quant_intro,[status(thm)],[1795])).
% 0.94/0.92 tff(1797,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.94/0.92 tff(1798,plain,
% 0.94/0.92 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1797, 1796])).
% 0.94/0.92 tff(1799,plain,
% 0.94/0.92 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1798, 1794])).
% 0.94/0.92 tff(1800,plain,(
% 0.94/0.92 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.94/0.92 inference(skolemize,[status(sab)],[1799])).
% 0.94/0.92 tff(1801,plain,
% 0.94/0.92 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.94/0.92 inference(modus_ponens,[status(thm)],[1800, 1793])).
% 0.94/0.92 tff(1802,plain,
% 0.94/0.92 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c1_1(a1919) | c2_1(a1919) | c3_1(a1863) | (~ndr1_0) | c0_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c1_1(a1919) | c2_1(a1919) | c3_1(a1863) | (~ndr1_0) | c0_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1919)))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1803,plain,
% 0.94/0.93 ((hskp27 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)) | c3_1(a1863) | c0_1(a1863) | (~c2_1(a1863))) <=> (hskp27 | c1_1(a1919) | c2_1(a1919) | c3_1(a1863) | (~ndr1_0) | c0_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1919)))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1804,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)) | c3_1(a1863) | c0_1(a1863) | (~c2_1(a1863)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | c1_1(a1919) | c2_1(a1919) | c3_1(a1863) | (~ndr1_0) | c0_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1919))))),
% 0.94/0.93 inference(monotonicity,[status(thm)],[1803])).
% 0.94/0.93 tff(1805,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)) | c3_1(a1863) | c0_1(a1863) | (~c2_1(a1863)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c1_1(a1919) | c2_1(a1919) | c3_1(a1863) | (~ndr1_0) | c0_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1919)))),
% 0.94/0.93 inference(transitivity,[status(thm)],[1804, 1802])).
% 0.94/0.93 tff(1806,plain,
% 0.94/0.93 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c0_1(a1919)) | c3_1(a1863) | c0_1(a1863) | (~c2_1(a1863)))),
% 0.94/0.93 inference(quant_inst,[status(thm)],[])).
% 0.94/0.93 tff(1807,plain,
% 0.94/0.93 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp27 | c1_1(a1919) | c2_1(a1919) | c3_1(a1863) | (~ndr1_0) | c0_1(a1863) | (~c2_1(a1863)) | (~c0_1(a1919))),
% 0.94/0.93 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 0.94/0.93 tff(1808,plain,
% 0.94/0.93 (~c0_1(a1919)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1807, 140, 1228, 1784, 473, 460, 1782, 1801, 1791])).
% 0.94/0.93 tff(1809,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c0_1(a1919))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c0_1(a1919))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1810,plain,
% 0.94/0.93 ((hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919)) <=> (hskp0 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c0_1(a1919))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1811,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c0_1(a1919)))),
% 0.94/0.93 inference(monotonicity,[status(thm)],[1810])).
% 0.94/0.93 tff(1812,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c0_1(a1919))),
% 0.94/0.93 inference(transitivity,[status(thm)],[1811, 1809])).
% 0.94/0.93 tff(1813,plain,
% 0.94/0.93 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a1872) | c0_1(a1872) | (~c2_1(a1872)) | c1_1(a1919) | c0_1(a1919) | c2_1(a1919))),
% 0.94/0.93 inference(quant_inst,[status(thm)],[])).
% 0.94/0.93 tff(1814,plain,
% 0.94/0.93 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c1_1(a1919) | c2_1(a1919) | c0_1(a1872) | (~ndr1_0) | (~c2_1(a1872)) | c1_1(a1872) | c0_1(a1919)),
% 0.94/0.93 inference(modus_ponens,[status(thm)],[1813, 1812])).
% 0.94/0.93 tff(1815,plain,
% 0.94/0.93 ($false),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1814, 140, 43, 1616, 473, 460, 1614, 1690, 1808, 1780])).
% 0.94/0.93 tff(1816,plain,(c2_1(a1919) | hskp0 | c1_1(a1919) | hskp27 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.94/0.93 tff(1817,plain,
% 0.94/0.93 ($false),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1816, 1741, 1740, 43, 1228, 21])).
% 0.94/0.93 tff(1818,plain,(hskp0 | hskp27 | hskp8), inference(lemma,lemma(discharge,[]))).
% 0.94/0.93 tff(1819,plain,
% 0.94/0.93 (hskp0),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1818, 21, 1228])).
% 0.94/0.93 tff(1820,plain,
% 0.94/0.93 (~c2_1(a1852)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1328, 1819])).
% 0.94/0.93 tff(1821,plain,
% 0.94/0.93 (c3_1(a1852)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1339, 1819])).
% 0.94/0.93 tff(1822,plain,
% 0.94/0.93 (c1_1(a1852)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1350, 1819])).
% 0.94/0.93 tff(1823,plain,
% 0.94/0.93 (~hskp10),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1493, 1822, 1615, 1616, 1821, 1614, 1820])).
% 0.94/0.93 tff(1824,plain,
% 0.94/0.93 (hskp24),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1642, 1823, 21])).
% 0.94/0.93 tff(1825,plain,
% 0.94/0.93 (~c2_1(a1919)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[375, 1824])).
% 0.94/0.93 tff(1826,plain,
% 0.94/0.93 (~c1_1(a1919)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[381, 1824])).
% 0.94/0.93 tff(1827,plain,
% 0.94/0.93 (c3_1(a1919)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[392, 1824])).
% 0.94/0.93 tff(1828,plain,
% 0.94/0.93 ($false),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1101, 140, 21, 1827, 1616, 1826, 1825, 1614, 562, 1627])).
% 0.94/0.93 tff(1829,plain,(hskp8 | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.94/0.93 tff(1830,plain,
% 0.94/0.93 (hskp8),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1829, 1228])).
% 0.94/0.93 tff(1831,plain,
% 0.94/0.93 (~c2_1(a1862)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[574, 1830])).
% 0.94/0.93 tff(1832,plain,
% 0.94/0.93 (c0_1(a1862)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[743, 1830])).
% 0.94/0.93 tff(1833,plain,
% 0.94/0.93 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c0_1(a1862)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c0_1(a1862)))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1834,plain,
% 0.94/0.93 ((hskp27 | hskp22 | (~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c0_1(a1862))) <=> (hskp27 | hskp22 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c0_1(a1862)))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1835,plain,
% 0.94/0.93 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c0_1(a1862)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c0_1(a1862))))),
% 0.94/0.93 inference(monotonicity,[status(thm)],[1834])).
% 0.94/0.93 tff(1836,plain,
% 0.94/0.93 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c0_1(a1862)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c0_1(a1862)))),
% 0.94/0.93 inference(transitivity,[status(thm)],[1835, 1833])).
% 0.94/0.93 tff(1837,plain,
% 0.94/0.93 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c0_1(a1862)))),
% 0.94/0.93 inference(quant_inst,[status(thm)],[])).
% 0.94/0.93 tff(1838,plain,
% 0.94/0.93 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp27 | hskp22 | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c0_1(a1862))),
% 0.94/0.93 inference(modus_ponens,[status(thm)],[1837, 1836])).
% 0.94/0.93 tff(1839,plain,
% 0.94/0.93 (hskp22 | (~c3_1(a1862))),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1838, 140, 1228, 1832, 1831, 459])).
% 0.94/0.93 tff(1840,plain,
% 0.94/0.93 (hskp22),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1839, 1538])).
% 0.94/0.93 tff(1841,plain,
% 0.94/0.93 (~c3_1(a1899)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1167, 1840])).
% 0.94/0.93 tff(1842,plain,
% 0.94/0.93 (~c2_1(a1899)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1173, 1840])).
% 0.94/0.93 tff(1843,plain,
% 0.94/0.93 (c1_1(a1862)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[621, 1830])).
% 0.94/0.93 tff(1844,plain,
% 0.94/0.93 (c0_1(a1899)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1184, 1840])).
% 0.94/0.93 tff(1845,plain,
% 0.94/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c0_1(a1899)))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1846,plain,
% 0.94/0.93 (((~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899))) <=> (c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c0_1(a1899)))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1847,plain,
% 0.94/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | (c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c0_1(a1899))))),
% 0.94/0.93 inference(monotonicity,[status(thm)],[1846])).
% 0.94/0.93 tff(1848,plain,
% 0.94/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c0_1(a1899)))),
% 0.94/0.93 inference(transitivity,[status(thm)],[1847, 1845])).
% 0.94/0.93 tff(1849,plain,
% 0.94/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c3_1(a1899) | c2_1(a1899) | (~c0_1(a1899)))),
% 0.94/0.93 inference(quant_inst,[status(thm)],[])).
% 0.94/0.93 tff(1850,plain,
% 0.94/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)) | c3_1(W) | c2_1(W) | (~c0_1(W)))) | c2_1(a1899) | c3_1(a1899) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c0_1(a1862)) | (~c0_1(a1899))),
% 0.94/0.93 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 0.94/0.93 tff(1851,plain,
% 0.94/0.93 ($false),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1850, 140, 1844, 1832, 1843, 1842, 1841, 1831, 1362, 1538])).
% 0.94/0.93 tff(1852,plain,((~c3_1(a1862)) | hskp27), inference(lemma,lemma(discharge,[]))).
% 0.94/0.93 tff(1853,plain,
% 0.94/0.93 (~c3_1(a1862)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1852, 1228])).
% 0.94/0.93 tff(1854,plain,
% 0.94/0.93 ($false),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[750, 140, 1832, 1843, 1831, 410, 1853])).
% 0.94/0.93 tff(1855,plain,(hskp27), inference(lemma,lemma(discharge,[]))).
% 0.94/0.93 tff(1856,plain,
% 0.94/0.93 (c3_1(a1877)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[160, 1855])).
% 0.94/0.93 tff(1857,plain,
% 0.94/0.93 (c2_1(a1877)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[171, 1855])).
% 0.94/0.93 tff(1858,plain,
% 0.94/0.93 (c0_1(a1877)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[182, 1855])).
% 0.94/0.93 tff(1859,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1860,plain,
% 0.94/0.93 ((hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853))) <=> (hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1861,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.94/0.93 inference(monotonicity,[status(thm)],[1860])).
% 0.94/0.93 tff(1862,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.93 inference(transitivity,[status(thm)],[1861, 1859])).
% 0.94/0.93 tff(1863,plain,
% 0.94/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c0_1(a1853) | c2_1(a1853) | (~c1_1(a1853)))),
% 0.94/0.93 inference(quant_inst,[status(thm)],[])).
% 0.94/0.93 tff(1864,plain,
% 0.94/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c0_1(a1853) | (~ndr1_0) | c2_1(a1853) | (~c1_1(a1853)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.94/0.93 inference(modus_ponens,[status(thm)],[1863, 1862])).
% 0.94/0.93 tff(1865,plain,
% 0.94/0.93 (hskp8 | c2_1(a1853)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1864, 140, 1858, 1857, 1856, 1537, 1526, 31])).
% 0.94/0.93 tff(1866,plain,
% 0.94/0.93 (c2_1(a1853)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1865, 21])).
% 0.94/0.93 tff(1867,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1919)))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1868,plain,
% 0.94/0.93 ((hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853))) <=> (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1919)))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1869,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1919))))),
% 0.94/0.93 inference(monotonicity,[status(thm)],[1868])).
% 0.94/0.93 tff(1870,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1919)))),
% 0.94/0.93 inference(transitivity,[status(thm)],[1869, 1867])).
% 0.94/0.93 tff(1871,plain,
% 0.94/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1919) | c1_1(a1919) | (~c3_1(a1919)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)))),
% 0.94/0.93 inference(quant_inst,[status(thm)],[])).
% 0.94/0.93 tff(1872,plain,
% 0.94/0.93 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1919))),
% 0.94/0.93 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 0.94/0.93 tff(1873,plain,
% 0.94/0.93 (c1_1(a1919) | (~c3_1(a1919))),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1872, 140, 21, 1537, 460, 1526, 562, 1866])).
% 0.94/0.93 tff(1874,plain,
% 0.94/0.93 (~c3_1(a1919)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1873, 473])).
% 0.94/0.93 tff(1875,plain,
% 0.94/0.93 (~hskp24),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[392, 1874])).
% 0.94/0.93 tff(1876,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c3_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1877,plain,
% 0.94/0.93 ((hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1919) | c2_1(a1919) | (~c0_1(a1919))) <=> (hskp24 | c3_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1878,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1919) | c2_1(a1919) | (~c0_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | c3_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))))),
% 0.94/0.93 inference(monotonicity,[status(thm)],[1877])).
% 0.94/0.93 tff(1879,plain,
% 0.94/0.93 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1919) | c2_1(a1919) | (~c0_1(a1919)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877)))),
% 0.94/0.93 inference(transitivity,[status(thm)],[1878, 1876])).
% 0.94/0.93 tff(1880,plain,
% 0.94/0.93 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1877)) | (~c3_1(a1877)) | (~c0_1(a1877)) | c3_1(a1919) | c2_1(a1919) | (~c0_1(a1919)))),
% 0.94/0.93 inference(quant_inst,[status(thm)],[])).
% 0.94/0.93 tff(1881,plain,
% 0.94/0.93 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp24 | c3_1(a1919) | c2_1(a1919) | (~ndr1_0) | (~c0_1(a1919)) | (~c3_1(a1877)) | (~c0_1(a1877)) | (~c2_1(a1877))),
% 0.94/0.93 inference(modus_ponens,[status(thm)],[1880, 1879])).
% 0.94/0.93 tff(1882,plain,
% 0.94/0.93 (~c0_1(a1919)),
% 0.94/0.93 inference(unit_resolution,[status(thm)],[1881, 140, 1875, 1858, 1857, 1856, 1874, 460, 284])).
% 0.94/0.93 tff(1883,plain,
% 0.94/0.93 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.94/0.93 inference(bind,[status(th)],[])).
% 0.94/0.93 tff(1884,plain,
% 0.94/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.94/0.93 inference(quant_intro,[status(thm)],[1883])).
% 0.94/0.93 tff(1885,plain,
% 0.94/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.94/0.93 inference(rewrite,[status(thm)],[])).
% 0.94/0.93 tff(1886,plain,
% 0.94/0.93 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.01/0.93 inference(bind,[status(th)],[])).
% 1.01/0.93 tff(1887,plain,
% 1.01/0.93 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.01/0.93 inference(quant_intro,[status(thm)],[1886])).
% 1.01/0.93 tff(1888,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 1.01/0.93 tff(1889,plain,
% 1.01/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1888, 1887])).
% 1.01/0.93 tff(1890,plain,
% 1.01/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1889, 1885])).
% 1.01/0.93 tff(1891,plain,(
% 1.01/0.93 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.01/0.93 inference(skolemize,[status(sab)],[1890])).
% 1.01/0.93 tff(1892,plain,
% 1.01/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1891, 1884])).
% 1.01/0.93 tff(1893,plain,
% 1.01/0.93 (hskp10),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1642, 1875, 21])).
% 1.01/0.93 tff(1894,plain,
% 1.01/0.93 (~c1_1(a1864)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1482, 1893])).
% 1.01/0.93 tff(1895,plain,
% 1.01/0.93 (c0_1(a1864)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[507, 1893])).
% 1.01/0.93 tff(1896,plain,
% 1.01/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1919) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c0_1(a1864)) | (~c2_1(a1864)) | c0_1(a1919))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1919) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c0_1(a1864)) | (~c2_1(a1864)) | c0_1(a1919))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1897,plain,
% 1.01/0.93 (((~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919)) <=> (c1_1(a1919) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c0_1(a1864)) | (~c2_1(a1864)) | c0_1(a1919))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1898,plain,
% 1.01/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1919) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c0_1(a1864)) | (~c2_1(a1864)) | c0_1(a1919)))),
% 1.01/0.93 inference(monotonicity,[status(thm)],[1897])).
% 1.01/0.93 tff(1899,plain,
% 1.01/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1919) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c0_1(a1864)) | (~c2_1(a1864)) | c0_1(a1919))),
% 1.01/0.93 inference(transitivity,[status(thm)],[1898, 1896])).
% 1.01/0.93 tff(1900,plain,
% 1.01/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a1864) | (~c2_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919))),
% 1.01/0.93 inference(quant_inst,[status(thm)],[])).
% 1.01/0.93 tff(1901,plain,
% 1.01/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1919) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c0_1(a1864)) | (~c2_1(a1864)) | c0_1(a1919)),
% 1.01/0.93 inference(modus_ponens,[status(thm)],[1900, 1899])).
% 1.01/0.93 tff(1902,plain,
% 1.01/0.93 (~c2_1(a1864)),
% 1.01/0.93 inference(unit_resolution,[status(thm)],[1901, 140, 1895, 1537, 473, 460, 1894, 1526, 1892, 1882, 1866])).
% 1.01/0.93 tff(1903,plain,
% 1.01/0.93 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.01/0.93 inference(bind,[status(th)],[])).
% 1.01/0.93 tff(1904,plain,
% 1.01/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.01/0.93 inference(quant_intro,[status(thm)],[1903])).
% 1.01/0.93 tff(1905,plain,
% 1.01/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.01/0.93 inference(rewrite,[status(thm)],[])).
% 1.01/0.93 tff(1906,plain,
% 1.01/0.93 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.01/0.94 inference(bind,[status(th)],[])).
% 1.01/0.94 tff(1907,plain,
% 1.01/0.94 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.01/0.94 inference(quant_intro,[status(thm)],[1906])).
% 1.01/0.94 tff(1908,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.01/0.94 tff(1909,plain,
% 1.01/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 1.01/0.94 tff(1910,plain,
% 1.01/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1909, 1905])).
% 1.01/0.94 tff(1911,plain,(
% 1.01/0.94 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.01/0.94 inference(skolemize,[status(sab)],[1910])).
% 1.01/0.94 tff(1912,plain,
% 1.01/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1911, 1904])).
% 1.01/0.94 tff(1913,plain,
% 1.01/0.94 (c3_1(a1864)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[496, 1893])).
% 1.01/0.94 tff(1914,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864) | c0_1(a1919))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864) | c0_1(a1919))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1915,plain,
% 1.01/0.94 (((~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919)) <=> (c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864) | c0_1(a1919))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1916,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864) | c0_1(a1919)))),
% 1.01/0.94 inference(monotonicity,[status(thm)],[1915])).
% 1.01/0.94 tff(1917,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864) | c0_1(a1919))),
% 1.01/0.94 inference(transitivity,[status(thm)],[1916, 1914])).
% 1.01/0.94 tff(1918,plain,
% 1.01/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)) | c2_1(a1919) | c1_1(a1919) | c0_1(a1919))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1919,plain,
% 1.01/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a1919) | c2_1(a1919) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | c2_1(a1864) | c0_1(a1919)),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.01/0.94 tff(1920,plain,
% 1.01/0.94 ($false),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1919, 140, 1895, 1913, 1537, 473, 460, 1526, 1912, 1882, 1866, 1902])).
% 1.01/0.94 tff(1921,plain,(c1_1(a1919) | c2_1(a1919) | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.01/0.94 tff(1922,plain,
% 1.01/0.94 (c1_1(a1919)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1921, 460, 21])).
% 1.01/0.94 tff(1923,plain,
% 1.01/0.94 (~hskp24),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[381, 1922])).
% 1.01/0.94 tff(1924,plain,
% 1.01/0.94 (hskp10),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1642, 1923, 21])).
% 1.01/0.94 tff(1925,plain,
% 1.01/0.94 (~c1_1(a1864)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1482, 1924])).
% 1.01/0.94 tff(1926,plain,
% 1.01/0.94 (c3_1(a1864)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[496, 1924])).
% 1.01/0.94 tff(1927,plain,
% 1.01/0.94 (c0_1(a1864)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[507, 1924])).
% 1.01/0.94 tff(1928,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1919)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1919)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1929,plain,
% 1.01/0.94 (((~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c1_1(a1919)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853))) <=> ((~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1919)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1930,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c1_1(a1919)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1919))))),
% 1.01/0.94 inference(monotonicity,[status(thm)],[1929])).
% 1.01/0.94 tff(1931,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c1_1(a1919)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1919)))),
% 1.01/0.94 inference(transitivity,[status(thm)],[1930, 1928])).
% 1.01/0.94 tff(1932,plain,
% 1.01/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1919) | (~c3_1(a1919)) | (~c1_1(a1919)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1933,plain,
% 1.01/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1919))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1932, 1931])).
% 1.01/0.94 tff(1934,plain,
% 1.01/0.94 (~c3_1(a1919)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1933, 140, 1927, 1926, 1575, 1922, 460, 1925, 1526, 10, 1866])).
% 1.01/0.94 tff(1935,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1919) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c2_1(a1864)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1919) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c2_1(a1864)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1936,plain,
% 1.01/0.94 (((~ndr1_0) | c2_1(a1919) | c3_1(a1919) | (~c1_1(a1919)) | c1_1(a1864) | (~c2_1(a1864)) | (~c3_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853))) <=> (c3_1(a1919) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c2_1(a1864)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1937,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1919) | c3_1(a1919) | (~c1_1(a1919)) | c1_1(a1864) | (~c2_1(a1864)) | (~c3_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c3_1(a1919) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c2_1(a1864))))),
% 1.01/0.94 inference(monotonicity,[status(thm)],[1936])).
% 1.01/0.94 tff(1938,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1919) | c3_1(a1919) | (~c1_1(a1919)) | c1_1(a1864) | (~c2_1(a1864)) | (~c3_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1919) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c2_1(a1864)))),
% 1.01/0.94 inference(transitivity,[status(thm)],[1937, 1935])).
% 1.01/0.94 tff(1939,plain,
% 1.01/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1919) | c3_1(a1919) | (~c1_1(a1919)) | c1_1(a1864) | (~c2_1(a1864)) | (~c3_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1940,plain,
% 1.01/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c3_1(a1919) | (~c1_1(a1919)) | c2_1(a1919) | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c2_1(a1864))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1939, 1938])).
% 1.01/0.94 tff(1941,plain,
% 1.01/0.94 (~c2_1(a1864)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1940, 140, 1934, 1926, 1575, 1922, 460, 1925, 1526, 689, 1866])).
% 1.01/0.94 tff(1942,plain,
% 1.01/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | c2_1(a1864))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | c2_1(a1864))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1943,plain,
% 1.01/0.94 ((hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853))) <=> (hskp8 | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | c2_1(a1864))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1944,plain,
% 1.01/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | c2_1(a1864)))),
% 1.01/0.94 inference(monotonicity,[status(thm)],[1943])).
% 1.01/0.94 tff(1945,plain,
% 1.01/0.94 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | c2_1(a1864))),
% 1.01/0.94 inference(transitivity,[status(thm)],[1944, 1942])).
% 1.01/0.94 tff(1946,plain,
% 1.01/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a1864) | c1_1(a1864) | (~c3_1(a1864)) | c0_1(a1853) | (~c2_1(a1853)) | (~c1_1(a1853)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1947,plain,
% 1.01/0.94 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp8 | c1_1(a1864) | c0_1(a1853) | (~ndr1_0) | (~c2_1(a1853)) | (~c1_1(a1853)) | (~c3_1(a1864)) | c2_1(a1864)),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 1.01/0.94 tff(1948,plain,
% 1.01/0.94 ($false),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1947, 140, 21, 1926, 1537, 1925, 1526, 562, 1866, 1941])).
% 1.01/0.94 tff(1949,plain,(c2_1(a1919) | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.01/0.94 tff(1950,plain,
% 1.01/0.94 (c2_1(a1919)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1949, 21])).
% 1.01/0.94 tff(1951,plain,
% 1.01/0.94 (~hskp24),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[375, 1950])).
% 1.01/0.94 tff(1952,plain,
% 1.01/0.94 (hskp10),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1642, 1951, 21])).
% 1.01/0.94 tff(1953,plain,
% 1.01/0.94 (~c1_1(a1864)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1482, 1952])).
% 1.01/0.94 tff(1954,plain,
% 1.01/0.94 (c3_1(a1864)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[496, 1952])).
% 1.01/0.94 tff(1955,plain,
% 1.01/0.94 (c0_1(a1864)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[507, 1952])).
% 1.01/0.94 tff(1956,assumption,(c2_1(a1853)), introduced(assumption)).
% 1.01/0.94 tff(1957,assumption,(hskp0), introduced(assumption)).
% 1.01/0.94 tff(1958,plain,
% 1.01/0.94 (~c2_1(a1852)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1328, 1957])).
% 1.01/0.94 tff(1959,assumption,(~c1_1(a1864)), introduced(assumption)).
% 1.01/0.94 tff(1960,plain,
% 1.01/0.94 (c3_1(a1852)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1339, 1957])).
% 1.01/0.94 tff(1961,plain,
% 1.01/0.94 (c1_1(a1852)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1350, 1957])).
% 1.01/0.94 tff(1962,assumption,(c3_1(a1864)), introduced(assumption)).
% 1.01/0.94 tff(1963,assumption,(c0_1(a1864)), introduced(assumption)).
% 1.01/0.94 tff(1964,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1864) | c0_1(a1853) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1864) | c0_1(a1853) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1965,plain,
% 1.01/0.94 (((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853))) <=> (c1_1(a1864) | c0_1(a1853) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1966,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1864) | c0_1(a1853) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864))))),
% 1.01/0.94 inference(monotonicity,[status(thm)],[1965])).
% 1.01/0.94 tff(1967,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1864) | c0_1(a1853) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864)))),
% 1.01/0.94 inference(transitivity,[status(thm)],[1966, 1964])).
% 1.01/0.94 tff(1968,plain,
% 1.01/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1852) | (~c3_1(a1852)) | (~c1_1(a1852)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1853) | (~c3_1(a1853)) | (~c2_1(a1853)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1969,plain,
% 1.01/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1864) | c0_1(a1853) | c2_1(a1852) | (~ndr1_0) | (~c3_1(a1852)) | (~c1_1(a1852)) | (~c2_1(a1853)) | (~c3_1(a1853)) | (~c3_1(a1864)) | (~c0_1(a1864))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1968, 1967])).
% 1.01/0.94 tff(1970,plain,
% 1.01/0.94 ($false),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1969, 140, 1963, 1962, 1575, 1961, 1960, 1959, 1526, 1958, 10, 1956])).
% 1.01/0.94 tff(1971,plain,((~hskp0) | (~c0_1(a1864)) | (~c3_1(a1864)) | c1_1(a1864) | (~c2_1(a1853))), inference(lemma,lemma(discharge,[]))).
% 1.01/0.94 tff(1972,plain,
% 1.01/0.94 (~hskp0),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1971, 1955, 1954, 1953, 1866])).
% 1.01/0.94 tff(1973,plain,
% 1.01/0.94 (~c2_1(a1864)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1672, 1972, 21, 1951])).
% 1.01/0.94 tff(1974,plain,
% 1.01/0.94 (~hskp29),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[148, 1972, 1951])).
% 1.01/0.94 tff(1975,plain,
% 1.01/0.94 (hskp29 | hskp20 | c2_1(a1864)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1721, 140, 1954, 1953, 1715])).
% 1.01/0.94 tff(1976,plain,
% 1.01/0.94 (hskp20),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1975, 1974, 1973])).
% 1.01/0.94 tff(1977,plain,
% 1.01/0.94 (~c1_1(a1890)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[853, 1976])).
% 1.01/0.94 tff(1978,plain,
% 1.01/0.94 (~c0_1(a1890)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[859, 1976])).
% 1.01/0.94 tff(1979,plain,
% 1.01/0.94 (c2_1(a1890)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[889, 1976])).
% 1.01/0.94 tff(1980,plain,
% 1.01/0.94 (hskp23),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[842, 810, 21])).
% 1.01/0.94 tff(1981,plain,
% 1.01/0.94 (~c3_1(a1911)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[247, 1980])).
% 1.01/0.94 tff(1982,plain,
% 1.01/0.94 (c0_1(a1911)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[264, 1980])).
% 1.01/0.94 tff(1983,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a1911) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c2_1(a1863)) | (~c0_1(a1911)) | (~c2_1(a1911)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1911) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c2_1(a1863)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1984,plain,
% 1.01/0.94 (((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853))) <=> (c3_1(a1911) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c2_1(a1863)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 1.01/0.94 inference(rewrite,[status(thm)],[])).
% 1.01/0.94 tff(1985,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c3_1(a1911) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c2_1(a1863)) | (~c0_1(a1911)) | (~c2_1(a1911))))),
% 1.01/0.94 inference(monotonicity,[status(thm)],[1984])).
% 1.01/0.94 tff(1986,plain,
% 1.01/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1911) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c2_1(a1863)) | (~c0_1(a1911)) | (~c2_1(a1911)))),
% 1.01/0.94 inference(transitivity,[status(thm)],[1985, 1983])).
% 1.01/0.94 tff(1987,plain,
% 1.01/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c3_1(a1911) | (~c2_1(a1911)) | (~c0_1(a1911)) | c3_1(a1863) | c1_1(a1863) | (~c2_1(a1863)) | c0_1(a1853) | (~c3_1(a1853)) | (~c1_1(a1853)))),
% 1.01/0.94 inference(quant_inst,[status(thm)],[])).
% 1.01/0.94 tff(1988,plain,
% 1.01/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c3_1(a1911) | c1_1(a1863) | c3_1(a1863) | c0_1(a1853) | (~ndr1_0) | (~c1_1(a1853)) | (~c3_1(a1853)) | (~c2_1(a1863)) | (~c0_1(a1911)) | (~c2_1(a1911))),
% 1.01/0.94 inference(modus_ponens,[status(thm)],[1987, 1986])).
% 1.01/0.94 tff(1989,plain,
% 1.01/0.94 (~c2_1(a1911)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1988, 140, 1982, 833, 1537, 1575, 1981, 822, 816, 1526, 241])).
% 1.01/0.94 tff(1990,plain,
% 1.01/0.94 ($false),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[293, 140, 1951, 1858, 1857, 1856, 1982, 1981, 284, 1989])).
% 1.01/0.94 tff(1991,plain,((~hskp9) | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.01/0.94 tff(1992,plain,
% 1.01/0.94 (~hskp9),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1991, 21])).
% 1.01/0.94 tff(1993,plain,
% 1.01/0.94 ($false),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[1731, 140, 1992, 21, 1979, 1978, 1977, 20])).
% 1.01/0.94 tff(1994,plain,(hskp8), inference(lemma,lemma(discharge,[]))).
% 1.01/0.94 tff(1995,plain,
% 1.01/0.94 (~c2_1(a1862)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[574, 1994])).
% 1.01/0.94 tff(1996,plain,
% 1.01/0.94 (c1_1(a1862)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[621, 1994])).
% 1.01/0.94 tff(1997,plain,
% 1.01/0.94 (c0_1(a1862)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[743, 1994])).
% 1.01/0.94 tff(1998,plain,
% 1.01/0.94 (hskp16),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[752, 1994, 1858, 1857, 1856])).
% 1.01/0.94 tff(1999,plain,
% 1.01/0.94 (~c0_1(a1872)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[610, 1998])).
% 1.01/0.94 tff(2000,plain,
% 1.01/0.94 (c3_1(a1872)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[632, 1998])).
% 1.01/0.94 tff(2001,plain,
% 1.01/0.94 (c2_1(a1872)),
% 1.01/0.94 inference(unit_resolution,[status(thm)],[643, 1998])).
% 1.01/0.95 tff(2002,plain,
% 1.01/0.95 ((~hskp10) | (~c1_1(a1852)) | (~c3_1(a1852)) | c2_1(a1852)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1493, 2001, 2000, 1999])).
% 1.01/0.95 tff(2003,plain,
% 1.01/0.95 (~hskp10),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[2002, 1961, 1960, 1958])).
% 1.01/0.95 tff(2004,plain,
% 1.01/0.95 (c1_1(a1877) | (~c1_1(a1852)) | (~c3_1(a1852)) | c2_1(a1852)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1465, 1856, 2001, 2000, 1999, 1858])).
% 1.01/0.95 tff(2005,plain,
% 1.01/0.95 (c1_1(a1877)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[2004, 1958, 1961, 1960])).
% 1.01/0.95 tff(2006,plain,
% 1.01/0.95 (hskp10 | (~c1_1(a1877))),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1518, 140, 1857, 1856, 1997, 1996, 1995, 1476])).
% 1.01/0.95 tff(2007,plain,
% 1.01/0.95 ($false),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[2006, 2005, 2003])).
% 1.01/0.95 tff(2008,plain,(~hskp0), inference(lemma,lemma(discharge,[]))).
% 1.01/0.95 tff(2009,plain,
% 1.01/0.95 (hskp28 | hskp0),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[189, 140, 1858, 1857, 1856, 63])).
% 1.01/0.95 tff(2010,plain,
% 1.01/0.95 (hskp28),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[2009, 2008])).
% 1.01/0.95 tff(2011,plain,
% 1.01/0.95 (c3_1(a1878)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[229, 2010])).
% 1.01/0.95 tff(2012,plain,
% 1.01/0.95 (c2_1(a1878)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[200, 2010])).
% 1.01/0.95 tff(2013,plain,
% 1.01/0.95 (c1_1(a1878)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[211, 2010])).
% 1.01/0.95 tff(2014,plain,
% 1.01/0.95 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1862) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1862) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(2015,plain,
% 1.01/0.95 ((hskp10 | (~ndr1_0) | (~c2_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1878)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862))) <=> (hskp10 | c2_1(a1862) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(2016,plain,
% 1.01/0.95 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1878)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c2_1(a1862) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1862)) | (~c0_1(a1862))))),
% 1.01/0.95 inference(monotonicity,[status(thm)],[2015])).
% 1.01/0.95 tff(2017,plain,
% 1.01/0.95 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1878)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1862) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 1.01/0.95 inference(transitivity,[status(thm)],[2016, 2014])).
% 1.01/0.95 tff(2018,plain,
% 1.01/0.95 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c2_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1878)) | c2_1(a1862) | (~c1_1(a1862)) | (~c0_1(a1862)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(2019,plain,
% 1.01/0.95 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c2_1(a1862) | (~ndr1_0) | (~c2_1(a1878)) | (~c1_1(a1878)) | (~c3_1(a1878)) | (~c1_1(a1862)) | (~c0_1(a1862))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 1.01/0.95 tff(2020,plain,
% 1.01/0.95 (hskp10),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[2019, 140, 2013, 2012, 2011, 1997, 1996, 1995, 1476])).
% 1.01/0.95 tff(2021,plain,
% 1.01/0.95 (~c1_1(a1864)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[1482, 2020])).
% 1.01/0.95 tff(2022,plain,
% 1.01/0.95 (c3_1(a1864)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[496, 2020])).
% 1.01/0.95 tff(2023,plain,
% 1.01/0.95 (c0_1(a1864)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[507, 2020])).
% 1.01/0.95 tff(2024,plain,
% 1.01/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c1_1(a1864) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c1_1(a1864) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(2025,plain,
% 1.01/0.95 (((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872))) <=> (c0_1(a1872) | c1_1(a1864) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 1.01/0.95 inference(rewrite,[status(thm)],[])).
% 1.01/0.95 tff(2026,plain,
% 1.01/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c0_1(a1872) | c1_1(a1864) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872))))),
% 1.01/0.95 inference(monotonicity,[status(thm)],[2025])).
% 1.01/0.95 tff(2027,plain,
% 1.01/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c1_1(a1864) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 1.01/0.95 inference(transitivity,[status(thm)],[2026, 2024])).
% 1.01/0.95 tff(2028,plain,
% 1.01/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a1862) | (~c3_1(a1862)) | (~c1_1(a1862)) | c1_1(a1864) | (~c3_1(a1864)) | (~c0_1(a1864)) | c0_1(a1872) | (~c3_1(a1872)) | (~c2_1(a1872)))),
% 1.01/0.95 inference(quant_inst,[status(thm)],[])).
% 1.01/0.95 tff(2029,plain,
% 1.01/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c0_1(a1872) | c1_1(a1864) | c2_1(a1862) | (~ndr1_0) | (~c3_1(a1862)) | (~c1_1(a1862)) | (~c3_1(a1864)) | (~c0_1(a1864)) | (~c3_1(a1872)) | (~c2_1(a1872))),
% 1.01/0.95 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 1.01/0.95 tff(2030,plain,
% 1.01/0.95 (~c3_1(a1862)),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[2029, 140, 2001, 2000, 2023, 2022, 1996, 1999, 2021, 1995, 10])).
% 1.01/0.95 tff(2031,plain,
% 1.01/0.95 ($false),
% 1.01/0.95 inference(unit_resolution,[status(thm)],[750, 140, 1997, 1996, 1995, 410, 2030])).
% 1.01/0.95 % SZS output end Proof
%------------------------------------------------------------------------------