TSTP Solution File: SYN454-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN454-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 23:55:32 EDT 2022
% Result : Unsatisfiable 0.63s 0.64s
% Output : Proof 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN454-1 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 04:00:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.63/0.64 % SZS status Unsatisfiable
% 0.63/0.64 % SZS output start Proof
% 0.63/0.64 tff(c2_1_type, type, (
% 0.63/0.64 c2_1: $i > $o)).
% 0.63/0.64 tff(a116_type, type, (
% 0.63/0.64 a116: $i)).
% 0.63/0.64 tff(c1_1_type, type, (
% 0.63/0.64 c1_1: $i > $o)).
% 0.63/0.64 tff(a133_type, type, (
% 0.63/0.64 a133: $i)).
% 0.63/0.64 tff(c0_1_type, type, (
% 0.63/0.64 c0_1: $i > $o)).
% 0.63/0.64 tff(c3_1_type, type, (
% 0.63/0.64 c3_1: $i > $o)).
% 0.63/0.64 tff(ndr1_0_type, type, (
% 0.63/0.64 ndr1_0: $o)).
% 0.63/0.64 tff(hskp20_type, type, (
% 0.63/0.64 hskp20: $o)).
% 0.63/0.64 tff(a101_type, type, (
% 0.63/0.64 a101: $i)).
% 0.63/0.64 tff(a104_type, type, (
% 0.63/0.64 a104: $i)).
% 0.63/0.64 tff(a106_type, type, (
% 0.63/0.64 a106: $i)).
% 0.63/0.64 tff(hskp10_type, type, (
% 0.63/0.64 hskp10: $o)).
% 0.63/0.64 tff(a99_type, type, (
% 0.63/0.64 a99: $i)).
% 0.63/0.64 tff(hskp3_type, type, (
% 0.63/0.64 hskp3: $o)).
% 0.63/0.64 tff(a115_type, type, (
% 0.63/0.64 a115: $i)).
% 0.63/0.64 tff(a165_type, type, (
% 0.63/0.64 a165: $i)).
% 0.63/0.64 tff(hskp14_type, type, (
% 0.63/0.64 hskp14: $o)).
% 0.63/0.64 tff(hskp1_type, type, (
% 0.63/0.64 hskp1: $o)).
% 0.63/0.64 tff(hskp13_type, type, (
% 0.63/0.64 hskp13: $o)).
% 0.63/0.64 tff(a112_type, type, (
% 0.63/0.64 a112: $i)).
% 0.63/0.64 tff(hskp0_type, type, (
% 0.63/0.64 hskp0: $o)).
% 0.63/0.64 tff(hskp29_type, type, (
% 0.63/0.64 hskp29: $o)).
% 0.63/0.64 tff(a97_type, type, (
% 0.63/0.64 a97: $i)).
% 0.63/0.64 tff(a96_type, type, (
% 0.63/0.64 a96: $i)).
% 0.63/0.64 tff(a98_type, type, (
% 0.63/0.64 a98: $i)).
% 0.63/0.64 tff(hskp2_type, type, (
% 0.63/0.64 hskp2: $o)).
% 0.63/0.64 tff(a103_type, type, (
% 0.63/0.64 a103: $i)).
% 0.63/0.64 tff(hskp7_type, type, (
% 0.63/0.64 hskp7: $o)).
% 0.63/0.64 tff(hskp11_type, type, (
% 0.63/0.64 hskp11: $o)).
% 0.63/0.64 tff(hskp8_type, type, (
% 0.63/0.64 hskp8: $o)).
% 0.63/0.64 tff(hskp5_type, type, (
% 0.63/0.64 hskp5: $o)).
% 0.63/0.64 tff(a102_type, type, (
% 0.63/0.64 a102: $i)).
% 0.63/0.64 tff(hskp6_type, type, (
% 0.63/0.64 hskp6: $o)).
% 0.63/0.64 tff(a109_type, type, (
% 0.63/0.64 a109: $i)).
% 0.63/0.64 tff(hskp12_type, type, (
% 0.63/0.64 hskp12: $o)).
% 0.63/0.64 tff(a110_type, type, (
% 0.63/0.64 a110: $i)).
% 0.63/0.64 tff(hskp15_type, type, (
% 0.63/0.64 hskp15: $o)).
% 0.63/0.64 tff(1,assumption,(~c2_1(a116)), introduced(assumption)).
% 0.63/0.64 tff(2,plain,
% 0.63/0.64 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(3,plain,
% 0.63/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[2])).
% 0.63/0.64 tff(4,plain,
% 0.63/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(5,plain,
% 0.63/0.64 (^[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)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_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)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_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)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_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)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_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))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c2_1(V)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c2_1(V)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(6,plain,
% 0.63/0.64 (![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))) | (~c1_1(W))) | c2_1(V)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[5])).
% 0.63/0.64 tff(7,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))) | (~c1_1(W))) | c2_1(V)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 0.63/0.64 tff(8,plain,
% 0.63/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.63/0.64 tff(9,plain,
% 0.63/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.63/0.64 tff(10,plain,(
% 0.63/0.64 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.63/0.64 inference(skolemize,[status(sab)],[9])).
% 0.63/0.64 tff(11,plain,
% 0.63/0.64 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.63/0.64 tff(12,plain,
% 0.63/0.64 (^[V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(13,plain,
% 0.63/0.64 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[12])).
% 0.63/0.64 tff(14,plain,
% 0.63/0.64 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(15,plain,
% 0.63/0.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(16,plain,
% 0.63/0.64 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[15])).
% 0.63/0.64 tff(17,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 0.63/0.64 tff(18,plain,
% 0.63/0.64 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.63/0.64 tff(19,plain,
% 0.63/0.64 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.63/0.64 tff(20,plain,(
% 0.63/0.64 ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.65 inference(skolemize,[status(sab)],[19])).
% 0.63/0.65 tff(21,plain,
% 0.63/0.65 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.63/0.65 tff(22,assumption,(~hskp20), introduced(assumption)).
% 0.63/0.65 tff(23,assumption,(~hskp3), introduced(assumption)).
% 0.63/0.65 tff(24,plain,
% 0.63/0.65 (^[U: $i] : refl((hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(25,plain,
% 0.63/0.65 (![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.63/0.65 inference(quant_intro,[status(thm)],[24])).
% 0.63/0.65 tff(26,plain,
% 0.63/0.65 (![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(27,plain,
% 0.63/0.65 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp10) <=> ((hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp10))), rewrite(((hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp10) <=> (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp10) <=> (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(28,plain,
% 0.63/0.65 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp10) <=> ![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.63/0.65 inference(quant_intro,[status(thm)],[27])).
% 0.63/0.65 tff(29,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.63/0.65 tff(30,plain,
% 0.63/0.65 (![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.63/0.65 tff(31,plain,
% 0.63/0.65 (![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.63/0.65 tff(32,plain,(
% 0.63/0.65 ![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.63/0.65 inference(skolemize,[status(sab)],[31])).
% 0.63/0.65 tff(33,plain,
% 0.63/0.65 (![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.63/0.65 tff(34,assumption,(~hskp10), introduced(assumption)).
% 0.63/0.65 tff(35,assumption,(hskp13), introduced(assumption)).
% 0.63/0.65 tff(36,plain,
% 0.63/0.65 (((~hskp13) | (~c1_1(a112))) <=> ((~hskp13) | (~c1_1(a112)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(37,plain,
% 0.63/0.65 (((~c1_1(a112)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a112)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(38,axiom,((~c1_1(a112)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.63/0.65 tff(39,plain,
% 0.63/0.65 ((~hskp13) | (~c1_1(a112))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.63/0.65 tff(40,plain,
% 0.63/0.65 ((~hskp13) | (~c1_1(a112))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.63/0.65 tff(41,plain,
% 0.63/0.65 (~c1_1(a112)),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[40, 35])).
% 0.63/0.65 tff(42,plain,
% 0.63/0.65 (((~hskp13) | c0_1(a112)) <=> ((~hskp13) | c0_1(a112))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(43,axiom,((~hskp13) | c0_1(a112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.63/0.65 tff(44,plain,
% 0.63/0.65 ((~hskp13) | c0_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.63/0.65 tff(45,plain,
% 0.63/0.65 ((~hskp13) | c0_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[44, 42])).
% 0.63/0.65 tff(46,plain,
% 0.63/0.65 ((~hskp13) | c0_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[45, 42])).
% 0.63/0.65 tff(47,plain,
% 0.63/0.65 ((~hskp13) | c0_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.63/0.65 tff(48,plain,
% 0.63/0.65 ((~hskp13) | c0_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[47, 42])).
% 0.63/0.65 tff(49,plain,
% 0.63/0.65 ((~hskp13) | c0_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[48, 42])).
% 0.63/0.65 tff(50,plain,
% 0.63/0.65 ((~hskp13) | c0_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.63/0.65 tff(51,plain,
% 0.63/0.65 ((~hskp13) | c0_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[50, 42])).
% 0.63/0.65 tff(52,plain,
% 0.63/0.65 (c0_1(a112)),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[51, 35])).
% 0.63/0.65 tff(53,plain,
% 0.63/0.65 (((~hskp13) | c3_1(a112)) <=> ((~hskp13) | c3_1(a112))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(54,axiom,((~hskp13) | c3_1(a112)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.63/0.65 tff(55,plain,
% 0.63/0.65 ((~hskp13) | c3_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.63/0.65 tff(56,plain,
% 0.63/0.65 ((~hskp13) | c3_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[55, 53])).
% 0.63/0.65 tff(57,plain,
% 0.63/0.65 ((~hskp13) | c3_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[56, 53])).
% 0.63/0.65 tff(58,plain,
% 0.63/0.65 ((~hskp13) | c3_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.63/0.65 tff(59,plain,
% 0.63/0.65 ((~hskp13) | c3_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[58, 53])).
% 0.63/0.65 tff(60,plain,
% 0.63/0.65 ((~hskp13) | c3_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[59, 53])).
% 0.63/0.65 tff(61,plain,
% 0.63/0.65 ((~hskp13) | c3_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.63/0.65 tff(62,plain,
% 0.63/0.65 ((~hskp13) | c3_1(a112)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[61, 53])).
% 0.63/0.65 tff(63,plain,
% 0.63/0.65 (c3_1(a112)),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[62, 35])).
% 0.63/0.65 tff(64,plain,
% 0.63/0.65 (^[U: $i] : refl((hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(65,plain,
% 0.63/0.65 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.65 inference(quant_intro,[status(thm)],[64])).
% 0.63/0.65 tff(66,plain,
% 0.63/0.65 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(67,plain,
% 0.63/0.65 (^[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)) | hskp14) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp10) <=> ((hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp14 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp10) <=> (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(68,plain,
% 0.63/0.65 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp10) <=> ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.65 inference(quant_intro,[status(thm)],[67])).
% 0.63/0.65 tff(69,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 0.63/0.65 tff(70,plain,
% 0.63/0.65 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.63/0.65 tff(71,plain,
% 0.63/0.65 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.63/0.65 tff(72,plain,(
% 0.63/0.65 ![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.65 inference(skolemize,[status(sab)],[71])).
% 0.63/0.65 tff(73,plain,
% 0.63/0.65 (![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.63/0.65 tff(74,assumption,(~c1_1(a112)), introduced(assumption)).
% 0.63/0.65 tff(75,assumption,(c3_1(a112)), introduced(assumption)).
% 0.63/0.65 tff(76,assumption,(c0_1(a112)), introduced(assumption)).
% 0.63/0.65 tff(77,assumption,(~ndr1_0), introduced(assumption)).
% 0.63/0.65 tff(78,plain,
% 0.63/0.65 ((ndr1_0 | (~hskp0)) <=> (ndr1_0 | (~hskp0))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(79,plain,
% 0.63/0.65 (((~hskp0) | ndr1_0) <=> (ndr1_0 | (~hskp0))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(80,axiom,((~hskp0) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause30')).
% 0.63/0.65 tff(81,plain,
% 0.63/0.65 (ndr1_0 | (~hskp0)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.63/0.65 tff(82,plain,
% 0.63/0.65 (ndr1_0 | (~hskp0)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.63/0.65 tff(83,plain,
% 0.63/0.65 (~hskp0),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[82, 77])).
% 0.63/0.65 tff(84,plain,
% 0.63/0.65 (((~hskp29) | ndr1_0) <=> ((~hskp29) | ndr1_0)),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(85,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.63/0.65 tff(86,plain,
% 0.63/0.65 ((~hskp29) | ndr1_0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.63/0.65 tff(87,plain,
% 0.63/0.65 ((~hskp29) | ndr1_0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[86, 84])).
% 0.63/0.65 tff(88,plain,
% 0.63/0.65 ((~hskp29) | ndr1_0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[87, 84])).
% 0.63/0.65 tff(89,plain,
% 0.63/0.65 ((~hskp29) | ndr1_0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.63/0.65 tff(90,plain,
% 0.63/0.65 ((~hskp29) | ndr1_0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[89, 84])).
% 0.63/0.65 tff(91,plain,
% 0.63/0.65 ((~hskp29) | ndr1_0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[90, 84])).
% 0.63/0.65 tff(92,plain,
% 0.63/0.65 ((~hskp29) | ndr1_0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.63/0.65 tff(93,plain,
% 0.63/0.65 ((~hskp29) | ndr1_0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[92, 84])).
% 0.63/0.65 tff(94,plain,
% 0.63/0.65 (~hskp29),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[93, 77])).
% 0.63/0.65 tff(95,plain,
% 0.63/0.65 ((ndr1_0 | (~hskp20)) <=> (ndr1_0 | (~hskp20))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(96,plain,
% 0.63/0.65 (((~hskp20) | ndr1_0) <=> (ndr1_0 | (~hskp20))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(97,axiom,((~hskp20) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause10')).
% 0.63/0.65 tff(98,plain,
% 0.63/0.65 (ndr1_0 | (~hskp20)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.63/0.65 tff(99,plain,
% 0.63/0.65 (ndr1_0 | (~hskp20)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[98, 95])).
% 0.63/0.65 tff(100,plain,
% 0.63/0.65 (~hskp20),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[99, 77])).
% 0.63/0.65 tff(101,plain,
% 0.63/0.65 ((hskp29 | hskp20 | hskp0) <=> (hskp29 | hskp20 | hskp0)),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(102,plain,
% 0.63/0.65 (((hskp20 | hskp29) | hskp0) <=> (hskp29 | hskp20 | hskp0)),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(103,axiom,((hskp20 | hskp29) | hskp0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 0.63/0.65 tff(104,plain,
% 0.63/0.65 (hskp29 | hskp20 | hskp0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.63/0.65 tff(105,plain,
% 0.63/0.65 (hskp29 | hskp20 | hskp0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[104, 101])).
% 0.63/0.65 tff(106,plain,
% 0.63/0.65 (hskp29 | hskp20 | hskp0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.63/0.65 tff(107,plain,
% 0.63/0.65 (hskp29 | hskp20 | hskp0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[106, 101])).
% 0.63/0.65 tff(108,plain,
% 0.63/0.65 (hskp29 | hskp20 | hskp0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[107, 101])).
% 0.63/0.65 tff(109,plain,
% 0.63/0.65 (hskp29 | hskp20 | hskp0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.63/0.65 tff(110,plain,
% 0.63/0.65 (hskp29 | hskp20 | hskp0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[109, 101])).
% 0.63/0.65 tff(111,plain,
% 0.63/0.65 (hskp29 | hskp20 | hskp0),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[110, 101])).
% 0.63/0.65 tff(112,plain,
% 0.63/0.65 ($false),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[111, 100, 94, 83])).
% 0.63/0.65 tff(113,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.63/0.65 tff(114,plain,
% 0.63/0.65 (((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | c1_1(a112) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)))) <=> ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp14 | hskp10 | c1_1(a112) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(115,plain,
% 0.63/0.65 ((hskp14 | hskp10 | (~ndr1_0) | c1_1(a112) | (~c3_1(a112)) | (~c0_1(a112))) <=> (hskp14 | hskp10 | c1_1(a112) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(116,plain,
% 0.63/0.65 (((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | c1_1(a112) | (~c3_1(a112)) | (~c0_1(a112)))) <=> ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | c1_1(a112) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112))))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[115])).
% 0.63/0.65 tff(117,plain,
% 0.63/0.65 (((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | c1_1(a112) | (~c3_1(a112)) | (~c0_1(a112)))) <=> ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp14 | hskp10 | c1_1(a112) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)))),
% 0.63/0.65 inference(transitivity,[status(thm)],[116, 114])).
% 0.63/0.65 tff(118,plain,
% 0.63/0.65 ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp14 | hskp10 | (~ndr1_0) | c1_1(a112) | (~c3_1(a112)) | (~c0_1(a112)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(119,plain,
% 0.63/0.65 ((~![U: $i] : (hskp14 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp14 | hskp10 | c1_1(a112) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.63/0.65 tff(120,plain,
% 0.63/0.65 (hskp14 | hskp10),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[119, 113, 76, 75, 74, 73])).
% 0.63/0.65 tff(121,plain,
% 0.63/0.65 (hskp14),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[120, 34])).
% 0.63/0.65 tff(122,plain,
% 0.63/0.65 (((~hskp14) | (~c3_1(a115))) <=> ((~hskp14) | (~c3_1(a115)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(123,plain,
% 0.63/0.65 (((~c3_1(a115)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a115)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(124,axiom,((~c3_1(a115)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.63/0.65 tff(125,plain,
% 0.63/0.65 ((~hskp14) | (~c3_1(a115))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.63/0.65 tff(126,plain,
% 0.63/0.65 ((~hskp14) | (~c3_1(a115))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[125, 122])).
% 0.63/0.65 tff(127,plain,
% 0.63/0.65 (~c3_1(a115)),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[126, 121])).
% 0.63/0.65 tff(128,plain,
% 0.63/0.65 (((~hskp14) | (~c2_1(a115))) <=> ((~hskp14) | (~c2_1(a115)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(129,plain,
% 0.63/0.65 (((~c2_1(a115)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a115)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(130,axiom,((~c2_1(a115)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.63/0.65 tff(131,plain,
% 0.63/0.65 ((~hskp14) | (~c2_1(a115))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.63/0.65 tff(132,plain,
% 0.63/0.65 ((~hskp14) | (~c2_1(a115))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[131, 128])).
% 0.63/0.65 tff(133,plain,
% 0.63/0.65 (~c2_1(a115)),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[132, 121])).
% 0.63/0.65 tff(134,plain,
% 0.63/0.65 (((~hskp14) | c0_1(a115)) <=> ((~hskp14) | c0_1(a115))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(135,axiom,((~hskp14) | c0_1(a115)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.63/0.65 tff(136,plain,
% 0.63/0.65 ((~hskp14) | c0_1(a115)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.63/0.65 tff(137,plain,
% 0.63/0.65 ((~hskp14) | c0_1(a115)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[136, 134])).
% 0.63/0.65 tff(138,plain,
% 0.63/0.65 ((~hskp14) | c0_1(a115)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[137, 134])).
% 0.63/0.65 tff(139,plain,
% 0.63/0.65 ((~hskp14) | c0_1(a115)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.63/0.65 tff(140,plain,
% 0.63/0.65 ((~hskp14) | c0_1(a115)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[139, 134])).
% 0.63/0.65 tff(141,plain,
% 0.63/0.65 ((~hskp14) | c0_1(a115)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[140, 134])).
% 0.63/0.65 tff(142,plain,
% 0.63/0.65 ((~hskp14) | c0_1(a115)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.63/0.65 tff(143,plain,
% 0.63/0.65 ((~hskp14) | c0_1(a115)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[142, 134])).
% 0.63/0.65 tff(144,plain,
% 0.63/0.65 (c0_1(a115)),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[143, 121])).
% 0.63/0.65 tff(145,plain,
% 0.63/0.65 (((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp20 | hskp10 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c0_1(a115)))) <=> ((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp20 | hskp10 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c0_1(a115)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(146,plain,
% 0.63/0.65 ((hskp20 | hskp10 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | (~c0_1(a115))) <=> (hskp20 | hskp10 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c0_1(a115)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(147,plain,
% 0.63/0.65 (((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp20 | hskp10 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | (~c0_1(a115)))) <=> ((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp20 | hskp10 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c0_1(a115))))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[146])).
% 0.63/0.65 tff(148,plain,
% 0.63/0.65 (((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp20 | hskp10 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | (~c0_1(a115)))) <=> ((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp20 | hskp10 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c0_1(a115)))),
% 0.63/0.65 inference(transitivity,[status(thm)],[147, 145])).
% 0.63/0.65 tff(149,plain,
% 0.63/0.65 ((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp20 | hskp10 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | (~c0_1(a115)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(150,plain,
% 0.63/0.65 ((~![U: $i] : (hskp20 | hskp10 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp20 | hskp10 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c0_1(a115))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.63/0.65 tff(151,plain,
% 0.63/0.65 ($false),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[150, 113, 22, 34, 144, 133, 127, 33])).
% 0.63/0.65 tff(152,plain,(hskp10 | hskp20 | (~c0_1(a112)) | (~c3_1(a112)) | c1_1(a112)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.65 tff(153,plain,
% 0.63/0.65 ($false),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[152, 63, 52, 22, 34, 41])).
% 0.63/0.65 tff(154,plain,((~hskp13) | hskp20 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.63/0.65 tff(155,plain,
% 0.63/0.65 (~hskp13),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[154, 34, 22])).
% 0.63/0.65 tff(156,plain,
% 0.63/0.65 (^[U: $i] : refl((hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(157,plain,
% 0.63/0.65 (![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.63/0.65 inference(quant_intro,[status(thm)],[156])).
% 0.63/0.65 tff(158,plain,
% 0.63/0.65 (![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(159,plain,
% 0.63/0.65 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(160,plain,
% 0.63/0.65 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13) <=> ![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.63/0.65 inference(quant_intro,[status(thm)],[159])).
% 0.63/0.65 tff(161,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.63/0.65 tff(162,plain,
% 0.63/0.65 (![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.63/0.65 tff(163,plain,
% 0.63/0.65 (![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.63/0.65 tff(164,plain,(
% 0.63/0.65 ![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.63/0.65 inference(skolemize,[status(sab)],[163])).
% 0.63/0.65 tff(165,plain,
% 0.63/0.65 (![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.63/0.65 tff(166,assumption,(hskp1), introduced(assumption)).
% 0.63/0.65 tff(167,plain,
% 0.63/0.65 (((~hskp1) | (~c1_1(a97))) <=> ((~hskp1) | (~c1_1(a97)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(168,plain,
% 0.63/0.65 (((~c1_1(a97)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a97)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(169,axiom,((~c1_1(a97)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.63/0.65 tff(170,plain,
% 0.63/0.65 ((~hskp1) | (~c1_1(a97))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.63/0.65 tff(171,plain,
% 0.63/0.65 ((~hskp1) | (~c1_1(a97))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[170, 167])).
% 0.63/0.65 tff(172,plain,
% 0.63/0.65 (~c1_1(a97)),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[171, 166])).
% 0.63/0.65 tff(173,plain,
% 0.63/0.65 (((~hskp1) | c3_1(a97)) <=> ((~hskp1) | c3_1(a97))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(174,axiom,((~hskp1) | c3_1(a97)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.63/0.65 tff(175,plain,
% 0.63/0.65 ((~hskp1) | c3_1(a97)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.63/0.65 tff(176,plain,
% 0.63/0.65 ((~hskp1) | c3_1(a97)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[175, 173])).
% 0.63/0.65 tff(177,plain,
% 0.63/0.65 ((~hskp1) | c3_1(a97)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[176, 173])).
% 0.63/0.65 tff(178,plain,
% 0.63/0.65 ((~hskp1) | c3_1(a97)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.63/0.65 tff(179,plain,
% 0.63/0.65 ((~hskp1) | c3_1(a97)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[178, 173])).
% 0.63/0.65 tff(180,plain,
% 0.63/0.65 ((~hskp1) | c3_1(a97)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[179, 173])).
% 0.63/0.65 tff(181,plain,
% 0.63/0.65 ((~hskp1) | c3_1(a97)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.63/0.65 tff(182,plain,
% 0.63/0.65 ((~hskp1) | c3_1(a97)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[181, 173])).
% 0.63/0.65 tff(183,plain,
% 0.63/0.65 (c3_1(a97)),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[182, 166])).
% 0.63/0.65 tff(184,plain,
% 0.63/0.65 (((~hskp1) | c2_1(a97)) <=> ((~hskp1) | c2_1(a97))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(185,axiom,((~hskp1) | c2_1(a97)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.63/0.66 tff(186,plain,
% 0.63/0.66 ((~hskp1) | c2_1(a97)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.63/0.66 tff(187,plain,
% 0.63/0.66 ((~hskp1) | c2_1(a97)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[186, 184])).
% 0.63/0.66 tff(188,plain,
% 0.63/0.66 ((~hskp1) | c2_1(a97)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[187, 184])).
% 0.63/0.66 tff(189,plain,
% 0.63/0.66 ((~hskp1) | c2_1(a97)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.63/0.66 tff(190,plain,
% 0.63/0.66 ((~hskp1) | c2_1(a97)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[189, 184])).
% 0.63/0.66 tff(191,plain,
% 0.63/0.66 ((~hskp1) | c2_1(a97)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[190, 184])).
% 0.63/0.66 tff(192,plain,
% 0.63/0.66 ((~hskp1) | c2_1(a97)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.63/0.66 tff(193,plain,
% 0.63/0.66 ((~hskp1) | c2_1(a97)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[192, 184])).
% 0.63/0.66 tff(194,plain,
% 0.63/0.66 (c2_1(a97)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[193, 166])).
% 0.63/0.66 tff(195,assumption,(~hskp13), introduced(assumption)).
% 0.63/0.66 tff(196,plain,
% 0.63/0.66 (((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | c1_1(a97) | (~ndr1_0) | (~c2_1(a97)) | (~c3_1(a97)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | c1_1(a97) | (~ndr1_0) | (~c2_1(a97)) | (~c3_1(a97)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(197,plain,
% 0.63/0.66 ((hskp13 | (~ndr1_0) | c1_1(a97) | (~c3_1(a97)) | (~c2_1(a97))) <=> (hskp13 | c1_1(a97) | (~ndr1_0) | (~c2_1(a97)) | (~c3_1(a97)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(198,plain,
% 0.63/0.66 (((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | (~ndr1_0) | c1_1(a97) | (~c3_1(a97)) | (~c2_1(a97)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | c1_1(a97) | (~ndr1_0) | (~c2_1(a97)) | (~c3_1(a97))))),
% 0.63/0.66 inference(monotonicity,[status(thm)],[197])).
% 0.63/0.66 tff(199,plain,
% 0.63/0.66 (((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | (~ndr1_0) | c1_1(a97) | (~c3_1(a97)) | (~c2_1(a97)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | c1_1(a97) | (~ndr1_0) | (~c2_1(a97)) | (~c3_1(a97)))),
% 0.63/0.66 inference(transitivity,[status(thm)],[198, 196])).
% 0.63/0.66 tff(200,plain,
% 0.63/0.66 ((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp13 | (~ndr1_0) | c1_1(a97) | (~c3_1(a97)) | (~c2_1(a97)))),
% 0.63/0.66 inference(quant_inst,[status(thm)],[])).
% 0.63/0.66 tff(201,plain,
% 0.63/0.66 ((~![U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp13 | c1_1(a97) | (~ndr1_0) | (~c2_1(a97)) | (~c3_1(a97))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.63/0.66 tff(202,plain,
% 0.63/0.66 ($false),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[201, 113, 195, 194, 183, 172, 165])).
% 0.63/0.66 tff(203,plain,((~hskp1) | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.63/0.66 tff(204,plain,
% 0.63/0.66 (~hskp1),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[203, 155])).
% 0.63/0.66 tff(205,plain,
% 0.63/0.66 ((hskp14 | hskp3 | hskp1) <=> (hskp14 | hskp3 | hskp1)),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(206,plain,
% 0.63/0.66 (((hskp14 | hskp1) | hskp3) <=> (hskp14 | hskp3 | hskp1)),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(207,plain,
% 0.63/0.66 ((hskp14 | hskp1) <=> (hskp14 | hskp1)),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(208,plain,
% 0.63/0.66 (((hskp14 | hskp1) | hskp3) <=> ((hskp14 | hskp1) | hskp3)),
% 0.63/0.66 inference(monotonicity,[status(thm)],[207])).
% 0.63/0.66 tff(209,plain,
% 0.63/0.66 (((hskp14 | hskp1) | hskp3) <=> (hskp14 | hskp3 | hskp1)),
% 0.63/0.66 inference(transitivity,[status(thm)],[208, 206])).
% 0.63/0.66 tff(210,axiom,((hskp14 | hskp1) | hskp3), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 0.63/0.66 tff(211,plain,
% 0.63/0.66 (hskp14 | hskp3 | hskp1),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.63/0.66 tff(212,plain,
% 0.63/0.66 (hskp14 | hskp3 | hskp1),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[211, 205])).
% 0.63/0.66 tff(213,plain,
% 0.63/0.66 (hskp14 | hskp3 | hskp1),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[212, 205])).
% 0.63/0.66 tff(214,plain,
% 0.63/0.66 (hskp14 | hskp3 | hskp1),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[213, 205])).
% 0.63/0.66 tff(215,plain,
% 0.63/0.66 (hskp14 | hskp3 | hskp1),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[214, 205])).
% 0.63/0.66 tff(216,plain,
% 0.63/0.66 (hskp14 | hskp3 | hskp1),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[215, 205])).
% 0.63/0.66 tff(217,plain,
% 0.63/0.66 (hskp14 | hskp3 | hskp1),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[216, 205])).
% 0.63/0.66 tff(218,plain,
% 0.63/0.66 (hskp14 | hskp3 | hskp1),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[217, 205])).
% 0.63/0.66 tff(219,plain,
% 0.63/0.66 (hskp14),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[218, 204, 23])).
% 0.63/0.66 tff(220,plain,
% 0.63/0.66 (~c3_1(a115)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[126, 219])).
% 0.63/0.66 tff(221,plain,
% 0.63/0.66 (~c2_1(a115)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[132, 219])).
% 0.63/0.66 tff(222,plain,
% 0.63/0.66 (c0_1(a115)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[143, 219])).
% 0.63/0.66 tff(223,plain,
% 0.63/0.66 ($false),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[150, 113, 22, 34, 222, 221, 220, 33])).
% 0.63/0.66 tff(224,plain,(hskp10 | hskp20 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.63/0.66 tff(225,plain,
% 0.63/0.66 (hskp10),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[224, 23, 22])).
% 0.63/0.66 tff(226,plain,
% 0.63/0.66 (((~hskp10) | c1_1(a106)) <=> ((~hskp10) | c1_1(a106))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(227,axiom,((~hskp10) | c1_1(a106)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.63/0.66 tff(228,plain,
% 0.63/0.66 ((~hskp10) | c1_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.63/0.66 tff(229,plain,
% 0.63/0.66 ((~hskp10) | c1_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[228, 226])).
% 0.63/0.66 tff(230,plain,
% 0.63/0.66 ((~hskp10) | c1_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[229, 226])).
% 0.63/0.66 tff(231,plain,
% 0.63/0.66 ((~hskp10) | c1_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.63/0.66 tff(232,plain,
% 0.63/0.66 ((~hskp10) | c1_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[231, 226])).
% 0.63/0.66 tff(233,plain,
% 0.63/0.66 ((~hskp10) | c1_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[232, 226])).
% 0.63/0.66 tff(234,plain,
% 0.63/0.66 ((~hskp10) | c1_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.63/0.66 tff(235,plain,
% 0.63/0.66 ((~hskp10) | c1_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[234, 226])).
% 0.63/0.66 tff(236,plain,
% 0.63/0.66 (c1_1(a106)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[235, 225])).
% 0.63/0.66 tff(237,plain,
% 0.63/0.66 (((~hskp10) | (~c2_1(a106))) <=> ((~hskp10) | (~c2_1(a106)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(238,plain,
% 0.63/0.66 (((~c2_1(a106)) | (~hskp10)) <=> ((~hskp10) | (~c2_1(a106)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(239,axiom,((~c2_1(a106)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 0.63/0.66 tff(240,plain,
% 0.63/0.66 ((~hskp10) | (~c2_1(a106))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.63/0.66 tff(241,plain,
% 0.63/0.66 ((~hskp10) | (~c2_1(a106))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[240, 237])).
% 0.63/0.66 tff(242,plain,
% 0.63/0.66 (~c2_1(a106)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[241, 225])).
% 0.63/0.66 tff(243,plain,
% 0.63/0.66 (^[U: $i] : refl((hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 0.63/0.66 inference(bind,[status(th)],[])).
% 0.63/0.66 tff(244,plain,
% 0.63/0.66 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.63/0.66 inference(quant_intro,[status(thm)],[243])).
% 0.63/0.66 tff(245,plain,
% 0.63/0.66 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(246,plain,
% 0.63/0.66 (^[U: $i] : 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) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 0.63/0.66 inference(bind,[status(th)],[])).
% 0.63/0.66 tff(247,plain,
% 0.63/0.66 (![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1) <=> ![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.63/0.66 inference(quant_intro,[status(thm)],[246])).
% 0.63/0.66 tff(248,axiom,(![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.63/0.66 tff(249,plain,
% 0.63/0.66 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.63/0.66 tff(250,plain,
% 0.63/0.66 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[249, 245])).
% 0.63/0.66 tff(251,plain,(
% 0.63/0.66 ![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.63/0.66 inference(skolemize,[status(sab)],[250])).
% 0.63/0.66 tff(252,plain,
% 0.63/0.66 (![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[251, 244])).
% 0.63/0.66 tff(253,assumption,(hskp0), introduced(assumption)).
% 0.63/0.66 tff(254,plain,
% 0.63/0.66 (((~hskp0) | (~c3_1(a96))) <=> ((~hskp0) | (~c3_1(a96)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(255,plain,
% 0.63/0.66 (((~c3_1(a96)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a96)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(256,axiom,((~c3_1(a96)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.63/0.66 tff(257,plain,
% 0.63/0.66 ((~hskp0) | (~c3_1(a96))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.63/0.66 tff(258,plain,
% 0.63/0.66 ((~hskp0) | (~c3_1(a96))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[257, 254])).
% 0.63/0.66 tff(259,plain,
% 0.63/0.66 (~c3_1(a96)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[258, 253])).
% 0.63/0.66 tff(260,plain,
% 0.63/0.66 (((~hskp0) | (~c2_1(a96))) <=> ((~hskp0) | (~c2_1(a96)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(261,plain,
% 0.63/0.66 (((~c2_1(a96)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a96)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(262,axiom,((~c2_1(a96)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.63/0.66 tff(263,plain,
% 0.63/0.66 ((~hskp0) | (~c2_1(a96))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.63/0.66 tff(264,plain,
% 0.63/0.66 ((~hskp0) | (~c2_1(a96))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[263, 260])).
% 0.63/0.66 tff(265,plain,
% 0.63/0.66 (~c2_1(a96)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[264, 253])).
% 0.63/0.66 tff(266,plain,
% 0.63/0.66 (((~hskp0) | (~c1_1(a96))) <=> ((~hskp0) | (~c1_1(a96)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(267,plain,
% 0.63/0.66 (((~c1_1(a96)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a96)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(268,axiom,((~c1_1(a96)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.63/0.66 tff(269,plain,
% 0.63/0.66 ((~hskp0) | (~c1_1(a96))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.63/0.66 tff(270,plain,
% 0.63/0.66 ((~hskp0) | (~c1_1(a96))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[269, 266])).
% 0.63/0.66 tff(271,plain,
% 0.63/0.66 (~c1_1(a96)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[270, 253])).
% 0.63/0.66 tff(272,plain,
% 0.63/0.66 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp1 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(273,plain,
% 0.63/0.66 ((hskp1 | (~ndr1_0) | c3_1(a96) | c2_1(a96) | c1_1(a96)) <=> (hskp1 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(274,plain,
% 0.63/0.66 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a96) | c2_1(a96) | c1_1(a96))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0)))),
% 0.63/0.66 inference(monotonicity,[status(thm)],[273])).
% 0.63/0.66 tff(275,plain,
% 0.63/0.66 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a96) | c2_1(a96) | c1_1(a96))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp1 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0))),
% 0.63/0.66 inference(transitivity,[status(thm)],[274, 272])).
% 0.63/0.66 tff(276,plain,
% 0.63/0.66 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a96) | c2_1(a96) | c1_1(a96))),
% 0.63/0.66 inference(quant_inst,[status(thm)],[])).
% 0.63/0.66 tff(277,plain,
% 0.63/0.66 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp1 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.63/0.66 tff(278,plain,
% 0.63/0.66 (hskp1),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[277, 113, 271, 265, 259, 252])).
% 0.63/0.66 tff(279,plain,
% 0.63/0.66 (~c1_1(a97)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[171, 278])).
% 0.63/0.66 tff(280,plain,
% 0.63/0.66 (c3_1(a97)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[182, 278])).
% 0.63/0.66 tff(281,plain,
% 0.63/0.66 (c2_1(a97)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[193, 278])).
% 0.63/0.66 tff(282,plain,
% 0.63/0.66 (hskp13),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[201, 113, 281, 280, 279, 165])).
% 0.63/0.66 tff(283,plain,
% 0.63/0.66 (~c1_1(a112)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[40, 282])).
% 0.63/0.66 tff(284,plain,
% 0.63/0.66 (c3_1(a112)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[62, 282])).
% 0.63/0.66 tff(285,plain,
% 0.63/0.66 (c0_1(a112)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[51, 282])).
% 0.63/0.66 tff(286,plain,
% 0.63/0.66 (hskp10),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[152, 285, 22, 284, 283])).
% 0.63/0.66 tff(287,plain,
% 0.63/0.66 (~c2_1(a106)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[241, 286])).
% 0.63/0.66 tff(288,plain,
% 0.63/0.66 (((~hskp10) | c3_1(a106)) <=> ((~hskp10) | c3_1(a106))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(289,axiom,((~hskp10) | c3_1(a106)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.63/0.66 tff(290,plain,
% 0.63/0.66 ((~hskp10) | c3_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.63/0.66 tff(291,plain,
% 0.63/0.66 ((~hskp10) | c3_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[290, 288])).
% 0.63/0.66 tff(292,plain,
% 0.63/0.66 ((~hskp10) | c3_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[291, 288])).
% 0.63/0.66 tff(293,plain,
% 0.63/0.66 ((~hskp10) | c3_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[292, 288])).
% 0.63/0.66 tff(294,plain,
% 0.63/0.66 ((~hskp10) | c3_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[293, 288])).
% 0.63/0.66 tff(295,plain,
% 0.63/0.66 ((~hskp10) | c3_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[294, 288])).
% 0.63/0.66 tff(296,plain,
% 0.63/0.66 ((~hskp10) | c3_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[295, 288])).
% 0.63/0.66 tff(297,plain,
% 0.63/0.66 ((~hskp10) | c3_1(a106)),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[296, 288])).
% 0.63/0.66 tff(298,plain,
% 0.63/0.66 (c3_1(a106)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[297, 286])).
% 0.63/0.66 tff(299,plain,
% 0.63/0.66 (c1_1(a106)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[235, 286])).
% 0.63/0.66 tff(300,plain,
% 0.63/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a106)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(301,plain,
% 0.63/0.66 (((~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a106) | (~c0_1(a106)) | (~c1_1(a106))) <=> (c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a106)))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(302,plain,
% 0.63/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a106) | (~c0_1(a106)) | (~c1_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a106))))),
% 0.63/0.66 inference(monotonicity,[status(thm)],[301])).
% 0.63/0.66 tff(303,plain,
% 0.63/0.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a106) | (~c0_1(a106)) | (~c1_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a106)))),
% 0.63/0.66 inference(transitivity,[status(thm)],[302, 300])).
% 0.63/0.66 tff(304,plain,
% 0.63/0.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a106)) | (~c0_1(a106)) | (~c1_1(a106)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a106) | (~c0_1(a106)) | (~c1_1(a106)))),
% 0.63/0.66 inference(quant_inst,[status(thm)],[])).
% 0.63/0.66 tff(305,plain,
% 0.63/0.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a106) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a106))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.63/0.66 tff(306,plain,
% 0.63/0.66 (~c0_1(a106)),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[305, 113, 299, 298, 287, 11])).
% 0.63/0.66 tff(307,plain,
% 0.63/0.66 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.63/0.66 inference(bind,[status(th)],[])).
% 0.63/0.66 tff(308,plain,
% 0.63/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.66 inference(quant_intro,[status(thm)],[307])).
% 0.63/0.66 tff(309,plain,
% 0.63/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(310,plain,
% 0.63/0.66 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.63/0.66 inference(bind,[status(th)],[])).
% 0.63/0.66 tff(311,plain,
% 0.63/0.66 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.66 inference(quant_intro,[status(thm)],[310])).
% 0.63/0.66 tff(312,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.63/0.66 tff(313,plain,
% 0.63/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.63/0.66 tff(314,plain,
% 0.63/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[313, 309])).
% 0.63/0.66 tff(315,plain,(
% 0.63/0.66 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.66 inference(skolemize,[status(sab)],[314])).
% 0.63/0.66 tff(316,plain,
% 0.63/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[315, 308])).
% 0.63/0.66 tff(317,plain,
% 0.63/0.66 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))),
% 0.63/0.66 inference(bind,[status(th)],[])).
% 0.63/0.66 tff(318,plain,
% 0.63/0.66 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.63/0.66 inference(quant_intro,[status(thm)],[317])).
% 0.63/0.66 tff(319,plain,
% 0.63/0.66 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(320,plain,
% 0.63/0.66 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp3))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))))),
% 0.63/0.66 inference(bind,[status(th)],[])).
% 0.63/0.66 tff(321,plain,
% 0.63/0.66 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.63/0.66 inference(quant_intro,[status(thm)],[320])).
% 0.63/0.66 tff(322,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 0.63/0.66 tff(323,plain,
% 0.63/0.66 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.63/0.67 tff(324,plain,
% 0.63/0.67 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[323, 319])).
% 0.63/0.67 tff(325,plain,(
% 0.63/0.67 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.63/0.67 inference(skolemize,[status(sab)],[324])).
% 0.63/0.67 tff(326,plain,
% 0.63/0.67 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[325, 318])).
% 0.63/0.67 tff(327,assumption,(~c3_1(a96)), introduced(assumption)).
% 0.63/0.67 tff(328,assumption,(~c2_1(a96)), introduced(assumption)).
% 0.63/0.67 tff(329,assumption,(~c1_1(a96)), introduced(assumption)).
% 0.63/0.67 tff(330,plain,
% 0.63/0.67 (hskp1),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[277, 113, 329, 328, 327, 252])).
% 0.63/0.67 tff(331,plain,
% 0.63/0.67 (~c1_1(a97)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[171, 330])).
% 0.63/0.67 tff(332,plain,
% 0.63/0.67 (c3_1(a97)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[182, 330])).
% 0.63/0.67 tff(333,plain,
% 0.63/0.67 (c2_1(a97)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[193, 330])).
% 0.63/0.67 tff(334,plain,
% 0.63/0.67 (hskp13),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[201, 113, 333, 332, 331, 165])).
% 0.63/0.67 tff(335,plain,
% 0.63/0.67 (c3_1(a112)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[62, 334])).
% 0.63/0.67 tff(336,plain,
% 0.63/0.67 (c0_1(a112)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[51, 334])).
% 0.63/0.67 tff(337,plain,
% 0.63/0.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)) | (~c2_1(a112)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)) | (~c2_1(a112)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(338,plain,
% 0.63/0.67 ((hskp3 | (~ndr1_0) | (~c3_1(a112)) | (~c2_1(a112)) | (~c0_1(a112)) | c3_1(a96) | c2_1(a96) | c1_1(a96)) <=> (hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)) | (~c2_1(a112)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(339,plain,
% 0.63/0.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a112)) | (~c2_1(a112)) | (~c0_1(a112)) | c3_1(a96) | c2_1(a96) | c1_1(a96))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)) | (~c2_1(a112))))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[338])).
% 0.63/0.67 tff(340,plain,
% 0.63/0.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a112)) | (~c2_1(a112)) | (~c0_1(a112)) | c3_1(a96) | c2_1(a96) | c1_1(a96))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)) | (~c2_1(a112)))),
% 0.63/0.67 inference(transitivity,[status(thm)],[339, 337])).
% 0.63/0.67 tff(341,plain,
% 0.63/0.67 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a112)) | (~c2_1(a112)) | (~c0_1(a112)) | c3_1(a96) | c2_1(a96) | c1_1(a96))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(342,plain,
% 0.63/0.67 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a112)) | (~c3_1(a112)) | (~c2_1(a112))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.63/0.67 tff(343,plain,
% 0.63/0.67 (hskp3 | (~c2_1(a112))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[342, 113, 336, 335, 329, 328, 327, 326])).
% 0.63/0.67 tff(344,plain,
% 0.63/0.67 (~c2_1(a112)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[343, 23])).
% 0.63/0.67 tff(345,plain,
% 0.63/0.67 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.63/0.67 inference(bind,[status(th)],[])).
% 0.63/0.67 tff(346,plain,
% 0.63/0.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.67 inference(quant_intro,[status(thm)],[345])).
% 0.63/0.67 tff(347,plain,
% 0.63/0.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(348,plain,
% 0.63/0.67 (^[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)) | (~c0_1(V)) | (~c3_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))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.63/0.67 inference(bind,[status(th)],[])).
% 0.63/0.67 tff(349,plain,
% 0.63/0.67 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.67 inference(quant_intro,[status(thm)],[348])).
% 0.63/0.67 tff(350,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 0.63/0.67 tff(351,plain,
% 0.63/0.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.63/0.67 tff(352,plain,
% 0.63/0.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[351, 347])).
% 0.63/0.67 tff(353,plain,(
% 0.63/0.67 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.67 inference(skolemize,[status(sab)],[352])).
% 0.63/0.67 tff(354,plain,
% 0.63/0.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[353, 346])).
% 0.63/0.67 tff(355,assumption,(~hskp2), introduced(assumption)).
% 0.63/0.67 tff(356,plain,
% 0.63/0.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(357,plain,
% 0.63/0.67 ((hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c2_1(a96) | c1_1(a96)) <=> (hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(358,plain,
% 0.63/0.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c2_1(a96) | c1_1(a96))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97))))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[357])).
% 0.63/0.67 tff(359,plain,
% 0.63/0.67 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c2_1(a96) | c1_1(a96))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)))),
% 0.63/0.67 inference(transitivity,[status(thm)],[358, 356])).
% 0.63/0.67 tff(360,plain,
% 0.63/0.67 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c2_1(a96) | c1_1(a96))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(361,plain,
% 0.63/0.67 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c1_1(a96) | c2_1(a96) | c3_1(a96) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.63/0.67 tff(362,plain,
% 0.63/0.67 (hskp3 | (~c0_1(a97))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[361, 113, 333, 332, 329, 328, 327, 326])).
% 0.63/0.67 tff(363,plain,
% 0.63/0.67 (~c0_1(a97)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[362, 23])).
% 0.63/0.67 tff(364,plain,
% 0.63/0.67 (^[U: $i] : refl((hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 0.63/0.67 inference(bind,[status(th)],[])).
% 0.63/0.67 tff(365,plain,
% 0.63/0.67 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.67 inference(quant_intro,[status(thm)],[364])).
% 0.63/0.67 tff(366,plain,
% 0.63/0.67 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(367,plain,
% 0.63/0.67 (^[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)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3) <=> ((hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp3))), rewrite(((hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3) <=> (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 0.63/0.67 inference(bind,[status(th)],[])).
% 0.63/0.67 tff(368,plain,
% 0.63/0.67 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.67 inference(quant_intro,[status(thm)],[367])).
% 0.63/0.67 tff(369,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp2) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 0.63/0.67 tff(370,plain,
% 0.63/0.67 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.63/0.67 tff(371,plain,
% 0.63/0.67 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[370, 366])).
% 0.63/0.67 tff(372,plain,(
% 0.63/0.67 ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.67 inference(skolemize,[status(sab)],[371])).
% 0.63/0.67 tff(373,plain,
% 0.63/0.67 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[372, 365])).
% 0.63/0.67 tff(374,plain,
% 0.63/0.67 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp3 | hskp2 | c1_1(a97) | (~ndr1_0) | c0_1(a97) | (~c3_1(a97)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp3 | hskp2 | c1_1(a97) | (~ndr1_0) | c0_1(a97) | (~c3_1(a97)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(375,plain,
% 0.63/0.67 ((hskp3 | hskp2 | (~ndr1_0) | c1_1(a97) | c0_1(a97) | (~c3_1(a97))) <=> (hskp3 | hskp2 | c1_1(a97) | (~ndr1_0) | c0_1(a97) | (~c3_1(a97)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(376,plain,
% 0.63/0.67 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a97) | c0_1(a97) | (~c3_1(a97)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp3 | hskp2 | c1_1(a97) | (~ndr1_0) | c0_1(a97) | (~c3_1(a97))))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[375])).
% 0.63/0.67 tff(377,plain,
% 0.63/0.67 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a97) | c0_1(a97) | (~c3_1(a97)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp3 | hskp2 | c1_1(a97) | (~ndr1_0) | c0_1(a97) | (~c3_1(a97)))),
% 0.63/0.67 inference(transitivity,[status(thm)],[376, 374])).
% 0.63/0.67 tff(378,plain,
% 0.63/0.67 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c1_1(a97) | c0_1(a97) | (~c3_1(a97)))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(379,plain,
% 0.63/0.67 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp3 | hskp2 | c1_1(a97) | (~ndr1_0) | c0_1(a97) | (~c3_1(a97))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.63/0.67 tff(380,plain,
% 0.63/0.67 (hskp3 | hskp2 | c0_1(a97)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[379, 113, 332, 331, 373])).
% 0.63/0.67 tff(381,plain,
% 0.63/0.67 ($false),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[380, 363, 23, 355])).
% 0.63/0.67 tff(382,plain,(hskp3 | hskp2 | c1_1(a96) | c2_1(a96) | c3_1(a96)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.67 tff(383,plain,
% 0.63/0.67 (hskp2),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[382, 23, 329, 328, 327])).
% 0.63/0.67 tff(384,plain,
% 0.63/0.67 (((~hskp2) | (~c3_1(a98))) <=> ((~hskp2) | (~c3_1(a98)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(385,plain,
% 0.63/0.67 (((~c3_1(a98)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a98)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(386,axiom,((~c3_1(a98)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.63/0.67 tff(387,plain,
% 0.63/0.67 ((~hskp2) | (~c3_1(a98))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.63/0.67 tff(388,plain,
% 0.63/0.67 ((~hskp2) | (~c3_1(a98))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[387, 384])).
% 0.63/0.67 tff(389,plain,
% 0.63/0.67 (~c3_1(a98)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[388, 383])).
% 0.63/0.67 tff(390,plain,
% 0.63/0.67 (((~hskp2) | (~c0_1(a98))) <=> ((~hskp2) | (~c0_1(a98)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(391,plain,
% 0.63/0.67 (((~c0_1(a98)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a98)))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(392,axiom,((~c0_1(a98)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.63/0.67 tff(393,plain,
% 0.63/0.67 ((~hskp2) | (~c0_1(a98))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.63/0.67 tff(394,plain,
% 0.63/0.67 ((~hskp2) | (~c0_1(a98))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[393, 390])).
% 0.63/0.67 tff(395,plain,
% 0.63/0.67 (~c0_1(a98)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[394, 383])).
% 0.63/0.67 tff(396,assumption,(~c2_1(a106)), introduced(assumption)).
% 0.63/0.67 tff(397,plain,
% 0.63/0.67 (((~hskp2) | c1_1(a98)) <=> ((~hskp2) | c1_1(a98))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(398,axiom,((~hskp2) | c1_1(a98)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.63/0.67 tff(399,plain,
% 0.63/0.67 ((~hskp2) | c1_1(a98)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.63/0.67 tff(400,plain,
% 0.63/0.67 ((~hskp2) | c1_1(a98)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[399, 397])).
% 0.63/0.67 tff(401,plain,
% 0.63/0.67 ((~hskp2) | c1_1(a98)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[400, 397])).
% 0.63/0.67 tff(402,plain,
% 0.63/0.67 ((~hskp2) | c1_1(a98)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[401, 397])).
% 0.63/0.67 tff(403,plain,
% 0.63/0.67 ((~hskp2) | c1_1(a98)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[402, 397])).
% 0.63/0.67 tff(404,plain,
% 0.63/0.67 ((~hskp2) | c1_1(a98)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[403, 397])).
% 0.63/0.67 tff(405,plain,
% 0.63/0.67 ((~hskp2) | c1_1(a98)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[404, 397])).
% 0.63/0.67 tff(406,plain,
% 0.63/0.67 ((~hskp2) | c1_1(a98)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[405, 397])).
% 0.63/0.67 tff(407,plain,
% 0.63/0.67 (c1_1(a98)),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[406, 383])).
% 0.63/0.67 tff(408,assumption,(c3_1(a106)), introduced(assumption)).
% 0.63/0.67 tff(409,assumption,(c1_1(a106)), introduced(assumption)).
% 0.63/0.67 tff(410,plain,
% 0.63/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a106) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a112)) | (~c3_1(a112)) | c2_1(a112))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a106) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a112)) | (~c3_1(a112)) | c2_1(a112))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(411,plain,
% 0.63/0.67 (((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a112) | (~c0_1(a112)) | (~c3_1(a112)) | c3_1(a98) | c0_1(a98) | (~c1_1(a98))) <=> (c2_1(a106) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a112)) | (~c3_1(a112)) | c2_1(a112))),
% 0.63/0.67 inference(rewrite,[status(thm)],[])).
% 0.63/0.67 tff(412,plain,
% 0.63/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a112) | (~c0_1(a112)) | (~c3_1(a112)) | c3_1(a98) | c0_1(a98) | (~c1_1(a98)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a106) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a112)) | (~c3_1(a112)) | c2_1(a112)))),
% 0.63/0.67 inference(monotonicity,[status(thm)],[411])).
% 0.63/0.67 tff(413,plain,
% 0.63/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a112) | (~c0_1(a112)) | (~c3_1(a112)) | c3_1(a98) | c0_1(a98) | (~c1_1(a98)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a106) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a112)) | (~c3_1(a112)) | c2_1(a112))),
% 0.63/0.67 inference(transitivity,[status(thm)],[412, 410])).
% 0.63/0.67 tff(414,plain,
% 0.63/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a112) | (~c0_1(a112)) | (~c3_1(a112)) | c3_1(a98) | c0_1(a98) | (~c1_1(a98)))),
% 0.63/0.67 inference(quant_inst,[status(thm)],[])).
% 0.63/0.67 tff(415,plain,
% 0.63/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a106) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c0_1(a112)) | (~c3_1(a112)) | c2_1(a112)),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.63/0.67 tff(416,plain,
% 0.63/0.67 ($false),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[415, 113, 336, 335, 409, 408, 407, 396, 395, 389, 354, 344])).
% 0.68/0.68 tff(417,plain,(hskp3 | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a106) | c1_1(a96) | c2_1(a96) | c3_1(a96)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.68 tff(418,plain,
% 0.68/0.68 (hskp3),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[417, 299, 298, 287, 271, 265, 259])).
% 0.68/0.68 tff(419,plain,
% 0.68/0.68 (((~hskp3) | (~c3_1(a99))) <=> ((~hskp3) | (~c3_1(a99)))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(420,plain,
% 0.68/0.68 (((~c3_1(a99)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a99)))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(421,axiom,((~c3_1(a99)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.68/0.68 tff(422,plain,
% 0.68/0.68 ((~hskp3) | (~c3_1(a99))),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.68/0.68 tff(423,plain,
% 0.68/0.68 ((~hskp3) | (~c3_1(a99))),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[422, 419])).
% 0.68/0.68 tff(424,plain,
% 0.68/0.68 (~c3_1(a99)),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[423, 418])).
% 0.68/0.68 tff(425,plain,
% 0.68/0.68 (((~hskp3) | (~c1_1(a99))) <=> ((~hskp3) | (~c1_1(a99)))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(426,plain,
% 0.68/0.68 (((~c1_1(a99)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a99)))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(427,axiom,((~c1_1(a99)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.68/0.68 tff(428,plain,
% 0.68/0.68 ((~hskp3) | (~c1_1(a99))),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.68/0.68 tff(429,plain,
% 0.68/0.68 ((~hskp3) | (~c1_1(a99))),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[428, 425])).
% 0.68/0.68 tff(430,plain,
% 0.68/0.68 (~c1_1(a99)),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[429, 418])).
% 0.68/0.68 tff(431,plain,
% 0.68/0.68 (((~hskp3) | c2_1(a99)) <=> ((~hskp3) | c2_1(a99))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(432,axiom,((~hskp3) | c2_1(a99)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.68/0.68 tff(433,plain,
% 0.68/0.68 ((~hskp3) | c2_1(a99)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[432, 431])).
% 0.68/0.68 tff(434,plain,
% 0.68/0.68 ((~hskp3) | c2_1(a99)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[433, 431])).
% 0.68/0.68 tff(435,plain,
% 0.68/0.68 ((~hskp3) | c2_1(a99)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[434, 431])).
% 0.68/0.68 tff(436,plain,
% 0.68/0.68 ((~hskp3) | c2_1(a99)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[435, 431])).
% 0.68/0.68 tff(437,plain,
% 0.68/0.68 ((~hskp3) | c2_1(a99)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[436, 431])).
% 0.68/0.68 tff(438,plain,
% 0.68/0.68 ((~hskp3) | c2_1(a99)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[437, 431])).
% 0.68/0.68 tff(439,plain,
% 0.68/0.68 ((~hskp3) | c2_1(a99)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[438, 431])).
% 0.68/0.68 tff(440,plain,
% 0.68/0.68 ((~hskp3) | c2_1(a99)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[439, 431])).
% 0.68/0.68 tff(441,plain,
% 0.68/0.68 (c2_1(a99)),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[440, 418])).
% 0.68/0.68 tff(442,plain,
% 0.68/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a99) | c3_1(a99) | c1_1(a96) | c2_1(a96) | (~ndr1_0) | c0_1(a96) | (~c2_1(a99)) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a99) | c3_1(a99) | c1_1(a96) | c2_1(a96) | (~ndr1_0) | c0_1(a96) | (~c2_1(a99)) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(443,plain,
% 0.68/0.68 (((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a96) | c1_1(a96) | c0_1(a96)) <=> (c1_1(a99) | c3_1(a99) | c1_1(a96) | c2_1(a96) | (~ndr1_0) | c0_1(a96) | (~c2_1(a99)) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(444,plain,
% 0.68/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a96) | c1_1(a96) | c0_1(a96))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a99) | c3_1(a99) | c1_1(a96) | c2_1(a96) | (~ndr1_0) | c0_1(a96) | (~c2_1(a99)) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106)))),
% 0.68/0.68 inference(monotonicity,[status(thm)],[443])).
% 0.68/0.68 tff(445,plain,
% 0.68/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a96) | c1_1(a96) | c0_1(a96))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a99) | c3_1(a99) | c1_1(a96) | c2_1(a96) | (~ndr1_0) | c0_1(a96) | (~c2_1(a99)) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.68 inference(transitivity,[status(thm)],[444, 442])).
% 0.68/0.68 tff(446,plain,
% 0.68/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a96) | c1_1(a96) | c0_1(a96))),
% 0.68/0.68 inference(quant_inst,[status(thm)],[])).
% 0.68/0.68 tff(447,plain,
% 0.68/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a99) | c3_1(a99) | c1_1(a96) | c2_1(a96) | (~ndr1_0) | c0_1(a96) | (~c2_1(a99)) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.68/0.68 tff(448,plain,
% 0.68/0.68 (c0_1(a96)),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[447, 113, 299, 298, 441, 430, 424, 271, 265, 316, 306])).
% 0.68/0.68 tff(449,plain,
% 0.68/0.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (c1_1(a97) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | (~c0_1(a97)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a97) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | (~c0_1(a97)))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(450,plain,
% 0.68/0.68 (((~ndr1_0) | c1_1(a97) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c1_1(a96) | (~c0_1(a96))) <=> (c1_1(a97) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | (~c0_1(a97)))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(451,plain,
% 0.68/0.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c1_1(a97) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (c1_1(a97) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | (~c0_1(a97))))),
% 0.68/0.68 inference(monotonicity,[status(thm)],[450])).
% 0.68/0.68 tff(452,plain,
% 0.68/0.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c1_1(a97) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a97) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | (~c0_1(a97)))),
% 0.68/0.68 inference(transitivity,[status(thm)],[451, 449])).
% 0.68/0.68 tff(453,plain,
% 0.68/0.68 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c1_1(a97) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)))),
% 0.68/0.68 inference(quant_inst,[status(thm)],[])).
% 0.68/0.68 tff(454,plain,
% 0.68/0.68 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a97) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | (~c0_1(a97))),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.68/0.68 tff(455,plain,
% 0.68/0.68 ((~c0_1(a96)) | (~c0_1(a97))),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[454, 113, 281, 279, 271, 259, 21])).
% 0.68/0.68 tff(456,plain,
% 0.68/0.68 (~c0_1(a97)),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[455, 448])).
% 0.68/0.68 tff(457,plain,
% 0.68/0.68 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.68/0.68 inference(bind,[status(th)],[])).
% 0.68/0.68 tff(458,plain,
% 0.68/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.68 inference(quant_intro,[status(thm)],[457])).
% 0.68/0.68 tff(459,plain,
% 0.68/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(460,plain,
% 0.68/0.68 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | 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)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.68/0.68 inference(bind,[status(th)],[])).
% 0.68/0.68 tff(461,plain,
% 0.68/0.68 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.68 inference(quant_intro,[status(thm)],[460])).
% 0.68/0.68 tff(462,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.68/0.68 tff(463,plain,
% 0.68/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.68/0.68 tff(464,plain,
% 0.68/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[463, 459])).
% 0.68/0.68 tff(465,plain,(
% 0.68/0.68 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.68 inference(skolemize,[status(sab)],[464])).
% 0.68/0.68 tff(466,plain,
% 0.68/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[465, 458])).
% 0.68/0.68 tff(467,plain,
% 0.68/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a106) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | c0_1(a97) | (~c3_1(a97)) | (~c3_1(a106)) | c0_1(a106))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a106) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | c0_1(a97) | (~c3_1(a97)) | (~c3_1(a106)) | c0_1(a106))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(468,plain,
% 0.68/0.68 (((~ndr1_0) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)) | c0_1(a97) | (~c2_1(a97)) | (~c3_1(a97)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106))) <=> (c2_1(a106) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | c0_1(a97) | (~c3_1(a97)) | (~c3_1(a106)) | c0_1(a106))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(469,plain,
% 0.68/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)) | c0_1(a97) | (~c2_1(a97)) | (~c3_1(a97)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a106) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | c0_1(a97) | (~c3_1(a97)) | (~c3_1(a106)) | c0_1(a106)))),
% 0.68/0.68 inference(monotonicity,[status(thm)],[468])).
% 0.68/0.68 tff(470,plain,
% 0.68/0.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)) | c0_1(a97) | (~c2_1(a97)) | (~c3_1(a97)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a106) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | c0_1(a97) | (~c3_1(a97)) | (~c3_1(a106)) | c0_1(a106))),
% 0.68/0.68 inference(transitivity,[status(thm)],[469, 467])).
% 0.68/0.68 tff(471,plain,
% 0.68/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a96) | c1_1(a96) | (~c0_1(a96)) | c0_1(a97) | (~c2_1(a97)) | (~c3_1(a97)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))),
% 0.68/0.68 inference(quant_inst,[status(thm)],[])).
% 0.68/0.68 tff(472,plain,
% 0.68/0.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a106) | c1_1(a96) | c3_1(a96) | (~ndr1_0) | (~c0_1(a96)) | (~c2_1(a97)) | c0_1(a97) | (~c3_1(a97)) | (~c3_1(a106)) | c0_1(a106)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.68/0.68 tff(473,plain,
% 0.68/0.68 ($false),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[472, 113, 298, 281, 280, 287, 271, 259, 466, 448, 456, 306])).
% 0.68/0.68 tff(474,plain,((~hskp0) | hskp20), inference(lemma,lemma(discharge,[]))).
% 0.68/0.68 tff(475,plain,
% 0.68/0.68 (~hskp0),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[474, 22])).
% 0.68/0.68 tff(476,plain,
% 0.68/0.68 (hskp29),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[111, 475, 22])).
% 0.68/0.68 tff(477,plain,
% 0.68/0.68 (((~hskp29) | c2_1(a165)) <=> ((~hskp29) | c2_1(a165))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(478,axiom,((~hskp29) | c2_1(a165)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.68/0.68 tff(479,plain,
% 0.68/0.68 ((~hskp29) | c2_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.68/0.68 tff(480,plain,
% 0.68/0.68 ((~hskp29) | c2_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[479, 477])).
% 0.68/0.68 tff(481,plain,
% 0.68/0.68 ((~hskp29) | c2_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[480, 477])).
% 0.68/0.68 tff(482,plain,
% 0.68/0.68 ((~hskp29) | c2_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[481, 477])).
% 0.68/0.68 tff(483,plain,
% 0.68/0.68 ((~hskp29) | c2_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[482, 477])).
% 0.68/0.68 tff(484,plain,
% 0.68/0.68 ((~hskp29) | c2_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[483, 477])).
% 0.68/0.68 tff(485,plain,
% 0.68/0.68 ((~hskp29) | c2_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[484, 477])).
% 0.68/0.68 tff(486,plain,
% 0.68/0.68 ((~hskp29) | c2_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[485, 477])).
% 0.68/0.68 tff(487,plain,
% 0.68/0.68 (c2_1(a165)),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[486, 476])).
% 0.68/0.68 tff(488,plain,
% 0.68/0.68 (((~hskp29) | c3_1(a165)) <=> ((~hskp29) | c3_1(a165))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(489,axiom,((~hskp29) | c3_1(a165)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.68/0.68 tff(490,plain,
% 0.68/0.68 ((~hskp29) | c3_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.68/0.68 tff(491,plain,
% 0.68/0.68 ((~hskp29) | c3_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[490, 488])).
% 0.68/0.68 tff(492,plain,
% 0.68/0.68 ((~hskp29) | c3_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[491, 488])).
% 0.68/0.68 tff(493,plain,
% 0.68/0.68 ((~hskp29) | c3_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[492, 488])).
% 0.68/0.68 tff(494,plain,
% 0.68/0.68 ((~hskp29) | c3_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[493, 488])).
% 0.68/0.68 tff(495,plain,
% 0.68/0.68 ((~hskp29) | c3_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[494, 488])).
% 0.68/0.68 tff(496,plain,
% 0.68/0.68 ((~hskp29) | c3_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[495, 488])).
% 0.68/0.68 tff(497,plain,
% 0.68/0.68 ((~hskp29) | c3_1(a165)),
% 0.68/0.68 inference(modus_ponens,[status(thm)],[496, 488])).
% 0.68/0.68 tff(498,plain,
% 0.68/0.68 (c3_1(a165)),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[497, 476])).
% 0.68/0.68 tff(499,plain,
% 0.68/0.68 (c3_1(a106)),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[297, 225])).
% 0.68/0.68 tff(500,plain,
% 0.68/0.68 (~c0_1(a106)),
% 0.68/0.68 inference(unit_resolution,[status(thm)],[305, 113, 409, 408, 396, 11])).
% 0.68/0.68 tff(501,assumption,(~c0_1(a165)), introduced(assumption)).
% 0.68/0.68 tff(502,plain,
% 0.68/0.68 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.68/0.68 inference(bind,[status(th)],[])).
% 0.68/0.68 tff(503,plain,
% 0.68/0.68 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.68/0.68 inference(quant_intro,[status(thm)],[502])).
% 0.68/0.68 tff(504,plain,
% 0.68/0.68 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.68/0.68 inference(rewrite,[status(thm)],[])).
% 0.68/0.68 tff(505,plain,
% 0.68/0.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.68/0.68 inference(bind,[status(th)],[])).
% 0.68/0.68 tff(506,plain,
% 0.68/0.68 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.68/0.69 inference(quant_intro,[status(thm)],[505])).
% 0.68/0.69 tff(507,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.68/0.69 tff(508,plain,
% 0.68/0.69 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[507, 506])).
% 0.68/0.69 tff(509,plain,
% 0.68/0.69 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[508, 504])).
% 0.68/0.69 tff(510,plain,(
% 0.68/0.69 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.68/0.69 inference(skolemize,[status(sab)],[509])).
% 0.68/0.69 tff(511,plain,
% 0.68/0.69 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[510, 503])).
% 0.68/0.69 tff(512,assumption,(c3_1(a165)), introduced(assumption)).
% 0.68/0.69 tff(513,assumption,(c2_1(a165)), introduced(assumption)).
% 0.68/0.69 tff(514,plain,
% 0.68/0.69 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c1_1(a106)) | c0_1(a106))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(515,plain,
% 0.68/0.69 ((hskp7 | (~ndr1_0) | c0_1(a165) | (~c3_1(a165)) | (~c2_1(a165)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106))) <=> (hskp7 | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(516,plain,
% 0.68/0.69 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a165) | (~c3_1(a165)) | (~c2_1(a165)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c1_1(a106)) | c0_1(a106)))),
% 0.68/0.69 inference(monotonicity,[status(thm)],[515])).
% 0.68/0.69 tff(517,plain,
% 0.68/0.69 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a165) | (~c3_1(a165)) | (~c2_1(a165)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.69 inference(transitivity,[status(thm)],[516, 514])).
% 0.68/0.69 tff(518,plain,
% 0.68/0.69 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a165) | (~c3_1(a165)) | (~c2_1(a165)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)))),
% 0.68/0.69 inference(quant_inst,[status(thm)],[])).
% 0.68/0.69 tff(519,plain,
% 0.68/0.69 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp7 | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c1_1(a106)) | c0_1(a106)),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.68/0.69 tff(520,plain,
% 0.68/0.69 (hskp7),
% 0.68/0.69 inference(unit_resolution,[status(thm)],[519, 113, 513, 512, 409, 396, 511, 501, 500])).
% 0.68/0.69 tff(521,plain,
% 0.68/0.69 (((~hskp7) | (~c3_1(a103))) <=> ((~hskp7) | (~c3_1(a103)))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(522,plain,
% 0.68/0.69 (((~c3_1(a103)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a103)))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(523,axiom,((~c3_1(a103)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.68/0.69 tff(524,plain,
% 0.68/0.69 ((~hskp7) | (~c3_1(a103))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.68/0.69 tff(525,plain,
% 0.68/0.69 ((~hskp7) | (~c3_1(a103))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[524, 521])).
% 0.68/0.69 tff(526,plain,
% 0.68/0.69 (~c3_1(a103)),
% 0.68/0.69 inference(unit_resolution,[status(thm)],[525, 520])).
% 0.68/0.69 tff(527,plain,
% 0.68/0.69 (((~hskp7) | (~c1_1(a103))) <=> ((~hskp7) | (~c1_1(a103)))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(528,plain,
% 0.68/0.69 (((~c1_1(a103)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a103)))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(529,axiom,((~c1_1(a103)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.68/0.69 tff(530,plain,
% 0.68/0.69 ((~hskp7) | (~c1_1(a103))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.68/0.69 tff(531,plain,
% 0.68/0.69 ((~hskp7) | (~c1_1(a103))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[530, 527])).
% 0.68/0.69 tff(532,plain,
% 0.68/0.69 (~c1_1(a103)),
% 0.68/0.69 inference(unit_resolution,[status(thm)],[531, 520])).
% 0.68/0.69 tff(533,plain,
% 0.68/0.69 (((~hskp7) | c0_1(a103)) <=> ((~hskp7) | c0_1(a103))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(534,axiom,((~hskp7) | c0_1(a103)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.68/0.69 tff(535,plain,
% 0.68/0.69 ((~hskp7) | c0_1(a103)),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[534, 533])).
% 0.68/0.69 tff(536,plain,
% 0.68/0.69 ((~hskp7) | c0_1(a103)),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[535, 533])).
% 0.68/0.69 tff(537,plain,
% 0.68/0.69 ((~hskp7) | c0_1(a103)),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[536, 533])).
% 0.68/0.69 tff(538,plain,
% 0.68/0.69 ((~hskp7) | c0_1(a103)),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[537, 533])).
% 0.68/0.69 tff(539,plain,
% 0.68/0.69 ((~hskp7) | c0_1(a103)),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[538, 533])).
% 0.68/0.69 tff(540,plain,
% 0.68/0.69 ((~hskp7) | c0_1(a103)),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[539, 533])).
% 0.68/0.69 tff(541,plain,
% 0.68/0.69 ((~hskp7) | c0_1(a103)),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[540, 533])).
% 0.68/0.69 tff(542,plain,
% 0.68/0.69 ((~hskp7) | c0_1(a103)),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[541, 533])).
% 0.68/0.69 tff(543,plain,
% 0.68/0.69 (c0_1(a103)),
% 0.68/0.69 inference(unit_resolution,[status(thm)],[542, 520])).
% 0.68/0.69 tff(544,plain,
% 0.68/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(545,plain,
% 0.68/0.69 (((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a165) | (~c2_1(a165)) | (~c3_1(a165)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106))) <=> (c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(546,plain,
% 0.68/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a165) | (~c2_1(a165)) | (~c3_1(a165)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106)))),
% 0.68/0.69 inference(monotonicity,[status(thm)],[545])).
% 0.68/0.69 tff(547,plain,
% 0.68/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a165) | (~c2_1(a165)) | (~c3_1(a165)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106))),
% 0.68/0.69 inference(transitivity,[status(thm)],[546, 544])).
% 0.68/0.69 tff(548,plain,
% 0.68/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a165) | (~c2_1(a165)) | (~c3_1(a165)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))),
% 0.68/0.69 inference(quant_inst,[status(thm)],[])).
% 0.68/0.69 tff(549,plain,
% 0.68/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | c0_1(a165) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106)),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[548, 547])).
% 0.68/0.69 tff(550,plain,
% 0.68/0.69 ($false),
% 0.68/0.69 inference(unit_resolution,[status(thm)],[549, 113, 513, 512, 408, 543, 396, 532, 526, 466, 501, 500])).
% 0.68/0.69 tff(551,plain,(c0_1(a165) | (~c2_1(a165)) | (~c3_1(a165)) | (~c3_1(a106)) | c2_1(a106) | (~c1_1(a106))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.69 tff(552,plain,
% 0.68/0.69 (c0_1(a165)),
% 0.68/0.69 inference(unit_resolution,[status(thm)],[551, 499, 498, 487, 242, 236])).
% 0.68/0.69 tff(553,plain,
% 0.68/0.69 ((hskp20 | hskp8 | hskp3) <=> (hskp20 | hskp8 | hskp3)),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(554,plain,
% 0.68/0.69 (((hskp20 | hskp3) | hskp8) <=> (hskp20 | hskp8 | hskp3)),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(555,axiom,((hskp20 | hskp3) | hskp8), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 0.68/0.69 tff(556,plain,
% 0.68/0.69 (hskp20 | hskp8 | hskp3),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.68/0.69 tff(557,plain,
% 0.68/0.69 (hskp20 | hskp8 | hskp3),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[556, 553])).
% 0.68/0.69 tff(558,plain,
% 0.68/0.69 (hskp20 | hskp8 | hskp3),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[557, 553])).
% 0.68/0.69 tff(559,plain,
% 0.68/0.69 (hskp20 | hskp8 | hskp3),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[558, 553])).
% 0.68/0.69 tff(560,plain,
% 0.68/0.69 (hskp20 | hskp8 | hskp3),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[559, 553])).
% 0.68/0.69 tff(561,plain,
% 0.68/0.69 (hskp20 | hskp8 | hskp3),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[560, 553])).
% 0.68/0.69 tff(562,plain,
% 0.68/0.69 (hskp20 | hskp8 | hskp3),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[561, 553])).
% 0.68/0.69 tff(563,plain,
% 0.68/0.69 (hskp20 | hskp8 | hskp3),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[562, 553])).
% 0.68/0.69 tff(564,plain,
% 0.68/0.69 (hskp8),
% 0.68/0.69 inference(unit_resolution,[status(thm)],[563, 23, 22])).
% 0.68/0.69 tff(565,plain,
% 0.68/0.69 (((~hskp8) | (~c3_1(a104))) <=> ((~hskp8) | (~c3_1(a104)))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(566,plain,
% 0.68/0.69 (((~c3_1(a104)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a104)))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(567,axiom,((~c3_1(a104)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.68/0.69 tff(568,plain,
% 0.68/0.69 ((~hskp8) | (~c3_1(a104))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.68/0.69 tff(569,plain,
% 0.68/0.69 ((~hskp8) | (~c3_1(a104))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[568, 565])).
% 0.68/0.69 tff(570,plain,
% 0.68/0.69 (~c3_1(a104)),
% 0.68/0.69 inference(unit_resolution,[status(thm)],[569, 564])).
% 0.68/0.69 tff(571,plain,
% 0.68/0.69 (((~hskp8) | (~c2_1(a104))) <=> ((~hskp8) | (~c2_1(a104)))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(572,plain,
% 0.68/0.69 (((~c2_1(a104)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a104)))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(573,axiom,((~c2_1(a104)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 0.68/0.69 tff(574,plain,
% 0.68/0.69 ((~hskp8) | (~c2_1(a104))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.68/0.69 tff(575,plain,
% 0.68/0.69 ((~hskp8) | (~c2_1(a104))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[574, 571])).
% 0.68/0.69 tff(576,plain,
% 0.68/0.69 (~c2_1(a104)),
% 0.68/0.69 inference(unit_resolution,[status(thm)],[575, 564])).
% 0.68/0.69 tff(577,plain,
% 0.68/0.69 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a104))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a104))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(578,plain,
% 0.68/0.69 ((hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a104) | c2_1(a104) | c1_1(a104)) <=> (hskp3 | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a104))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(579,plain,
% 0.68/0.69 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a104) | c2_1(a104) | c1_1(a104))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a104)))),
% 0.68/0.69 inference(monotonicity,[status(thm)],[578])).
% 0.68/0.69 tff(580,plain,
% 0.68/0.69 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a104) | c2_1(a104) | c1_1(a104))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a104))),
% 0.68/0.69 inference(transitivity,[status(thm)],[579, 577])).
% 0.68/0.69 tff(581,plain,
% 0.68/0.69 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a104) | c2_1(a104) | c1_1(a104))),
% 0.68/0.69 inference(quant_inst,[status(thm)],[])).
% 0.68/0.69 tff(582,plain,
% 0.68/0.69 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a104)),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[581, 580])).
% 0.68/0.69 tff(583,plain,
% 0.68/0.69 ((~c0_1(a165)) | c1_1(a104)),
% 0.68/0.69 inference(unit_resolution,[status(thm)],[582, 113, 23, 487, 498, 576, 570, 326])).
% 0.68/0.69 tff(584,plain,
% 0.68/0.69 (c1_1(a104)),
% 0.68/0.69 inference(unit_resolution,[status(thm)],[583, 552])).
% 0.68/0.69 tff(585,plain,
% 0.68/0.69 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.68/0.69 inference(bind,[status(th)],[])).
% 0.68/0.69 tff(586,plain,
% 0.68/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.69 inference(quant_intro,[status(thm)],[585])).
% 0.68/0.69 tff(587,plain,
% 0.68/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(588,plain,
% 0.68/0.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.68/0.69 inference(bind,[status(th)],[])).
% 0.68/0.69 tff(589,plain,
% 0.68/0.69 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.69 inference(quant_intro,[status(thm)],[588])).
% 0.68/0.69 tff(590,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 0.68/0.69 tff(591,plain,
% 0.68/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[590, 589])).
% 0.68/0.69 tff(592,plain,
% 0.68/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[591, 587])).
% 0.68/0.69 tff(593,plain,(
% 0.68/0.69 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.69 inference(skolemize,[status(sab)],[592])).
% 0.68/0.69 tff(594,plain,
% 0.68/0.69 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[593, 586])).
% 0.68/0.69 tff(595,plain,
% 0.68/0.69 (~c0_1(a106)),
% 0.68/0.69 inference(unit_resolution,[status(thm)],[305, 113, 236, 499, 242, 11])).
% 0.68/0.69 tff(596,plain,
% 0.68/0.69 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))),
% 0.68/0.69 inference(bind,[status(th)],[])).
% 0.68/0.69 tff(597,plain,
% 0.68/0.69 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.68/0.69 inference(quant_intro,[status(thm)],[596])).
% 0.68/0.69 tff(598,plain,
% 0.68/0.69 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(599,plain,
% 0.68/0.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | 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)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))))),
% 0.68/0.69 inference(bind,[status(th)],[])).
% 0.68/0.69 tff(600,plain,
% 0.68/0.69 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.68/0.69 inference(quant_intro,[status(thm)],[599])).
% 0.68/0.69 tff(601,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.68/0.69 tff(602,plain,
% 0.68/0.69 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.68/0.69 tff(603,plain,
% 0.68/0.69 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[602, 598])).
% 0.68/0.69 tff(604,plain,(
% 0.68/0.69 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.68/0.69 inference(skolemize,[status(sab)],[603])).
% 0.68/0.69 tff(605,plain,
% 0.68/0.69 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))),
% 0.68/0.69 inference(modus_ponens,[status(thm)],[604, 597])).
% 0.68/0.69 tff(606,plain,
% 0.68/0.69 (((~hskp8) | (~c0_1(a104))) <=> ((~hskp8) | (~c0_1(a104)))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(607,plain,
% 0.68/0.69 (((~c0_1(a104)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a104)))),
% 0.68/0.69 inference(rewrite,[status(thm)],[])).
% 0.68/0.69 tff(608,axiom,((~c0_1(a104)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.68/0.70 tff(609,plain,
% 0.68/0.70 ((~hskp8) | (~c0_1(a104))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.68/0.70 tff(610,plain,
% 0.68/0.70 ((~hskp8) | (~c0_1(a104))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[609, 606])).
% 0.68/0.70 tff(611,plain,
% 0.68/0.70 (~c0_1(a104)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[610, 564])).
% 0.68/0.70 tff(612,plain,
% 0.68/0.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a106) | c0_1(a104) | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a106) | c0_1(a104) | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(613,plain,
% 0.68/0.70 ((hskp6 | (~ndr1_0) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)) | c3_1(a104) | c2_1(a104) | c0_1(a104)) <=> (hskp6 | c2_1(a106) | c0_1(a104) | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(614,plain,
% 0.68/0.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)) | c3_1(a104) | c2_1(a104) | c0_1(a104))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c2_1(a106) | c0_1(a104) | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106)))),
% 0.68/0.70 inference(monotonicity,[status(thm)],[613])).
% 0.68/0.70 tff(615,plain,
% 0.68/0.70 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)) | c3_1(a104) | c2_1(a104) | c0_1(a104))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a106) | c0_1(a104) | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.70 inference(transitivity,[status(thm)],[614, 612])).
% 0.68/0.70 tff(616,plain,
% 0.68/0.70 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)) | c3_1(a104) | c2_1(a104) | c0_1(a104))),
% 0.68/0.70 inference(quant_inst,[status(thm)],[])).
% 0.68/0.70 tff(617,plain,
% 0.68/0.70 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c2_1(a106) | c0_1(a104) | c2_1(a104) | c3_1(a104) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[616, 615])).
% 0.68/0.70 tff(618,plain,
% 0.68/0.70 (hskp6),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[617, 113, 236, 242, 611, 576, 570, 605, 595])).
% 0.68/0.70 tff(619,plain,
% 0.68/0.70 (((~hskp6) | (~c3_1(a102))) <=> ((~hskp6) | (~c3_1(a102)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(620,plain,
% 0.68/0.70 (((~c3_1(a102)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a102)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(621,axiom,((~c3_1(a102)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.68/0.70 tff(622,plain,
% 0.68/0.70 ((~hskp6) | (~c3_1(a102))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[621, 620])).
% 0.68/0.70 tff(623,plain,
% 0.68/0.70 ((~hskp6) | (~c3_1(a102))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[622, 619])).
% 0.68/0.70 tff(624,plain,
% 0.68/0.70 (~c3_1(a102)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[623, 618])).
% 0.68/0.70 tff(625,plain,
% 0.68/0.70 (((~hskp6) | c2_1(a102)) <=> ((~hskp6) | c2_1(a102))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(626,axiom,((~hskp6) | c2_1(a102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.68/0.70 tff(627,plain,
% 0.68/0.70 ((~hskp6) | c2_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.68/0.70 tff(628,plain,
% 0.68/0.70 ((~hskp6) | c2_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[627, 625])).
% 0.68/0.70 tff(629,plain,
% 0.68/0.70 ((~hskp6) | c2_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[628, 625])).
% 0.68/0.70 tff(630,plain,
% 0.68/0.70 ((~hskp6) | c2_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[629, 625])).
% 0.68/0.70 tff(631,plain,
% 0.68/0.70 ((~hskp6) | c2_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[630, 625])).
% 0.68/0.70 tff(632,plain,
% 0.68/0.70 ((~hskp6) | c2_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[631, 625])).
% 0.68/0.70 tff(633,plain,
% 0.68/0.70 ((~hskp6) | c2_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[632, 625])).
% 0.68/0.70 tff(634,plain,
% 0.68/0.70 ((~hskp6) | c2_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[633, 625])).
% 0.68/0.70 tff(635,plain,
% 0.68/0.70 (c2_1(a102)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[634, 618])).
% 0.68/0.70 tff(636,plain,
% 0.68/0.70 (((~hskp6) | c1_1(a102)) <=> ((~hskp6) | c1_1(a102))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(637,axiom,((~hskp6) | c1_1(a102)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.68/0.70 tff(638,plain,
% 0.68/0.70 ((~hskp6) | c1_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.68/0.70 tff(639,plain,
% 0.68/0.70 ((~hskp6) | c1_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[638, 636])).
% 0.68/0.70 tff(640,plain,
% 0.68/0.70 ((~hskp6) | c1_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[639, 636])).
% 0.68/0.70 tff(641,plain,
% 0.68/0.70 ((~hskp6) | c1_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[640, 636])).
% 0.68/0.70 tff(642,plain,
% 0.68/0.70 ((~hskp6) | c1_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[641, 636])).
% 0.68/0.70 tff(643,plain,
% 0.68/0.70 ((~hskp6) | c1_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[642, 636])).
% 0.68/0.70 tff(644,plain,
% 0.68/0.70 ((~hskp6) | c1_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[643, 636])).
% 0.68/0.70 tff(645,plain,
% 0.68/0.70 ((~hskp6) | c1_1(a102)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[644, 636])).
% 0.68/0.70 tff(646,plain,
% 0.68/0.70 (c1_1(a102)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[645, 618])).
% 0.68/0.70 tff(647,plain,
% 0.68/0.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c2_1(a104) | c3_1(a104) | c3_1(a102) | (~ndr1_0) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c2_1(a104) | c3_1(a104) | c3_1(a102) | (~ndr1_0) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a104)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(648,plain,
% 0.68/0.70 ((hskp5 | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c1_1(a102)) | c3_1(a104) | c2_1(a104) | (~c1_1(a104))) <=> (hskp5 | c2_1(a104) | c3_1(a104) | c3_1(a102) | (~ndr1_0) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a104)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(649,plain,
% 0.68/0.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c1_1(a102)) | c3_1(a104) | c2_1(a104) | (~c1_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | c2_1(a104) | c3_1(a104) | c3_1(a102) | (~ndr1_0) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a104))))),
% 0.68/0.70 inference(monotonicity,[status(thm)],[648])).
% 0.68/0.70 tff(650,plain,
% 0.68/0.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c1_1(a102)) | c3_1(a104) | c2_1(a104) | (~c1_1(a104)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c2_1(a104) | c3_1(a104) | c3_1(a102) | (~ndr1_0) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a104)))),
% 0.68/0.70 inference(transitivity,[status(thm)],[649, 647])).
% 0.68/0.70 tff(651,plain,
% 0.68/0.70 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp5 | (~ndr1_0) | c3_1(a102) | (~c2_1(a102)) | (~c1_1(a102)) | c3_1(a104) | c2_1(a104) | (~c1_1(a104)))),
% 0.68/0.70 inference(quant_inst,[status(thm)],[])).
% 0.68/0.70 tff(652,plain,
% 0.68/0.70 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)))) | hskp5 | c2_1(a104) | c3_1(a104) | c3_1(a102) | (~ndr1_0) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a104))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[651, 650])).
% 0.68/0.70 tff(653,plain,
% 0.68/0.70 (hskp5 | (~c1_1(a104))),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[652, 113, 646, 635, 576, 570, 624, 594])).
% 0.68/0.70 tff(654,plain,
% 0.68/0.70 (hskp5),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[653, 584])).
% 0.68/0.70 tff(655,plain,
% 0.68/0.70 (((~hskp5) | (~c2_1(a101))) <=> ((~hskp5) | (~c2_1(a101)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(656,plain,
% 0.68/0.70 (((~c2_1(a101)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a101)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(657,axiom,((~c2_1(a101)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.68/0.70 tff(658,plain,
% 0.68/0.70 ((~hskp5) | (~c2_1(a101))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[657, 656])).
% 0.68/0.70 tff(659,plain,
% 0.68/0.70 ((~hskp5) | (~c2_1(a101))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[658, 655])).
% 0.68/0.70 tff(660,plain,
% 0.68/0.70 (~c2_1(a101)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[659, 654])).
% 0.68/0.70 tff(661,plain,
% 0.68/0.70 (((~hskp5) | c3_1(a101)) <=> ((~hskp5) | c3_1(a101))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(662,axiom,((~hskp5) | c3_1(a101)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.68/0.70 tff(663,plain,
% 0.68/0.70 ((~hskp5) | c3_1(a101)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.68/0.70 tff(664,plain,
% 0.68/0.70 ((~hskp5) | c3_1(a101)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[663, 661])).
% 0.68/0.70 tff(665,plain,
% 0.68/0.70 ((~hskp5) | c3_1(a101)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[664, 661])).
% 0.68/0.70 tff(666,plain,
% 0.68/0.70 ((~hskp5) | c3_1(a101)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[665, 661])).
% 0.68/0.70 tff(667,plain,
% 0.68/0.70 ((~hskp5) | c3_1(a101)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[666, 661])).
% 0.68/0.70 tff(668,plain,
% 0.68/0.70 ((~hskp5) | c3_1(a101)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[667, 661])).
% 0.68/0.70 tff(669,plain,
% 0.68/0.70 ((~hskp5) | c3_1(a101)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[668, 661])).
% 0.68/0.70 tff(670,plain,
% 0.68/0.70 ((~hskp5) | c3_1(a101)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[669, 661])).
% 0.68/0.70 tff(671,plain,
% 0.68/0.70 (c3_1(a101)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[670, 654])).
% 0.68/0.70 tff(672,plain,
% 0.68/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a106) | c0_1(a104) | c3_1(a104) | c2_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a104)) | (~c3_1(a106)) | (~c1_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a106) | c0_1(a104) | c3_1(a104) | c2_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a104)) | (~c3_1(a106)) | (~c1_1(a106)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(673,plain,
% 0.68/0.70 (((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a101) | (~c0_1(a101)) | (~c3_1(a101)) | c3_1(a104) | c0_1(a104) | (~c1_1(a104))) <=> (c2_1(a106) | c0_1(a104) | c3_1(a104) | c2_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a104)) | (~c3_1(a106)) | (~c1_1(a106)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(674,plain,
% 0.68/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a101) | (~c0_1(a101)) | (~c3_1(a101)) | c3_1(a104) | c0_1(a104) | (~c1_1(a104)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a106) | c0_1(a104) | c3_1(a104) | c2_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a104)) | (~c3_1(a106)) | (~c1_1(a106))))),
% 0.68/0.70 inference(monotonicity,[status(thm)],[673])).
% 0.68/0.70 tff(675,plain,
% 0.68/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a101) | (~c0_1(a101)) | (~c3_1(a101)) | c3_1(a104) | c0_1(a104) | (~c1_1(a104)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a106) | c0_1(a104) | c3_1(a104) | c2_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a104)) | (~c3_1(a106)) | (~c1_1(a106)))),
% 0.68/0.70 inference(transitivity,[status(thm)],[674, 672])).
% 0.68/0.70 tff(676,plain,
% 0.68/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c2_1(a101) | (~c0_1(a101)) | (~c3_1(a101)) | c3_1(a104) | c0_1(a104) | (~c1_1(a104)))),
% 0.68/0.70 inference(quant_inst,[status(thm)],[])).
% 0.68/0.70 tff(677,plain,
% 0.68/0.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a106) | c0_1(a104) | c3_1(a104) | c2_1(a101) | (~ndr1_0) | (~c3_1(a101)) | (~c0_1(a101)) | (~c1_1(a104)) | (~c3_1(a106)) | (~c1_1(a106))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[676, 675])).
% 0.68/0.70 tff(678,plain,
% 0.68/0.70 (~c0_1(a101)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[677, 113, 236, 499, 671, 242, 611, 570, 660, 354, 584])).
% 0.68/0.70 tff(679,plain,
% 0.68/0.70 (((~hskp5) | (~c1_1(a101))) <=> ((~hskp5) | (~c1_1(a101)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(680,plain,
% 0.68/0.70 (((~c1_1(a101)) | (~hskp5)) <=> ((~hskp5) | (~c1_1(a101)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(681,axiom,((~c1_1(a101)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.68/0.70 tff(682,plain,
% 0.68/0.70 ((~hskp5) | (~c1_1(a101))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[681, 680])).
% 0.68/0.70 tff(683,plain,
% 0.68/0.70 ((~hskp5) | (~c1_1(a101))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[682, 679])).
% 0.68/0.70 tff(684,plain,
% 0.68/0.70 (~c1_1(a101)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[683, 654])).
% 0.68/0.70 tff(685,assumption,(~c0_1(a106)), introduced(assumption)).
% 0.68/0.70 tff(686,plain,
% 0.68/0.70 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.68/0.70 inference(bind,[status(th)],[])).
% 0.68/0.70 tff(687,plain,
% 0.68/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.70 inference(quant_intro,[status(thm)],[686])).
% 0.68/0.70 tff(688,plain,
% 0.68/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(689,plain,
% 0.68/0.70 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.68/0.70 inference(bind,[status(th)],[])).
% 0.68/0.70 tff(690,plain,
% 0.68/0.70 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.70 inference(quant_intro,[status(thm)],[689])).
% 0.68/0.70 tff(691,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c2_1(W))) | c0_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 0.68/0.70 tff(692,plain,
% 0.68/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[691, 690])).
% 0.68/0.70 tff(693,plain,
% 0.68/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[692, 688])).
% 0.68/0.70 tff(694,plain,(
% 0.68/0.70 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.70 inference(skolemize,[status(sab)],[693])).
% 0.68/0.70 tff(695,plain,
% 0.68/0.70 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[694, 687])).
% 0.68/0.70 tff(696,assumption,(hskp11), introduced(assumption)).
% 0.68/0.70 tff(697,plain,
% 0.68/0.70 (((~hskp11) | (~c3_1(a109))) <=> ((~hskp11) | (~c3_1(a109)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(698,plain,
% 0.68/0.70 (((~c3_1(a109)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a109)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(699,axiom,((~c3_1(a109)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 0.68/0.70 tff(700,plain,
% 0.68/0.70 ((~hskp11) | (~c3_1(a109))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[699, 698])).
% 0.68/0.70 tff(701,plain,
% 0.68/0.70 ((~hskp11) | (~c3_1(a109))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[700, 697])).
% 0.68/0.70 tff(702,plain,
% 0.68/0.70 (~c3_1(a109)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[701, 696])).
% 0.68/0.70 tff(703,plain,
% 0.68/0.70 (((~hskp11) | (~c0_1(a109))) <=> ((~hskp11) | (~c0_1(a109)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(704,plain,
% 0.68/0.70 (((~c0_1(a109)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a109)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(705,axiom,((~c0_1(a109)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.68/0.70 tff(706,plain,
% 0.68/0.70 ((~hskp11) | (~c0_1(a109))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[705, 704])).
% 0.68/0.70 tff(707,plain,
% 0.68/0.70 ((~hskp11) | (~c0_1(a109))),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[706, 703])).
% 0.68/0.70 tff(708,plain,
% 0.68/0.70 (~c0_1(a109)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[707, 696])).
% 0.68/0.70 tff(709,plain,
% 0.68/0.70 (((~hskp11) | c2_1(a109)) <=> ((~hskp11) | c2_1(a109))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(710,axiom,((~hskp11) | c2_1(a109)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.68/0.70 tff(711,plain,
% 0.68/0.70 ((~hskp11) | c2_1(a109)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[710, 709])).
% 0.68/0.70 tff(712,plain,
% 0.68/0.70 ((~hskp11) | c2_1(a109)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[711, 709])).
% 0.68/0.70 tff(713,plain,
% 0.68/0.70 ((~hskp11) | c2_1(a109)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[712, 709])).
% 0.68/0.70 tff(714,plain,
% 0.68/0.70 ((~hskp11) | c2_1(a109)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[713, 709])).
% 0.68/0.70 tff(715,plain,
% 0.68/0.70 ((~hskp11) | c2_1(a109)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[714, 709])).
% 0.68/0.70 tff(716,plain,
% 0.68/0.70 ((~hskp11) | c2_1(a109)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[715, 709])).
% 0.68/0.70 tff(717,plain,
% 0.68/0.70 ((~hskp11) | c2_1(a109)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[716, 709])).
% 0.68/0.70 tff(718,plain,
% 0.68/0.70 ((~hskp11) | c2_1(a109)),
% 0.68/0.70 inference(modus_ponens,[status(thm)],[717, 709])).
% 0.68/0.70 tff(719,plain,
% 0.68/0.70 (c2_1(a109)),
% 0.68/0.70 inference(unit_resolution,[status(thm)],[718, 696])).
% 0.68/0.70 tff(720,plain,
% 0.68/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | (~c1_1(a109)) | (~c2_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | (~c1_1(a109)) | (~c2_1(a109)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(721,plain,
% 0.68/0.70 (((~ndr1_0) | c0_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c3_1(a109) | c0_1(a109) | (~c2_1(a109))) <=> (c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | (~c1_1(a109)) | (~c2_1(a109)))),
% 0.68/0.70 inference(rewrite,[status(thm)],[])).
% 0.68/0.70 tff(722,plain,
% 0.68/0.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c3_1(a109) | c0_1(a109) | (~c2_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | (~c1_1(a109)) | (~c2_1(a109))))),
% 0.68/0.71 inference(monotonicity,[status(thm)],[721])).
% 0.68/0.71 tff(723,plain,
% 0.68/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c3_1(a109) | c0_1(a109) | (~c2_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | (~c1_1(a109)) | (~c2_1(a109)))),
% 0.68/0.71 inference(transitivity,[status(thm)],[722, 720])).
% 0.68/0.71 tff(724,plain,
% 0.68/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a106) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a109) | (~c1_1(a109)) | (~c2_1(a109)) | c3_1(a109) | c0_1(a109) | (~c2_1(a109)))),
% 0.68/0.71 inference(quant_inst,[status(thm)],[])).
% 0.68/0.71 tff(725,plain,
% 0.68/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a109) | c3_1(a109) | (~ndr1_0) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | (~c1_1(a109)) | (~c2_1(a109))),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.68/0.71 tff(726,plain,
% 0.68/0.71 (~c1_1(a109)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[725, 113, 719, 409, 408, 708, 702, 695, 685])).
% 0.68/0.71 tff(727,assumption,(~c0_1(a101)), introduced(assumption)).
% 0.68/0.71 tff(728,assumption,(~c2_1(a101)), introduced(assumption)).
% 0.68/0.71 tff(729,assumption,(~c1_1(a101)), introduced(assumption)).
% 0.68/0.71 tff(730,plain,
% 0.68/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a109) | c1_1(a101) | c2_1(a101) | (~ndr1_0) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | c1_1(a109) | (~c2_1(a109)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a109) | c1_1(a101) | c2_1(a101) | (~ndr1_0) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | c1_1(a109) | (~c2_1(a109)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(731,plain,
% 0.68/0.71 (((~ndr1_0) | c3_1(a109) | c1_1(a109) | (~c2_1(a109)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101)) <=> (c3_1(a109) | c1_1(a101) | c2_1(a101) | (~ndr1_0) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | c1_1(a109) | (~c2_1(a109)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(732,plain,
% 0.68/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a109) | c1_1(a109) | (~c2_1(a109)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a109) | c1_1(a101) | c2_1(a101) | (~ndr1_0) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | c1_1(a109) | (~c2_1(a109))))),
% 0.68/0.71 inference(monotonicity,[status(thm)],[731])).
% 0.68/0.71 tff(733,plain,
% 0.68/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a109) | c1_1(a109) | (~c2_1(a109)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a109) | c1_1(a101) | c2_1(a101) | (~ndr1_0) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | c1_1(a109) | (~c2_1(a109)))),
% 0.68/0.71 inference(transitivity,[status(thm)],[732, 730])).
% 0.68/0.71 tff(734,plain,
% 0.68/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a109) | c1_1(a109) | (~c2_1(a109)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101))),
% 0.68/0.71 inference(quant_inst,[status(thm)],[])).
% 0.68/0.71 tff(735,plain,
% 0.68/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a109) | c1_1(a101) | c2_1(a101) | (~ndr1_0) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106) | c1_1(a109) | (~c2_1(a109))),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[734, 733])).
% 0.68/0.71 tff(736,plain,
% 0.68/0.71 ($false),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[735, 113, 719, 409, 408, 702, 729, 728, 316, 685, 727, 726])).
% 0.68/0.71 tff(737,plain,((~hskp11) | (~c1_1(a106)) | (~c3_1(a106)) | c1_1(a101) | c2_1(a101) | c0_1(a106) | c0_1(a101)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.71 tff(738,plain,
% 0.68/0.71 (~hskp11),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[737, 236, 499, 684, 660, 595, 678])).
% 0.68/0.71 tff(739,assumption,(hskp12), introduced(assumption)).
% 0.68/0.71 tff(740,plain,
% 0.68/0.71 (((~hskp12) | (~c0_1(a110))) <=> ((~hskp12) | (~c0_1(a110)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(741,plain,
% 0.68/0.71 (((~c0_1(a110)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a110)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(742,axiom,((~c0_1(a110)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 0.68/0.71 tff(743,plain,
% 0.68/0.71 ((~hskp12) | (~c0_1(a110))),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[742, 741])).
% 0.68/0.71 tff(744,plain,
% 0.68/0.71 ((~hskp12) | (~c0_1(a110))),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[743, 740])).
% 0.68/0.71 tff(745,plain,
% 0.68/0.71 (~c0_1(a110)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[744, 739])).
% 0.68/0.71 tff(746,plain,
% 0.68/0.71 (((~hskp12) | c3_1(a110)) <=> ((~hskp12) | c3_1(a110))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(747,axiom,((~hskp12) | c3_1(a110)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.68/0.71 tff(748,plain,
% 0.68/0.71 ((~hskp12) | c3_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[747, 746])).
% 0.68/0.71 tff(749,plain,
% 0.68/0.71 ((~hskp12) | c3_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[748, 746])).
% 0.68/0.71 tff(750,plain,
% 0.68/0.71 ((~hskp12) | c3_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[749, 746])).
% 0.68/0.71 tff(751,plain,
% 0.68/0.71 ((~hskp12) | c3_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[750, 746])).
% 0.68/0.71 tff(752,plain,
% 0.68/0.71 ((~hskp12) | c3_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[751, 746])).
% 0.68/0.71 tff(753,plain,
% 0.68/0.71 ((~hskp12) | c3_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[752, 746])).
% 0.68/0.71 tff(754,plain,
% 0.68/0.71 ((~hskp12) | c3_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[753, 746])).
% 0.68/0.71 tff(755,plain,
% 0.68/0.71 ((~hskp12) | c3_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[754, 746])).
% 0.68/0.71 tff(756,plain,
% 0.68/0.71 (c3_1(a110)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[755, 739])).
% 0.68/0.71 tff(757,plain,
% 0.68/0.71 (((~hskp12) | c2_1(a110)) <=> ((~hskp12) | c2_1(a110))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(758,axiom,((~hskp12) | c2_1(a110)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.68/0.71 tff(759,plain,
% 0.68/0.71 ((~hskp12) | c2_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.68/0.71 tff(760,plain,
% 0.68/0.71 ((~hskp12) | c2_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[759, 757])).
% 0.68/0.71 tff(761,plain,
% 0.68/0.71 ((~hskp12) | c2_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[760, 757])).
% 0.68/0.71 tff(762,plain,
% 0.68/0.71 ((~hskp12) | c2_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[761, 757])).
% 0.68/0.71 tff(763,plain,
% 0.68/0.71 ((~hskp12) | c2_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[762, 757])).
% 0.68/0.71 tff(764,plain,
% 0.68/0.71 ((~hskp12) | c2_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[763, 757])).
% 0.68/0.71 tff(765,plain,
% 0.68/0.71 ((~hskp12) | c2_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[764, 757])).
% 0.68/0.71 tff(766,plain,
% 0.68/0.71 ((~hskp12) | c2_1(a110)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[765, 757])).
% 0.68/0.71 tff(767,plain,
% 0.68/0.71 (c2_1(a110)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[766, 739])).
% 0.68/0.71 tff(768,plain,
% 0.68/0.71 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | c0_1(a110) | c2_1(a106) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp7 | c0_1(a110) | c2_1(a106) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(769,plain,
% 0.68/0.71 ((hskp7 | (~ndr1_0) | c0_1(a110) | (~c3_1(a110)) | (~c2_1(a110)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106))) <=> (hskp7 | c0_1(a110) | c2_1(a106) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(770,plain,
% 0.68/0.71 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a110) | (~c3_1(a110)) | (~c2_1(a110)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | c0_1(a110) | c2_1(a106) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110))))),
% 0.68/0.71 inference(monotonicity,[status(thm)],[769])).
% 0.68/0.71 tff(771,plain,
% 0.68/0.71 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a110) | (~c3_1(a110)) | (~c2_1(a110)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp7 | c0_1(a110) | c2_1(a106) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))),
% 0.68/0.71 inference(transitivity,[status(thm)],[770, 768])).
% 0.68/0.71 tff(772,plain,
% 0.68/0.71 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a110) | (~c3_1(a110)) | (~c2_1(a110)) | c2_1(a106) | c0_1(a106) | (~c1_1(a106)))),
% 0.68/0.71 inference(quant_inst,[status(thm)],[])).
% 0.68/0.71 tff(773,plain,
% 0.68/0.71 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp7 | c0_1(a110) | c2_1(a106) | (~ndr1_0) | (~c1_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110))),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[772, 771])).
% 0.68/0.71 tff(774,plain,
% 0.68/0.71 (hskp7),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[773, 113, 767, 756, 409, 745, 396, 511, 500])).
% 0.68/0.71 tff(775,plain,
% 0.68/0.71 (~c3_1(a103)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[525, 774])).
% 0.68/0.71 tff(776,plain,
% 0.68/0.71 (~c1_1(a103)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[531, 774])).
% 0.68/0.71 tff(777,plain,
% 0.68/0.71 (c0_1(a103)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[542, 774])).
% 0.68/0.71 tff(778,plain,
% 0.68/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a110) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a110) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(779,plain,
% 0.68/0.71 (((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a110) | (~c2_1(a110)) | (~c3_1(a110)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106))) <=> (c0_1(a110) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(780,plain,
% 0.68/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a110) | (~c2_1(a110)) | (~c3_1(a110)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a110) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110))))),
% 0.68/0.71 inference(monotonicity,[status(thm)],[779])).
% 0.68/0.71 tff(781,plain,
% 0.68/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a110) | (~c2_1(a110)) | (~c3_1(a110)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a110) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110)))),
% 0.68/0.71 inference(transitivity,[status(thm)],[780, 778])).
% 0.68/0.71 tff(782,plain,
% 0.68/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a103) | c1_1(a103) | (~c0_1(a103)) | c0_1(a110) | (~c2_1(a110)) | (~c3_1(a110)) | c2_1(a106) | c0_1(a106) | (~c3_1(a106)))),
% 0.68/0.71 inference(quant_inst,[status(thm)],[])).
% 0.68/0.71 tff(783,plain,
% 0.68/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a110) | c2_1(a106) | c1_1(a103) | c3_1(a103) | (~ndr1_0) | (~c0_1(a103)) | (~c3_1(a106)) | c0_1(a106) | (~c3_1(a110)) | (~c2_1(a110))),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[782, 781])).
% 0.68/0.71 tff(784,plain,
% 0.68/0.71 ($false),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[783, 113, 767, 756, 408, 777, 745, 396, 776, 775, 466, 500])).
% 0.68/0.71 tff(785,plain,((~hskp12) | (~c3_1(a106)) | c2_1(a106) | (~c1_1(a106))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.71 tff(786,plain,
% 0.68/0.71 (~hskp12),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[785, 499, 242, 236])).
% 0.68/0.71 tff(787,plain,
% 0.68/0.71 ((hskp14 | hskp12 | hskp11) <=> (hskp14 | hskp12 | hskp11)),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(788,plain,
% 0.68/0.71 (((hskp14 | hskp12) | hskp11) <=> (hskp14 | hskp12 | hskp11)),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(789,plain,
% 0.68/0.71 ((hskp14 | hskp12) <=> (hskp14 | hskp12)),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(790,plain,
% 0.68/0.71 (((hskp14 | hskp12) | hskp11) <=> ((hskp14 | hskp12) | hskp11)),
% 0.68/0.71 inference(monotonicity,[status(thm)],[789])).
% 0.68/0.71 tff(791,plain,
% 0.68/0.71 (((hskp14 | hskp12) | hskp11) <=> (hskp14 | hskp12 | hskp11)),
% 0.68/0.71 inference(transitivity,[status(thm)],[790, 788])).
% 0.68/0.71 tff(792,axiom,((hskp14 | hskp12) | hskp11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 0.68/0.71 tff(793,plain,
% 0.68/0.71 (hskp14 | hskp12 | hskp11),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[792, 791])).
% 0.68/0.71 tff(794,plain,
% 0.68/0.71 (hskp14 | hskp12 | hskp11),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[793, 787])).
% 0.68/0.71 tff(795,plain,
% 0.68/0.71 (hskp14 | hskp12 | hskp11),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[794, 787])).
% 0.68/0.71 tff(796,plain,
% 0.68/0.71 (hskp14 | hskp12 | hskp11),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[795, 787])).
% 0.68/0.71 tff(797,plain,
% 0.68/0.71 (hskp14 | hskp12 | hskp11),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[796, 787])).
% 0.68/0.71 tff(798,plain,
% 0.68/0.71 (hskp14 | hskp12 | hskp11),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[797, 787])).
% 0.68/0.71 tff(799,plain,
% 0.68/0.71 (hskp14 | hskp12 | hskp11),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[798, 787])).
% 0.68/0.71 tff(800,plain,
% 0.68/0.71 (hskp14 | hskp12 | hskp11),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[799, 787])).
% 0.68/0.71 tff(801,plain,
% 0.68/0.71 (hskp14),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[800, 786, 738])).
% 0.68/0.71 tff(802,plain,
% 0.68/0.71 (~c3_1(a115)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[126, 801])).
% 0.68/0.71 tff(803,plain,
% 0.68/0.71 (~c2_1(a115)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[132, 801])).
% 0.68/0.71 tff(804,plain,
% 0.68/0.71 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a115))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a115))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(805,plain,
% 0.68/0.71 ((hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a115) | c2_1(a115) | c1_1(a115)) <=> (hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a115))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(806,plain,
% 0.68/0.71 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a115) | c2_1(a115) | c1_1(a115))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a115)))),
% 0.68/0.71 inference(monotonicity,[status(thm)],[805])).
% 0.68/0.71 tff(807,plain,
% 0.68/0.71 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a115) | c2_1(a115) | c1_1(a115))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a115))),
% 0.68/0.71 inference(transitivity,[status(thm)],[806, 804])).
% 0.68/0.71 tff(808,plain,
% 0.68/0.71 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c3_1(a115) | c2_1(a115) | c1_1(a115))),
% 0.68/0.71 inference(quant_inst,[status(thm)],[])).
% 0.68/0.71 tff(809,plain,
% 0.68/0.71 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c0_1(a165)) | c1_1(a115)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[808, 807])).
% 0.68/0.71 tff(810,plain,
% 0.68/0.71 (c1_1(a115)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[809, 113, 23, 487, 498, 803, 802, 326, 552])).
% 0.68/0.71 tff(811,plain,
% 0.68/0.71 (c0_1(a115)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[143, 801])).
% 0.68/0.71 tff(812,plain,
% 0.68/0.71 (((~hskp29) | c1_1(a165)) <=> ((~hskp29) | c1_1(a165))),
% 0.68/0.71 inference(rewrite,[status(thm)],[])).
% 0.68/0.71 tff(813,axiom,((~hskp29) | c1_1(a165)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.68/0.71 tff(814,plain,
% 0.68/0.71 ((~hskp29) | c1_1(a165)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[813, 812])).
% 0.68/0.71 tff(815,plain,
% 0.68/0.71 ((~hskp29) | c1_1(a165)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[814, 812])).
% 0.68/0.71 tff(816,plain,
% 0.68/0.71 ((~hskp29) | c1_1(a165)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[815, 812])).
% 0.68/0.71 tff(817,plain,
% 0.68/0.71 ((~hskp29) | c1_1(a165)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[816, 812])).
% 0.68/0.71 tff(818,plain,
% 0.68/0.71 ((~hskp29) | c1_1(a165)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[817, 812])).
% 0.68/0.71 tff(819,plain,
% 0.68/0.71 ((~hskp29) | c1_1(a165)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[818, 812])).
% 0.68/0.71 tff(820,plain,
% 0.68/0.71 ((~hskp29) | c1_1(a165)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[819, 812])).
% 0.68/0.71 tff(821,plain,
% 0.68/0.71 ((~hskp29) | c1_1(a165)),
% 0.68/0.71 inference(modus_ponens,[status(thm)],[820, 812])).
% 0.68/0.71 tff(822,plain,
% 0.68/0.71 (c1_1(a165)),
% 0.68/0.71 inference(unit_resolution,[status(thm)],[821, 476])).
% 0.68/0.71 tff(823,plain,
% 0.68/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a115) | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c1_1(a165)) | (~c0_1(a165)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c1_1(a115)) | (~c0_1(a115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a115) | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c1_1(a165)) | (~c0_1(a165)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c1_1(a115)) | (~c0_1(a115)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(824,plain,
% 0.68/0.72 (((~ndr1_0) | (~c3_1(a165)) | (~c0_1(a165)) | (~c1_1(a165)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115))) <=> (c2_1(a115) | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c1_1(a165)) | (~c0_1(a165)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c1_1(a115)) | (~c0_1(a115)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(825,plain,
% 0.68/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a165)) | (~c0_1(a165)) | (~c1_1(a165)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a115) | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c1_1(a165)) | (~c0_1(a165)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c1_1(a115)) | (~c0_1(a115))))),
% 0.68/0.72 inference(monotonicity,[status(thm)],[824])).
% 0.68/0.72 tff(826,plain,
% 0.68/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a165)) | (~c0_1(a165)) | (~c1_1(a165)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a115) | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c1_1(a165)) | (~c0_1(a165)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c1_1(a115)) | (~c0_1(a115)))),
% 0.68/0.72 inference(transitivity,[status(thm)],[825, 823])).
% 0.68/0.72 tff(827,plain,
% 0.68/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a165)) | (~c0_1(a165)) | (~c1_1(a165)) | c2_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115)))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(828,plain,
% 0.68/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a115) | c2_1(a106) | (~ndr1_0) | (~c3_1(a165)) | (~c1_1(a165)) | (~c0_1(a165)) | (~c3_1(a106)) | (~c1_1(a106)) | (~c1_1(a115)) | (~c0_1(a115))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[827, 826])).
% 0.68/0.72 tff(829,plain,
% 0.68/0.72 ($false),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[828, 113, 822, 498, 811, 236, 499, 803, 242, 11, 552, 810])).
% 0.68/0.72 tff(830,plain,(hskp3 | hskp20), inference(lemma,lemma(discharge,[]))).
% 0.68/0.72 tff(831,plain,
% 0.68/0.72 (hskp3),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[830, 22])).
% 0.68/0.72 tff(832,plain,
% 0.68/0.72 (~c3_1(a99)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[423, 831])).
% 0.68/0.72 tff(833,plain,
% 0.68/0.72 (~c1_1(a99)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[429, 831])).
% 0.68/0.72 tff(834,plain,
% 0.68/0.72 (c2_1(a99)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[440, 831])).
% 0.68/0.72 tff(835,plain,
% 0.68/0.72 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c0_1(a99)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c0_1(a99)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(836,plain,
% 0.68/0.72 (((~ndr1_0) | c1_1(a99) | (~c2_1(a99)) | (~c0_1(a99)) | c3_1(a99) | c1_1(a99) | (~c0_1(a99))) <=> (c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c0_1(a99)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(837,plain,
% 0.68/0.72 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c1_1(a99) | (~c2_1(a99)) | (~c0_1(a99)) | c3_1(a99) | c1_1(a99) | (~c0_1(a99)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c0_1(a99))))),
% 0.68/0.72 inference(monotonicity,[status(thm)],[836])).
% 0.68/0.72 tff(838,plain,
% 0.68/0.72 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c1_1(a99) | (~c2_1(a99)) | (~c0_1(a99)) | c3_1(a99) | c1_1(a99) | (~c0_1(a99)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c0_1(a99)))),
% 0.68/0.72 inference(transitivity,[status(thm)],[837, 835])).
% 0.68/0.72 tff(839,plain,
% 0.68/0.72 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c1_1(a99) | (~c2_1(a99)) | (~c0_1(a99)) | c3_1(a99) | c1_1(a99) | (~c0_1(a99)))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(840,plain,
% 0.68/0.72 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | (~c0_1(a99))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[839, 838])).
% 0.68/0.72 tff(841,plain,
% 0.68/0.72 (~c0_1(a99)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[840, 113, 834, 833, 832, 21])).
% 0.68/0.72 tff(842,plain,
% 0.68/0.72 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.68/0.72 inference(bind,[status(th)],[])).
% 0.68/0.72 tff(843,plain,
% 0.68/0.72 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.72 inference(quant_intro,[status(thm)],[842])).
% 0.68/0.72 tff(844,plain,
% 0.68/0.72 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(845,plain,
% 0.68/0.72 (^[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))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.68/0.72 inference(bind,[status(th)],[])).
% 0.68/0.72 tff(846,plain,
% 0.68/0.72 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.72 inference(quant_intro,[status(thm)],[845])).
% 0.68/0.72 tff(847,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 0.68/0.72 tff(848,plain,
% 0.68/0.72 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[847, 846])).
% 0.68/0.72 tff(849,plain,
% 0.68/0.72 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[848, 844])).
% 0.68/0.72 tff(850,plain,(
% 0.68/0.72 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.72 inference(skolemize,[status(sab)],[849])).
% 0.68/0.72 tff(851,plain,
% 0.68/0.72 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[850, 843])).
% 0.68/0.72 tff(852,plain,
% 0.68/0.72 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a99) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a99) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(853,plain,
% 0.68/0.72 ((hskp10 | (~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99))) <=> (hskp10 | c1_1(a99) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(854,plain,
% 0.68/0.72 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c1_1(a99) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99))))),
% 0.68/0.72 inference(monotonicity,[status(thm)],[853])).
% 0.68/0.72 tff(855,plain,
% 0.68/0.72 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a99) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)))),
% 0.68/0.72 inference(transitivity,[status(thm)],[854, 852])).
% 0.68/0.72 tff(856,plain,
% 0.68/0.72 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99)))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(857,plain,
% 0.68/0.72 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c1_1(a99) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[856, 855])).
% 0.68/0.72 tff(858,plain,
% 0.68/0.72 (hskp10),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[857, 113, 834, 833, 832, 851, 841])).
% 0.68/0.72 tff(859,plain,
% 0.68/0.72 (~c2_1(a106)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[241, 858])).
% 0.68/0.72 tff(860,plain,
% 0.68/0.72 (c3_1(a106)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[297, 858])).
% 0.68/0.72 tff(861,plain,
% 0.68/0.72 (c1_1(a106)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[235, 858])).
% 0.68/0.72 tff(862,plain,
% 0.68/0.72 (~c0_1(a106)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[305, 113, 861, 860, 859, 11])).
% 0.68/0.72 tff(863,plain,
% 0.68/0.72 (~hskp12),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[785, 860, 859, 861])).
% 0.68/0.72 tff(864,plain,
% 0.68/0.72 (^[U: $i] : refl((hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))),
% 0.68/0.72 inference(bind,[status(th)],[])).
% 0.68/0.72 tff(865,plain,
% 0.68/0.72 (![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.68/0.72 inference(quant_intro,[status(thm)],[864])).
% 0.68/0.72 tff(866,plain,
% 0.68/0.72 (![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(867,plain,
% 0.68/0.72 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp12))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp8) <=> ((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp8))), rewrite(((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp8) <=> (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp8) <=> (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.68/0.72 inference(bind,[status(th)],[])).
% 0.68/0.72 tff(868,plain,
% 0.68/0.72 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp8) <=> ![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.68/0.72 inference(quant_intro,[status(thm)],[867])).
% 0.68/0.72 tff(869,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp12) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 0.68/0.72 tff(870,plain,
% 0.68/0.72 (![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[869, 868])).
% 0.68/0.72 tff(871,plain,
% 0.68/0.72 (![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[870, 866])).
% 0.68/0.72 tff(872,plain,(
% 0.68/0.72 ![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.68/0.72 inference(skolemize,[status(sab)],[871])).
% 0.68/0.72 tff(873,plain,
% 0.68/0.72 (![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[872, 865])).
% 0.68/0.72 tff(874,plain,
% 0.68/0.72 (((~![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c1_1(a165)))) <=> ((~![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp8 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c1_1(a165)))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(875,plain,
% 0.68/0.72 ((~![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c1_1(a165)))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(876,plain,
% 0.68/0.72 ((~![U: $i] : (hskp12 | hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp8 | (~ndr1_0) | (~c3_1(a165)) | (~c2_1(a165)) | (~c1_1(a165))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[875, 874])).
% 0.68/0.72 tff(877,plain,
% 0.68/0.72 (hskp12 | hskp8),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[876, 113, 822, 487, 498, 873])).
% 0.68/0.72 tff(878,plain,
% 0.68/0.72 (hskp8),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[877, 863])).
% 0.68/0.72 tff(879,plain,
% 0.68/0.72 (~c2_1(a104)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[575, 878])).
% 0.68/0.72 tff(880,plain,
% 0.68/0.72 (~c0_1(a104)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[610, 878])).
% 0.68/0.72 tff(881,plain,
% 0.68/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a104) | c2_1(a104) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c1_1(a104) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a104) | c2_1(a104) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c1_1(a104) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(882,plain,
% 0.68/0.72 (((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a104) | c1_1(a104) | c0_1(a104)) <=> (c0_1(a104) | c2_1(a104) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c1_1(a104) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(883,plain,
% 0.68/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a104) | c1_1(a104) | c0_1(a104))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a104) | c2_1(a104) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c1_1(a104) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106)))),
% 0.68/0.72 inference(monotonicity,[status(thm)],[882])).
% 0.68/0.72 tff(884,plain,
% 0.68/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a104) | c1_1(a104) | c0_1(a104))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a104) | c2_1(a104) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c1_1(a104) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.72 inference(transitivity,[status(thm)],[883, 881])).
% 0.68/0.72 tff(885,plain,
% 0.68/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a104) | c1_1(a104) | c0_1(a104))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(886,plain,
% 0.68/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a104) | c2_1(a104) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c1_1(a104) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106)),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[885, 884])).
% 0.68/0.72 tff(887,plain,
% 0.68/0.72 (c1_1(a104)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[886, 113, 861, 860, 834, 880, 879, 833, 832, 316, 862])).
% 0.68/0.72 tff(888,plain,
% 0.68/0.72 (~c3_1(a104)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[569, 878])).
% 0.68/0.72 tff(889,plain,
% 0.68/0.72 (hskp6),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[617, 113, 861, 859, 880, 879, 888, 605, 862])).
% 0.68/0.73 tff(890,plain,
% 0.68/0.73 (~c3_1(a102)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[623, 889])).
% 0.68/0.73 tff(891,plain,
% 0.68/0.73 (c2_1(a102)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[634, 889])).
% 0.68/0.73 tff(892,plain,
% 0.68/0.73 (c1_1(a102)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[645, 889])).
% 0.68/0.73 tff(893,plain,
% 0.68/0.73 (hskp5),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[652, 113, 892, 891, 879, 888, 890, 594, 887])).
% 0.68/0.73 tff(894,plain,
% 0.68/0.73 (~c2_1(a101)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[659, 893])).
% 0.68/0.73 tff(895,plain,
% 0.68/0.73 (c3_1(a101)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[670, 893])).
% 0.68/0.73 tff(896,plain,
% 0.68/0.73 (~c0_1(a101)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[677, 113, 861, 860, 895, 859, 880, 888, 894, 354, 887])).
% 0.68/0.73 tff(897,plain,
% 0.68/0.73 (~c1_1(a101)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[683, 893])).
% 0.68/0.73 tff(898,plain,
% 0.68/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a101) | c2_1(a101) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a101) | c2_1(a101) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(899,plain,
% 0.68/0.73 (((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101)) <=> (c1_1(a101) | c2_1(a101) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(900,plain,
% 0.68/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a101) | c2_1(a101) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106)))),
% 0.68/0.73 inference(monotonicity,[status(thm)],[899])).
% 0.68/0.73 tff(901,plain,
% 0.68/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a101) | c2_1(a101) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106))),
% 0.68/0.73 inference(transitivity,[status(thm)],[900, 898])).
% 0.68/0.73 tff(902,plain,
% 0.68/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a99) | c1_1(a99) | (~c2_1(a99)) | c0_1(a106) | (~c1_1(a106)) | (~c3_1(a106)) | c2_1(a101) | c1_1(a101) | c0_1(a101))),
% 0.68/0.73 inference(quant_inst,[status(thm)],[])).
% 0.68/0.73 tff(903,plain,
% 0.68/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a101) | c2_1(a101) | c1_1(a99) | c3_1(a99) | (~ndr1_0) | (~c2_1(a99)) | c0_1(a101) | (~c3_1(a106)) | (~c1_1(a106)) | c0_1(a106)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[902, 901])).
% 0.68/0.73 tff(904,plain,
% 0.68/0.73 ($false),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[903, 113, 861, 860, 834, 897, 894, 833, 832, 316, 862, 896])).
% 0.68/0.73 tff(905,plain,(hskp20), inference(lemma,lemma(discharge,[]))).
% 0.68/0.73 tff(906,plain,
% 0.68/0.73 (((~hskp20) | (~c2_1(a133))) <=> ((~hskp20) | (~c2_1(a133)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(907,plain,
% 0.68/0.73 (((~c2_1(a133)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a133)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(908,axiom,((~c2_1(a133)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.68/0.73 tff(909,plain,
% 0.68/0.73 ((~hskp20) | (~c2_1(a133))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[908, 907])).
% 0.68/0.73 tff(910,plain,
% 0.68/0.73 ((~hskp20) | (~c2_1(a133))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[909, 906])).
% 0.68/0.73 tff(911,plain,
% 0.68/0.73 (~c2_1(a133)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[910, 905])).
% 0.68/0.73 tff(912,plain,
% 0.68/0.73 (((~hskp20) | c3_1(a133)) <=> ((~hskp20) | c3_1(a133))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(913,axiom,((~hskp20) | c3_1(a133)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 0.68/0.73 tff(914,plain,
% 0.68/0.73 ((~hskp20) | c3_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[913, 912])).
% 0.68/0.73 tff(915,plain,
% 0.68/0.73 ((~hskp20) | c3_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[914, 912])).
% 0.68/0.73 tff(916,plain,
% 0.68/0.73 ((~hskp20) | c3_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[915, 912])).
% 0.68/0.73 tff(917,plain,
% 0.68/0.73 ((~hskp20) | c3_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[916, 912])).
% 0.68/0.73 tff(918,plain,
% 0.68/0.73 ((~hskp20) | c3_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[917, 912])).
% 0.68/0.73 tff(919,plain,
% 0.68/0.73 ((~hskp20) | c3_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[918, 912])).
% 0.68/0.73 tff(920,plain,
% 0.68/0.73 ((~hskp20) | c3_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[919, 912])).
% 0.68/0.73 tff(921,plain,
% 0.68/0.73 ((~hskp20) | c3_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[920, 912])).
% 0.68/0.73 tff(922,plain,
% 0.68/0.73 (c3_1(a133)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[921, 905])).
% 0.68/0.73 tff(923,plain,
% 0.68/0.73 (((~hskp20) | c0_1(a133)) <=> ((~hskp20) | c0_1(a133))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(924,axiom,((~hskp20) | c0_1(a133)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.68/0.73 tff(925,plain,
% 0.68/0.73 ((~hskp20) | c0_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[924, 923])).
% 0.68/0.73 tff(926,plain,
% 0.68/0.73 ((~hskp20) | c0_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[925, 923])).
% 0.68/0.73 tff(927,plain,
% 0.68/0.73 ((~hskp20) | c0_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[926, 923])).
% 0.68/0.73 tff(928,plain,
% 0.68/0.73 ((~hskp20) | c0_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[927, 923])).
% 0.68/0.73 tff(929,plain,
% 0.68/0.73 ((~hskp20) | c0_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[928, 923])).
% 0.68/0.73 tff(930,plain,
% 0.68/0.73 ((~hskp20) | c0_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[929, 923])).
% 0.68/0.73 tff(931,plain,
% 0.68/0.73 ((~hskp20) | c0_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[930, 923])).
% 0.68/0.73 tff(932,plain,
% 0.68/0.73 ((~hskp20) | c0_1(a133)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[931, 923])).
% 0.68/0.73 tff(933,plain,
% 0.68/0.73 (c0_1(a133)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[932, 905])).
% 0.68/0.73 tff(934,plain,
% 0.68/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(935,plain,
% 0.68/0.73 (((~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c1_1(a133)) | c2_1(a133) | (~c1_1(a133)) | (~c3_1(a133)) | c2_1(a133) | (~c0_1(a133)) | (~c1_1(a133))) <=> (c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(936,plain,
% 0.68/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c1_1(a133)) | c2_1(a133) | (~c1_1(a133)) | (~c3_1(a133)) | c2_1(a133) | (~c0_1(a133)) | (~c1_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | (c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133))))),
% 0.68/0.73 inference(monotonicity,[status(thm)],[935])).
% 0.68/0.73 tff(937,plain,
% 0.68/0.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c1_1(a133)) | c2_1(a133) | (~c1_1(a133)) | (~c3_1(a133)) | c2_1(a133) | (~c0_1(a133)) | (~c1_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133)))),
% 0.68/0.73 inference(transitivity,[status(thm)],[936, 934])).
% 0.68/0.73 tff(938,plain,
% 0.68/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c3_1(a133)) | (~c0_1(a133)) | (~c1_1(a133)) | c2_1(a133) | (~c1_1(a133)) | (~c3_1(a133)) | c2_1(a133) | (~c0_1(a133)) | (~c1_1(a133)))),
% 0.68/0.73 inference(quant_inst,[status(thm)],[])).
% 0.68/0.73 tff(939,plain,
% 0.68/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c1_1(W)))) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | (~c1_1(a133)) | (~c0_1(a133))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[938, 937])).
% 0.68/0.73 tff(940,plain,
% 0.68/0.73 (~c1_1(a133)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[939, 113, 933, 922, 911, 11])).
% 0.68/0.73 tff(941,plain,
% 0.68/0.73 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.68/0.73 inference(bind,[status(th)],[])).
% 0.68/0.73 tff(942,plain,
% 0.68/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.68/0.73 inference(quant_intro,[status(thm)],[941])).
% 0.68/0.73 tff(943,plain,
% 0.68/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(944,plain,
% 0.68/0.73 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.68/0.73 inference(bind,[status(th)],[])).
% 0.68/0.73 tff(945,plain,
% 0.68/0.73 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.68/0.73 inference(quant_intro,[status(thm)],[944])).
% 0.68/0.73 tff(946,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.68/0.73 tff(947,plain,
% 0.68/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[946, 945])).
% 0.68/0.73 tff(948,plain,
% 0.68/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[947, 943])).
% 0.68/0.73 tff(949,plain,(
% 0.68/0.73 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.68/0.73 inference(skolemize,[status(sab)],[948])).
% 0.68/0.73 tff(950,plain,
% 0.68/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[949, 942])).
% 0.68/0.73 tff(951,plain,
% 0.68/0.73 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.68/0.73 inference(bind,[status(th)],[])).
% 0.68/0.73 tff(952,plain,
% 0.68/0.73 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.68/0.73 inference(quant_intro,[status(thm)],[951])).
% 0.68/0.73 tff(953,plain,
% 0.68/0.73 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(954,plain,
% 0.68/0.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.68/0.73 inference(bind,[status(th)],[])).
% 0.68/0.73 tff(955,plain,
% 0.68/0.73 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.68/0.73 inference(quant_intro,[status(thm)],[954])).
% 0.68/0.73 tff(956,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 0.68/0.73 tff(957,plain,
% 0.68/0.73 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[956, 955])).
% 0.68/0.73 tff(958,plain,
% 0.68/0.73 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[957, 953])).
% 0.68/0.73 tff(959,plain,(
% 0.68/0.73 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.68/0.73 inference(skolemize,[status(sab)],[958])).
% 0.68/0.73 tff(960,plain,
% 0.68/0.73 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[959, 952])).
% 0.68/0.73 tff(961,plain,
% 0.68/0.73 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(962,plain,
% 0.68/0.73 ((hskp15 | (~ndr1_0) | c2_1(a133) | (~c3_1(a133)) | (~c0_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133))) <=> (hskp15 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(963,plain,
% 0.68/0.73 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a133) | (~c3_1(a133)) | (~c0_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133))))),
% 0.68/0.73 inference(monotonicity,[status(thm)],[962])).
% 0.68/0.73 tff(964,plain,
% 0.68/0.73 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a133) | (~c3_1(a133)) | (~c0_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.68/0.73 inference(transitivity,[status(thm)],[963, 961])).
% 0.68/0.73 tff(965,plain,
% 0.68/0.73 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a133) | (~c3_1(a133)) | (~c0_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))),
% 0.68/0.73 inference(quant_inst,[status(thm)],[])).
% 0.68/0.73 tff(966,plain,
% 0.68/0.73 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp15 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133))),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[965, 964])).
% 0.68/0.73 tff(967,plain,
% 0.68/0.73 (hskp15),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[966, 113, 933, 922, 911, 960, 940])).
% 0.68/0.73 tff(968,plain,
% 0.68/0.73 (((~hskp15) | c3_1(a116)) <=> ((~hskp15) | c3_1(a116))),
% 0.68/0.73 inference(rewrite,[status(thm)],[])).
% 0.68/0.73 tff(969,axiom,((~hskp15) | c3_1(a116)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 0.68/0.73 tff(970,plain,
% 0.68/0.73 ((~hskp15) | c3_1(a116)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[969, 968])).
% 0.68/0.73 tff(971,plain,
% 0.68/0.73 ((~hskp15) | c3_1(a116)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[970, 968])).
% 0.68/0.73 tff(972,plain,
% 0.68/0.73 ((~hskp15) | c3_1(a116)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[971, 968])).
% 0.68/0.73 tff(973,plain,
% 0.68/0.73 ((~hskp15) | c3_1(a116)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[972, 968])).
% 0.68/0.73 tff(974,plain,
% 0.68/0.73 ((~hskp15) | c3_1(a116)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[973, 968])).
% 0.68/0.73 tff(975,plain,
% 0.68/0.73 ((~hskp15) | c3_1(a116)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[974, 968])).
% 0.68/0.73 tff(976,plain,
% 0.68/0.73 ((~hskp15) | c3_1(a116)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[975, 968])).
% 0.68/0.73 tff(977,plain,
% 0.68/0.73 ((~hskp15) | c3_1(a116)),
% 0.68/0.73 inference(modus_ponens,[status(thm)],[976, 968])).
% 0.68/0.73 tff(978,plain,
% 0.68/0.73 (c3_1(a116)),
% 0.68/0.73 inference(unit_resolution,[status(thm)],[977, 967])).
% 0.68/0.74 tff(979,plain,
% 0.68/0.74 (((~hskp15) | c1_1(a116)) <=> ((~hskp15) | c1_1(a116))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(980,axiom,((~hskp15) | c1_1(a116)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 0.68/0.74 tff(981,plain,
% 0.68/0.74 ((~hskp15) | c1_1(a116)),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[980, 979])).
% 0.68/0.74 tff(982,plain,
% 0.68/0.74 ((~hskp15) | c1_1(a116)),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[981, 979])).
% 0.68/0.74 tff(983,plain,
% 0.68/0.74 ((~hskp15) | c1_1(a116)),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[982, 979])).
% 0.68/0.74 tff(984,plain,
% 0.68/0.74 ((~hskp15) | c1_1(a116)),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[983, 979])).
% 0.68/0.74 tff(985,plain,
% 0.68/0.74 ((~hskp15) | c1_1(a116)),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[984, 979])).
% 0.68/0.74 tff(986,plain,
% 0.68/0.74 ((~hskp15) | c1_1(a116)),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[985, 979])).
% 0.68/0.74 tff(987,plain,
% 0.68/0.74 ((~hskp15) | c1_1(a116)),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[986, 979])).
% 0.68/0.74 tff(988,plain,
% 0.68/0.74 ((~hskp15) | c1_1(a116)),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[987, 979])).
% 0.68/0.74 tff(989,plain,
% 0.68/0.74 (c1_1(a116)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[988, 967])).
% 0.68/0.74 tff(990,plain,
% 0.68/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a133) | (~ndr1_0) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a116) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a133) | (~ndr1_0) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a116) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(991,plain,
% 0.68/0.74 (((~ndr1_0) | c2_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133))) <=> (c2_1(a133) | (~ndr1_0) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a116) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(992,plain,
% 0.68/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a133) | (~ndr1_0) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a116) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133))))),
% 0.68/0.74 inference(monotonicity,[status(thm)],[991])).
% 0.68/0.74 tff(993,plain,
% 0.68/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a133) | (~ndr1_0) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a116) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.68/0.74 inference(transitivity,[status(thm)],[992, 990])).
% 0.68/0.74 tff(994,plain,
% 0.68/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c2_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))),
% 0.68/0.74 inference(quant_inst,[status(thm)],[])).
% 0.68/0.74 tff(995,plain,
% 0.68/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a133) | (~ndr1_0) | (~c3_1(a116)) | (~c1_1(a116)) | c2_1(a116) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[994, 993])).
% 0.68/0.74 tff(996,plain,
% 0.68/0.74 ($false),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[995, 113, 933, 922, 989, 978, 911, 950, 940, 1])).
% 0.68/0.74 tff(997,plain,(c2_1(a116)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.74 tff(998,assumption,(hskp6), introduced(assumption)).
% 0.68/0.74 tff(999,plain,
% 0.68/0.74 (~c3_1(a102)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[623, 998])).
% 0.68/0.74 tff(1000,plain,
% 0.68/0.74 (c1_1(a102)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[645, 998])).
% 0.68/0.74 tff(1001,plain,
% 0.68/0.74 (c2_1(a102)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[634, 998])).
% 0.68/0.74 tff(1002,assumption,(c2_1(a116)), introduced(assumption)).
% 0.68/0.74 tff(1003,assumption,(~c3_1(a102)), introduced(assumption)).
% 0.68/0.74 tff(1004,plain,
% 0.68/0.74 (((~hskp15) | (~c0_1(a116))) <=> ((~hskp15) | (~c0_1(a116)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(1005,plain,
% 0.68/0.74 (((~c0_1(a116)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a116)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(1006,axiom,((~c0_1(a116)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.68/0.74 tff(1007,plain,
% 0.68/0.74 ((~hskp15) | (~c0_1(a116))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[1006, 1005])).
% 0.68/0.74 tff(1008,plain,
% 0.68/0.74 ((~hskp15) | (~c0_1(a116))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[1007, 1004])).
% 0.68/0.74 tff(1009,plain,
% 0.68/0.74 (~c0_1(a116)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[1008, 967])).
% 0.68/0.74 tff(1010,assumption,(c2_1(a102)), introduced(assumption)).
% 0.68/0.74 tff(1011,plain,
% 0.68/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a116) | c3_1(a102) | (~ndr1_0) | c0_1(a102) | (~c2_1(a102)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c3_1(a102) | (~ndr1_0) | c0_1(a102) | (~c2_1(a102)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(1012,plain,
% 0.68/0.74 (((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a102) | c0_1(a102) | (~c2_1(a102))) <=> (c0_1(a116) | c3_1(a102) | (~ndr1_0) | c0_1(a102) | (~c2_1(a102)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(1013,plain,
% 0.68/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a102) | c0_1(a102) | (~c2_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a116) | c3_1(a102) | (~ndr1_0) | c0_1(a102) | (~c2_1(a102)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116))))),
% 0.68/0.74 inference(monotonicity,[status(thm)],[1012])).
% 0.68/0.74 tff(1014,plain,
% 0.68/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a102) | c0_1(a102) | (~c2_1(a102)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c3_1(a102) | (~ndr1_0) | c0_1(a102) | (~c2_1(a102)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.68/0.74 inference(transitivity,[status(thm)],[1013, 1011])).
% 0.68/0.74 tff(1015,plain,
% 0.68/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a102) | c0_1(a102) | (~c2_1(a102)))),
% 0.68/0.74 inference(quant_inst,[status(thm)],[])).
% 0.68/0.74 tff(1016,plain,
% 0.68/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c3_1(a102) | (~ndr1_0) | c0_1(a102) | (~c2_1(a102)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 0.68/0.74 tff(1017,plain,
% 0.68/0.74 (c0_1(a102) | (~c2_1(a116))),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[1016, 113, 989, 978, 1010, 1009, 1003, 695])).
% 0.68/0.74 tff(1018,plain,
% 0.68/0.74 (c0_1(a102)),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[1017, 1002])).
% 0.68/0.74 tff(1019,plain,
% 0.68/0.74 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 0.68/0.74 inference(bind,[status(th)],[])).
% 0.68/0.74 tff(1020,plain,
% 0.68/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.68/0.74 inference(quant_intro,[status(thm)],[1019])).
% 0.68/0.74 tff(1021,plain,
% 0.68/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(1022,plain,
% 0.68/0.74 (^[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))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 0.68/0.74 inference(bind,[status(th)],[])).
% 0.68/0.74 tff(1023,plain,
% 0.68/0.74 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.68/0.74 inference(quant_intro,[status(thm)],[1022])).
% 0.68/0.74 tff(1024,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 0.68/0.74 tff(1025,plain,
% 0.68/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 0.68/0.74 tff(1026,plain,
% 0.68/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[1025, 1021])).
% 0.68/0.74 tff(1027,plain,(
% 0.68/0.74 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.68/0.74 inference(skolemize,[status(sab)],[1026])).
% 0.68/0.74 tff(1028,plain,
% 0.68/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[1027, 1020])).
% 0.68/0.74 tff(1029,assumption,(c1_1(a102)), introduced(assumption)).
% 0.68/0.74 tff(1030,plain,
% 0.68/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a133) | c0_1(a116) | (~ndr1_0) | (~c0_1(a102)) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a116)) | (~c2_1(a116)) | (~c3_1(a133)) | (~c0_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a133) | c0_1(a116) | (~ndr1_0) | (~c0_1(a102)) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a116)) | (~c2_1(a116)) | (~c3_1(a133)) | (~c0_1(a133)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(1031,plain,
% 0.68/0.74 (((~ndr1_0) | (~c2_1(a102)) | (~c0_1(a102)) | (~c1_1(a102)) | c2_1(a133) | (~c0_1(a133)) | (~c3_1(a133)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116))) <=> (c2_1(a133) | c0_1(a116) | (~ndr1_0) | (~c0_1(a102)) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a116)) | (~c2_1(a116)) | (~c3_1(a133)) | (~c0_1(a133)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(1032,plain,
% 0.68/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a102)) | (~c0_1(a102)) | (~c1_1(a102)) | c2_1(a133) | (~c0_1(a133)) | (~c3_1(a133)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c2_1(a133) | c0_1(a116) | (~ndr1_0) | (~c0_1(a102)) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a116)) | (~c2_1(a116)) | (~c3_1(a133)) | (~c0_1(a133))))),
% 0.68/0.74 inference(monotonicity,[status(thm)],[1031])).
% 0.68/0.74 tff(1033,plain,
% 0.68/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a102)) | (~c0_1(a102)) | (~c1_1(a102)) | c2_1(a133) | (~c0_1(a133)) | (~c3_1(a133)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a133) | c0_1(a116) | (~ndr1_0) | (~c0_1(a102)) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a116)) | (~c2_1(a116)) | (~c3_1(a133)) | (~c0_1(a133)))),
% 0.68/0.74 inference(transitivity,[status(thm)],[1032, 1030])).
% 0.68/0.74 tff(1034,plain,
% 0.68/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a102)) | (~c0_1(a102)) | (~c1_1(a102)) | c2_1(a133) | (~c0_1(a133)) | (~c3_1(a133)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.68/0.74 inference(quant_inst,[status(thm)],[])).
% 0.68/0.74 tff(1035,plain,
% 0.68/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c2_1(a133) | c0_1(a116) | (~ndr1_0) | (~c0_1(a102)) | (~c1_1(a102)) | (~c2_1(a102)) | (~c1_1(a116)) | (~c2_1(a116)) | (~c3_1(a133)) | (~c0_1(a133))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 0.68/0.74 tff(1036,plain,
% 0.68/0.74 ((~c0_1(a102)) | (~c2_1(a116))),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[1035, 113, 933, 922, 989, 1029, 1010, 911, 1009, 1028])).
% 0.68/0.74 tff(1037,plain,
% 0.68/0.74 ($false),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[1036, 1018, 1002])).
% 0.68/0.74 tff(1038,plain,((~c2_1(a116)) | (~c1_1(a102)) | (~c2_1(a102)) | c3_1(a102)), inference(lemma,lemma(discharge,[]))).
% 0.68/0.74 tff(1039,plain,
% 0.68/0.74 ($false),
% 0.68/0.74 inference(unit_resolution,[status(thm)],[1038, 1001, 1000, 997, 999])).
% 0.68/0.74 tff(1040,plain,(~hskp6), inference(lemma,lemma(discharge,[]))).
% 0.68/0.74 tff(1041,plain,
% 0.68/0.74 (^[U: $i] : refl((hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))),
% 0.68/0.74 inference(bind,[status(th)],[])).
% 0.68/0.74 tff(1042,plain,
% 0.68/0.74 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.68/0.74 inference(quant_intro,[status(thm)],[1041])).
% 0.68/0.74 tff(1043,plain,
% 0.68/0.74 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(1044,plain,
% 0.68/0.74 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp3) <=> ((hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp3))), rewrite(((hskp6 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp3) <=> (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.68/0.74 inference(bind,[status(th)],[])).
% 0.68/0.74 tff(1045,plain,
% 0.68/0.74 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp3) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.68/0.74 inference(quant_intro,[status(thm)],[1044])).
% 0.68/0.74 tff(1046,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp6) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 0.68/0.74 tff(1047,plain,
% 0.68/0.74 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 0.68/0.74 tff(1048,plain,
% 0.68/0.74 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[1047, 1043])).
% 0.68/0.74 tff(1049,plain,(
% 0.68/0.74 ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.68/0.74 inference(skolemize,[status(sab)],[1048])).
% 0.68/0.74 tff(1050,plain,
% 0.68/0.74 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))),
% 0.68/0.74 inference(modus_ponens,[status(thm)],[1049, 1042])).
% 0.68/0.74 tff(1051,plain,
% 0.68/0.74 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.68/0.74 inference(bind,[status(th)],[])).
% 0.68/0.74 tff(1052,plain,
% 0.68/0.74 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.68/0.74 inference(quant_intro,[status(thm)],[1051])).
% 0.68/0.74 tff(1053,plain,
% 0.68/0.74 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.68/0.74 inference(rewrite,[status(thm)],[])).
% 0.68/0.74 tff(1054,plain,
% 0.68/0.74 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | 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)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | 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)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.75/0.75 inference(bind,[status(th)],[])).
% 0.75/0.75 tff(1055,plain,
% 0.75/0.75 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.75/0.75 inference(quant_intro,[status(thm)],[1054])).
% 0.75/0.75 tff(1056,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 0.75/0.75 tff(1057,plain,
% 0.75/0.75 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.75/0.75 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 0.75/0.75 tff(1058,plain,
% 0.75/0.75 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.75/0.75 inference(modus_ponens,[status(thm)],[1057, 1053])).
% 0.75/0.75 tff(1059,plain,(
% 0.75/0.75 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.75/0.75 inference(skolemize,[status(sab)],[1058])).
% 0.75/0.75 tff(1060,plain,
% 0.75/0.75 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.75/0.75 inference(modus_ponens,[status(thm)],[1059, 1052])).
% 0.75/0.75 tff(1061,plain,
% 0.75/0.75 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1062,plain,
% 0.75/0.75 ((hskp14 | (~ndr1_0) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133))) <=> (hskp14 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1063,plain,
% 0.75/0.75 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133))))),
% 0.75/0.75 inference(monotonicity,[status(thm)],[1062])).
% 0.75/0.75 tff(1064,plain,
% 0.75/0.75 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133)))),
% 0.75/0.75 inference(transitivity,[status(thm)],[1063, 1061])).
% 0.75/0.75 tff(1065,plain,
% 0.75/0.75 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp14 | (~ndr1_0) | c2_1(a133) | c1_1(a133) | (~c3_1(a133)) | c2_1(a133) | c1_1(a133) | (~c0_1(a133)))),
% 0.75/0.75 inference(quant_inst,[status(thm)],[])).
% 0.75/0.75 tff(1066,plain,
% 0.75/0.75 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp14 | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)) | c1_1(a133) | (~c0_1(a133))),
% 0.75/0.75 inference(modus_ponens,[status(thm)],[1065, 1064])).
% 0.75/0.75 tff(1067,plain,
% 0.75/0.75 (hskp14),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[1066, 113, 933, 922, 911, 1060, 940])).
% 0.75/0.75 tff(1068,plain,
% 0.75/0.75 (~c2_1(a115)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[132, 1067])).
% 0.75/0.75 tff(1069,plain,
% 0.75/0.75 (c0_1(a115)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[143, 1067])).
% 0.75/0.75 tff(1070,plain,
% 0.75/0.75 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | c2_1(a115) | (~ndr1_0) | (~c1_1(a115)) | (~c0_1(a115)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c2_1(a115) | (~ndr1_0) | (~c1_1(a115)) | (~c0_1(a115)))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1071,plain,
% 0.75/0.75 ((hskp6 | hskp3 | (~ndr1_0) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115))) <=> (hskp6 | hskp3 | c2_1(a115) | (~ndr1_0) | (~c1_1(a115)) | (~c0_1(a115)))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1072,plain,
% 0.75/0.75 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | c2_1(a115) | (~ndr1_0) | (~c1_1(a115)) | (~c0_1(a115))))),
% 0.75/0.75 inference(monotonicity,[status(thm)],[1071])).
% 0.75/0.75 tff(1073,plain,
% 0.75/0.75 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c2_1(a115) | (~ndr1_0) | (~c1_1(a115)) | (~c0_1(a115)))),
% 0.75/0.75 inference(transitivity,[status(thm)],[1072, 1070])).
% 0.75/0.75 tff(1074,plain,
% 0.75/0.75 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c2_1(a115) | (~c0_1(a115)) | (~c1_1(a115)))),
% 0.75/0.75 inference(quant_inst,[status(thm)],[])).
% 0.75/0.75 tff(1075,plain,
% 0.75/0.75 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c2_1(a115) | (~ndr1_0) | (~c1_1(a115)) | (~c0_1(a115))),
% 0.75/0.75 inference(modus_ponens,[status(thm)],[1074, 1073])).
% 0.75/0.75 tff(1076,plain,
% 0.75/0.75 (hskp6 | hskp3 | (~c1_1(a115))),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[1075, 113, 1069, 1068, 1050])).
% 0.75/0.75 tff(1077,plain,
% 0.75/0.75 (~c1_1(a115)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[1076, 23, 1040])).
% 0.75/0.75 tff(1078,plain,
% 0.75/0.75 (~c3_1(a115)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[126, 1067])).
% 0.75/0.75 tff(1079,plain,
% 0.75/0.75 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | c1_1(a115))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp1 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | c1_1(a115))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1080,plain,
% 0.75/0.75 ((hskp1 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | c1_1(a115)) <=> (hskp1 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | c1_1(a115))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1081,plain,
% 0.75/0.75 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | c1_1(a115))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | c1_1(a115)))),
% 0.75/0.75 inference(monotonicity,[status(thm)],[1080])).
% 0.75/0.75 tff(1082,plain,
% 0.75/0.75 (((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | c1_1(a115))) <=> ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp1 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | c1_1(a115))),
% 0.75/0.75 inference(transitivity,[status(thm)],[1081, 1079])).
% 0.75/0.75 tff(1083,plain,
% 0.75/0.75 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp1 | (~ndr1_0) | c3_1(a115) | c2_1(a115) | c1_1(a115))),
% 0.75/0.75 inference(quant_inst,[status(thm)],[])).
% 0.75/0.75 tff(1084,plain,
% 0.75/0.75 ((~![U: $i] : (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp1 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | c1_1(a115)),
% 0.75/0.75 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 0.75/0.75 tff(1085,plain,
% 0.75/0.75 (hskp1 | c1_1(a115)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[1084, 113, 1068, 1078, 252])).
% 0.75/0.75 tff(1086,plain,
% 0.75/0.75 (hskp1),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[1085, 1077])).
% 0.75/0.75 tff(1087,plain,
% 0.75/0.75 (c2_1(a97)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[193, 1086])).
% 0.75/0.75 tff(1088,plain,
% 0.75/0.75 (c3_1(a97)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[182, 1086])).
% 0.75/0.75 tff(1089,plain,
% 0.75/0.75 (~c1_1(a97)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[171, 1086])).
% 0.75/0.75 tff(1090,assumption,(~hskp6), introduced(assumption)).
% 0.75/0.75 tff(1091,plain,
% 0.75/0.75 (~c1_1(a115)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[1076, 1090, 23])).
% 0.75/0.75 tff(1092,assumption,(c3_1(a97)), introduced(assumption)).
% 0.75/0.75 tff(1093,assumption,(c2_1(a97)), introduced(assumption)).
% 0.75/0.75 tff(1094,plain,
% 0.75/0.75 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)) | c1_1(a115))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)) | c1_1(a115))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1095,plain,
% 0.75/0.75 ((hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a115) | c2_1(a115) | c1_1(a115)) <=> (hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)) | c1_1(a115))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1096,plain,
% 0.75/0.75 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a115) | c2_1(a115) | c1_1(a115))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)) | c1_1(a115)))),
% 0.75/0.75 inference(monotonicity,[status(thm)],[1095])).
% 0.75/0.75 tff(1097,plain,
% 0.75/0.75 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a115) | c2_1(a115) | c1_1(a115))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)) | c1_1(a115))),
% 0.75/0.75 inference(transitivity,[status(thm)],[1096, 1094])).
% 0.75/0.75 tff(1098,plain,
% 0.75/0.75 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | (hskp3 | (~ndr1_0) | (~c3_1(a97)) | (~c2_1(a97)) | (~c0_1(a97)) | c3_1(a115) | c2_1(a115) | c1_1(a115))),
% 0.75/0.75 inference(quant_inst,[status(thm)],[])).
% 0.75/0.75 tff(1099,plain,
% 0.75/0.75 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))) | hskp3 | c2_1(a115) | c3_1(a115) | (~ndr1_0) | (~c2_1(a97)) | (~c0_1(a97)) | (~c3_1(a97)) | c1_1(a115)),
% 0.75/0.75 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 0.75/0.75 tff(1100,plain,
% 0.75/0.75 (hskp3 | (~c0_1(a97)) | c1_1(a115)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[1099, 113, 1093, 1092, 1068, 1078, 326])).
% 0.75/0.75 tff(1101,plain,
% 0.75/0.75 (~c0_1(a97)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[1100, 1091, 23])).
% 0.75/0.75 tff(1102,assumption,(~c1_1(a97)), introduced(assumption)).
% 0.75/0.75 tff(1103,plain,
% 0.75/0.75 (hskp3 | hskp2 | c0_1(a97)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[379, 113, 1092, 1102, 373])).
% 0.75/0.75 tff(1104,plain,
% 0.75/0.75 (hskp2),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[1103, 1101, 23])).
% 0.75/0.75 tff(1105,plain,
% 0.75/0.75 (~c3_1(a98)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[388, 1104])).
% 0.75/0.75 tff(1106,plain,
% 0.75/0.75 (~c0_1(a98)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[394, 1104])).
% 0.75/0.75 tff(1107,plain,
% 0.75/0.75 (c1_1(a98)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[406, 1104])).
% 0.75/0.75 tff(1108,plain,
% 0.75/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a116) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c2_1(a98)) | (~c3_1(a116)) | (~c1_1(a116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c2_1(a98)) | (~c3_1(a116)) | (~c1_1(a116)))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1109,plain,
% 0.75/0.75 (((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a98) | (~c1_1(a98)) | (~c2_1(a98)) | c3_1(a98) | c0_1(a98) | (~c2_1(a98))) <=> (c0_1(a116) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c2_1(a98)) | (~c3_1(a116)) | (~c1_1(a116)))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1110,plain,
% 0.75/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a98) | (~c1_1(a98)) | (~c2_1(a98)) | c3_1(a98) | c0_1(a98) | (~c2_1(a98)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a116) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c2_1(a98)) | (~c3_1(a116)) | (~c1_1(a116))))),
% 0.75/0.75 inference(monotonicity,[status(thm)],[1109])).
% 0.75/0.75 tff(1111,plain,
% 0.75/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a98) | (~c1_1(a98)) | (~c2_1(a98)) | c3_1(a98) | c0_1(a98) | (~c2_1(a98)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c2_1(a98)) | (~c3_1(a116)) | (~c1_1(a116)))),
% 0.75/0.75 inference(transitivity,[status(thm)],[1110, 1108])).
% 0.75/0.75 tff(1112,plain,
% 0.75/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a98) | (~c1_1(a98)) | (~c2_1(a98)) | c3_1(a98) | c0_1(a98) | (~c2_1(a98)))),
% 0.75/0.75 inference(quant_inst,[status(thm)],[])).
% 0.75/0.75 tff(1113,plain,
% 0.75/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c0_1(a98) | c3_1(a98) | (~ndr1_0) | (~c1_1(a98)) | (~c2_1(a98)) | (~c3_1(a116)) | (~c1_1(a116))),
% 0.75/0.75 inference(modus_ponens,[status(thm)],[1112, 1111])).
% 0.75/0.75 tff(1114,plain,
% 0.75/0.75 (~c2_1(a98)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[1113, 113, 989, 978, 1107, 1009, 1106, 1105, 695])).
% 0.75/0.75 tff(1115,plain,
% 0.75/0.75 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c0_1(a98) | c3_1(a98) | (~ndr1_0) | c2_1(a98) | (~c1_1(a98)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a98) | c3_1(a98) | (~ndr1_0) | c2_1(a98) | (~c1_1(a98)))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1116,plain,
% 0.75/0.75 ((hskp6 | (~ndr1_0) | c2_1(a98) | c0_1(a98) | (~c1_1(a98)) | c3_1(a98) | c2_1(a98) | c0_1(a98)) <=> (hskp6 | c0_1(a98) | c3_1(a98) | (~ndr1_0) | c2_1(a98) | (~c1_1(a98)))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1117,plain,
% 0.75/0.75 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a98) | c0_1(a98) | (~c1_1(a98)) | c3_1(a98) | c2_1(a98) | c0_1(a98))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | c0_1(a98) | c3_1(a98) | (~ndr1_0) | c2_1(a98) | (~c1_1(a98))))),
% 0.75/0.75 inference(monotonicity,[status(thm)],[1116])).
% 0.75/0.75 tff(1118,plain,
% 0.75/0.75 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a98) | c0_1(a98) | (~c1_1(a98)) | c3_1(a98) | c2_1(a98) | c0_1(a98))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a98) | c3_1(a98) | (~ndr1_0) | c2_1(a98) | (~c1_1(a98)))),
% 0.75/0.75 inference(transitivity,[status(thm)],[1117, 1115])).
% 0.75/0.75 tff(1119,plain,
% 0.75/0.75 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | (hskp6 | (~ndr1_0) | c2_1(a98) | c0_1(a98) | (~c1_1(a98)) | c3_1(a98) | c2_1(a98) | c0_1(a98))),
% 0.75/0.75 inference(quant_inst,[status(thm)],[])).
% 0.75/0.75 tff(1120,plain,
% 0.75/0.75 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c2_1(V) | c0_1(V))) | hskp6 | c0_1(a98) | c3_1(a98) | (~ndr1_0) | c2_1(a98) | (~c1_1(a98))),
% 0.75/0.75 inference(modus_ponens,[status(thm)],[1119, 1118])).
% 0.75/0.75 tff(1121,plain,
% 0.75/0.75 ($false),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[1120, 113, 1090, 1107, 1106, 1105, 605, 1114])).
% 0.75/0.75 tff(1122,plain,(hskp6 | hskp3 | (~c3_1(a97)) | c1_1(a97) | (~c2_1(a97))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.75 tff(1123,plain,
% 0.75/0.75 ($false),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[1122, 1089, 1088, 1040, 23, 1087])).
% 0.75/0.75 tff(1124,plain,(hskp3), inference(lemma,lemma(discharge,[]))).
% 0.75/0.75 tff(1125,plain,
% 0.75/0.75 (~c3_1(a99)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[423, 1124])).
% 0.75/0.75 tff(1126,plain,
% 0.75/0.75 (~c1_1(a99)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[429, 1124])).
% 0.75/0.75 tff(1127,plain,
% 0.75/0.75 (c2_1(a99)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[440, 1124])).
% 0.75/0.75 tff(1128,plain,
% 0.75/0.75 (~c0_1(a99)),
% 0.75/0.75 inference(unit_resolution,[status(thm)],[840, 113, 1127, 1126, 1125, 21])).
% 0.75/0.75 tff(1129,plain,
% 0.75/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a116) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1130,plain,
% 0.75/0.75 (((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99))) <=> (c0_1(a116) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.75/0.75 inference(rewrite,[status(thm)],[])).
% 0.75/0.75 tff(1131,plain,
% 0.75/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a116) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116))))),
% 0.75/0.75 inference(monotonicity,[status(thm)],[1130])).
% 0.75/0.75 tff(1132,plain,
% 0.75/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116)))),
% 0.75/0.76 inference(transitivity,[status(thm)],[1131, 1129])).
% 0.75/0.76 tff(1133,plain,
% 0.75/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c0_1(a116) | (~c3_1(a116)) | (~c1_1(a116)) | c0_1(a116) | (~c1_1(a116)) | (~c2_1(a116)) | c3_1(a99) | c0_1(a99) | (~c2_1(a99)))),
% 0.75/0.76 inference(quant_inst,[status(thm)],[])).
% 0.75/0.76 tff(1134,plain,
% 0.75/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a116) | c3_1(a99) | (~ndr1_0) | c0_1(a99) | (~c2_1(a99)) | (~c3_1(a116)) | (~c1_1(a116)) | (~c2_1(a116))),
% 0.75/0.76 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 0.75/0.76 tff(1135,plain,
% 0.75/0.76 ($false),
% 0.75/0.76 inference(unit_resolution,[status(thm)],[1134, 113, 989, 978, 1127, 1009, 1125, 695, 1128, 997])).
% 0.75/0.76 % SZS output end Proof
%------------------------------------------------------------------------------