TSTP Solution File: SYN485-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN485-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 23:55:51 EDT 2022
% Result : Unsatisfiable 0.71s 0.72s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYN485-1 : TPTP v8.1.0. Released v2.1.0.
% 0.00/0.09 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.07/0.30 % Computer : n014.cluster.edu
% 0.07/0.30 % Model : x86_64 x86_64
% 0.07/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.30 % Memory : 8042.1875MB
% 0.07/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.30 % CPULimit : 300
% 0.07/0.30 % WCLimit : 300
% 0.07/0.30 % DateTime : Mon Sep 5 04:26:14 EDT 2022
% 0.07/0.30 % CPUTime :
% 0.07/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.07/0.30 Usage: tptp [options] [-file:]file
% 0.07/0.30 -h, -? prints this message.
% 0.07/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.07/0.30 -m, -model generate model.
% 0.07/0.30 -p, -proof generate proof.
% 0.07/0.30 -c, -core generate unsat core of named formulas.
% 0.07/0.30 -st, -statistics display statistics.
% 0.07/0.30 -t:timeout set timeout (in second).
% 0.07/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.07/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.07/0.30 -<param>:<value> configuration parameter and value.
% 0.07/0.30 -o:<output-file> file to place output in.
% 0.71/0.72 % SZS status Unsatisfiable
% 0.71/0.72 % SZS output start Proof
% 0.71/0.72 tff(c2_1_type, type, (
% 0.71/0.72 c2_1: $i > $o)).
% 0.71/0.72 tff(a2072_type, type, (
% 0.71/0.72 a2072: $i)).
% 0.71/0.72 tff(c3_1_type, type, (
% 0.71/0.72 c3_1: $i > $o)).
% 0.71/0.72 tff(c0_1_type, type, (
% 0.71/0.72 c0_1: $i > $o)).
% 0.71/0.72 tff(c1_1_type, type, (
% 0.71/0.72 c1_1: $i > $o)).
% 0.71/0.72 tff(ndr1_0_type, type, (
% 0.71/0.72 ndr1_0: $o)).
% 0.71/0.72 tff(a2070_type, type, (
% 0.71/0.72 a2070: $i)).
% 0.71/0.72 tff(hskp1_type, type, (
% 0.71/0.72 hskp1: $o)).
% 0.71/0.72 tff(a2076_type, type, (
% 0.71/0.72 a2076: $i)).
% 0.71/0.72 tff(hskp5_type, type, (
% 0.71/0.72 hskp5: $o)).
% 0.71/0.72 tff(hskp3_type, type, (
% 0.71/0.72 hskp3: $o)).
% 0.71/0.72 tff(hskp11_type, type, (
% 0.71/0.72 hskp11: $o)).
% 0.71/0.72 tff(a2082_type, type, (
% 0.71/0.72 a2082: $i)).
% 0.71/0.72 tff(hskp8_type, type, (
% 0.71/0.72 hskp8: $o)).
% 0.71/0.72 tff(a2087_type, type, (
% 0.71/0.72 a2087: $i)).
% 0.71/0.72 tff(hskp10_type, type, (
% 0.71/0.72 hskp10: $o)).
% 0.71/0.72 tff(a2110_type, type, (
% 0.71/0.72 a2110: $i)).
% 0.71/0.72 tff(hskp17_type, type, (
% 0.71/0.72 hskp17: $o)).
% 0.71/0.72 tff(hskp23_type, type, (
% 0.71/0.72 hskp23: $o)).
% 0.71/0.72 tff(a2149_type, type, (
% 0.71/0.72 a2149: $i)).
% 0.71/0.72 tff(hskp29_type, type, (
% 0.71/0.72 hskp29: $o)).
% 0.71/0.72 tff(a2074_type, type, (
% 0.71/0.72 a2074: $i)).
% 0.71/0.72 tff(hskp4_type, type, (
% 0.71/0.72 hskp4: $o)).
% 0.71/0.72 tff(a2068_type, type, (
% 0.71/0.72 a2068: $i)).
% 0.71/0.72 tff(hskp0_type, type, (
% 0.71/0.72 hskp0: $o)).
% 0.71/0.72 tff(a2077_type, type, (
% 0.71/0.72 a2077: $i)).
% 0.71/0.72 tff(a2093_type, type, (
% 0.71/0.72 a2093: $i)).
% 0.71/0.72 tff(a2069_type, type, (
% 0.71/0.72 a2069: $i)).
% 0.71/0.72 tff(hskp26_type, type, (
% 0.71/0.72 hskp26: $o)).
% 0.71/0.72 tff(a2073_type, type, (
% 0.71/0.72 a2073: $i)).
% 0.71/0.72 tff(hskp27_type, type, (
% 0.71/0.72 hskp27: $o)).
% 0.71/0.72 tff(a2075_type, type, (
% 0.71/0.72 a2075: $i)).
% 0.71/0.72 tff(hskp28_type, type, (
% 0.71/0.72 hskp28: $o)).
% 0.71/0.72 tff(a2079_type, type, (
% 0.71/0.72 a2079: $i)).
% 0.71/0.72 tff(hskp7_type, type, (
% 0.71/0.72 hskp7: $o)).
% 0.71/0.72 tff(hskp20_type, type, (
% 0.71/0.72 hskp20: $o)).
% 0.71/0.72 tff(a2130_type, type, (
% 0.71/0.72 a2130: $i)).
% 0.71/0.72 tff(hskp2_type, type, (
% 0.71/0.72 hskp2: $o)).
% 0.71/0.72 tff(a2140_type, type, (
% 0.71/0.72 a2140: $i)).
% 0.71/0.72 tff(hskp22_type, type, (
% 0.71/0.72 hskp22: $o)).
% 0.71/0.72 tff(a2071_type, type, (
% 0.71/0.72 a2071: $i)).
% 0.71/0.72 tff(a2116_type, type, (
% 0.71/0.72 a2116: $i)).
% 0.71/0.72 tff(hskp18_type, type, (
% 0.71/0.72 hskp18: $o)).
% 0.71/0.72 tff(a2104_type, type, (
% 0.71/0.72 a2104: $i)).
% 0.71/0.72 tff(hskp16_type, type, (
% 0.71/0.72 hskp16: $o)).
% 0.71/0.72 tff(a2099_type, type, (
% 0.71/0.72 a2099: $i)).
% 0.71/0.72 tff(hskp15_type, type, (
% 0.71/0.72 hskp15: $o)).
% 0.71/0.72 tff(a2097_type, type, (
% 0.71/0.72 a2097: $i)).
% 0.71/0.72 tff(hskp14_type, type, (
% 0.71/0.72 hskp14: $o)).
% 0.71/0.72 tff(a2095_type, type, (
% 0.71/0.72 a2095: $i)).
% 0.71/0.72 tff(hskp12_type, type, (
% 0.71/0.72 hskp12: $o)).
% 0.71/0.72 tff(a2160_type, type, (
% 0.71/0.72 a2160: $i)).
% 0.71/0.72 tff(hskp24_type, type, (
% 0.71/0.72 hskp24: $o)).
% 0.71/0.72 tff(a2122_type, type, (
% 0.71/0.72 a2122: $i)).
% 0.71/0.72 tff(hskp19_type, type, (
% 0.71/0.72 hskp19: $o)).
% 0.71/0.72 tff(1,plain,
% 0.71/0.72 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.71/0.72 inference(bind,[status(th)],[])).
% 0.71/0.72 tff(2,plain,
% 0.71/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.72 inference(quant_intro,[status(thm)],[1])).
% 0.71/0.72 tff(3,plain,
% 0.71/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(4,plain,
% 0.71/0.72 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_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) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_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) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | 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) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.71/0.72 inference(bind,[status(th)],[])).
% 0.71/0.72 tff(5,plain,
% 0.71/0.72 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_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) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.72 inference(quant_intro,[status(thm)],[4])).
% 0.71/0.72 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 0.71/0.72 tff(7,plain,
% 0.71/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.71/0.72 tff(8,plain,
% 0.71/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.71/0.72 tff(9,plain,(
% 0.71/0.72 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.72 inference(skolemize,[status(sab)],[8])).
% 0.71/0.72 tff(10,plain,
% 0.71/0.72 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.71/0.72 tff(11,assumption,(~hskp1), introduced(assumption)).
% 0.71/0.72 tff(12,plain,
% 0.71/0.72 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 0.71/0.72 inference(bind,[status(th)],[])).
% 0.71/0.72 tff(13,plain,
% 0.71/0.72 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.71/0.72 inference(quant_intro,[status(thm)],[12])).
% 0.71/0.72 tff(14,plain,
% 0.71/0.72 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(15,plain,
% 0.71/0.72 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 0.71/0.72 inference(bind,[status(th)],[])).
% 0.71/0.72 tff(16,plain,
% 0.71/0.72 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.71/0.72 inference(quant_intro,[status(thm)],[15])).
% 0.71/0.72 tff(17,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 0.71/0.72 tff(18,plain,
% 0.71/0.72 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.71/0.72 tff(19,plain,
% 0.71/0.72 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.71/0.72 tff(20,plain,(
% 0.71/0.72 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.71/0.72 inference(skolemize,[status(sab)],[19])).
% 0.71/0.72 tff(21,plain,
% 0.71/0.72 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.71/0.72 tff(22,assumption,(~hskp11), introduced(assumption)).
% 0.71/0.72 tff(23,plain,
% 0.71/0.72 (^[U: $i] : refl((hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.71/0.72 inference(bind,[status(th)],[])).
% 0.71/0.72 tff(24,plain,
% 0.71/0.72 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.72 inference(quant_intro,[status(thm)],[23])).
% 0.71/0.72 tff(25,plain,
% 0.71/0.72 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(26,plain,
% 0.71/0.72 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp10) <=> ((hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite(((hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp10) <=> (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.71/0.72 inference(bind,[status(th)],[])).
% 0.71/0.72 tff(27,plain,
% 0.71/0.72 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp10) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.72 inference(quant_intro,[status(thm)],[26])).
% 0.71/0.72 tff(28,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp11) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 0.71/0.72 tff(29,plain,
% 0.71/0.72 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.71/0.72 tff(30,plain,
% 0.71/0.72 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.71/0.72 tff(31,plain,(
% 0.71/0.72 ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.72 inference(skolemize,[status(sab)],[30])).
% 0.71/0.72 tff(32,plain,
% 0.71/0.72 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.71/0.72 tff(33,assumption,(~hskp10), introduced(assumption)).
% 0.71/0.72 tff(34,assumption,(hskp23), introduced(assumption)).
% 0.71/0.72 tff(35,plain,
% 0.71/0.72 (((~hskp23) | (~c1_1(a2149))) <=> ((~hskp23) | (~c1_1(a2149)))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(36,plain,
% 0.71/0.72 (((~c1_1(a2149)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a2149)))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(37,axiom,((~c1_1(a2149)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 0.71/0.72 tff(38,plain,
% 0.71/0.72 ((~hskp23) | (~c1_1(a2149))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.71/0.72 tff(39,plain,
% 0.71/0.72 ((~hskp23) | (~c1_1(a2149))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.71/0.72 tff(40,plain,
% 0.71/0.72 (~c1_1(a2149)),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[39, 34])).
% 0.71/0.72 tff(41,plain,
% 0.71/0.72 (((~hskp23) | c3_1(a2149)) <=> ((~hskp23) | c3_1(a2149))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(42,axiom,((~hskp23) | c3_1(a2149)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 0.71/0.72 tff(43,plain,
% 0.71/0.72 ((~hskp23) | c3_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.71/0.72 tff(44,plain,
% 0.71/0.72 ((~hskp23) | c3_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[43, 41])).
% 0.71/0.72 tff(45,plain,
% 0.71/0.72 ((~hskp23) | c3_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[44, 41])).
% 0.71/0.72 tff(46,plain,
% 0.71/0.72 ((~hskp23) | c3_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.71/0.72 tff(47,plain,
% 0.71/0.72 ((~hskp23) | c3_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[46, 41])).
% 0.71/0.72 tff(48,plain,
% 0.71/0.72 ((~hskp23) | c3_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[47, 41])).
% 0.71/0.72 tff(49,plain,
% 0.71/0.72 ((~hskp23) | c3_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.71/0.72 tff(50,plain,
% 0.71/0.72 ((~hskp23) | c3_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[49, 41])).
% 0.71/0.72 tff(51,plain,
% 0.71/0.72 (c3_1(a2149)),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[50, 34])).
% 0.71/0.72 tff(52,plain,
% 0.71/0.72 (((~hskp23) | c0_1(a2149)) <=> ((~hskp23) | c0_1(a2149))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(53,axiom,((~hskp23) | c0_1(a2149)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 0.71/0.72 tff(54,plain,
% 0.71/0.72 ((~hskp23) | c0_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.71/0.72 tff(55,plain,
% 0.71/0.72 ((~hskp23) | c0_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[54, 52])).
% 0.71/0.72 tff(56,plain,
% 0.71/0.72 ((~hskp23) | c0_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.71/0.72 tff(57,plain,
% 0.71/0.72 ((~hskp23) | c0_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.71/0.72 tff(58,plain,
% 0.71/0.72 ((~hskp23) | c0_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[57, 52])).
% 0.71/0.72 tff(59,plain,
% 0.71/0.72 ((~hskp23) | c0_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[58, 52])).
% 0.71/0.72 tff(60,plain,
% 0.71/0.72 ((~hskp23) | c0_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.71/0.72 tff(61,plain,
% 0.71/0.72 ((~hskp23) | c0_1(a2149)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[60, 52])).
% 0.71/0.72 tff(62,plain,
% 0.71/0.72 (c0_1(a2149)),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[61, 34])).
% 0.71/0.72 tff(63,assumption,(~ndr1_0), introduced(assumption)).
% 0.71/0.72 tff(64,plain,
% 0.71/0.72 ((ndr1_0 | (~hskp3)) <=> (ndr1_0 | (~hskp3))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(65,plain,
% 0.71/0.72 (((~hskp3) | ndr1_0) <=> (ndr1_0 | (~hskp3))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(66,axiom,((~hskp3) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause28')).
% 0.71/0.72 tff(67,plain,
% 0.71/0.72 (ndr1_0 | (~hskp3)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.71/0.72 tff(68,plain,
% 0.71/0.72 (ndr1_0 | (~hskp3)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[67, 64])).
% 0.71/0.72 tff(69,plain,
% 0.71/0.72 (~hskp3),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[68, 63])).
% 0.71/0.72 tff(70,plain,
% 0.71/0.72 (((~hskp29) | ndr1_0) <=> ((~hskp29) | ndr1_0)),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(71,axiom,((~hskp29) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.71/0.72 tff(72,plain,
% 0.71/0.72 ((~hskp29) | ndr1_0),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.71/0.72 tff(73,plain,
% 0.71/0.72 ((~hskp29) | ndr1_0),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[72, 70])).
% 0.71/0.72 tff(74,plain,
% 0.71/0.72 ((~hskp29) | ndr1_0),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[73, 70])).
% 0.71/0.72 tff(75,plain,
% 0.71/0.72 ((~hskp29) | ndr1_0),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.71/0.72 tff(76,plain,
% 0.71/0.72 ((~hskp29) | ndr1_0),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[75, 70])).
% 0.71/0.72 tff(77,plain,
% 0.71/0.72 ((~hskp29) | ndr1_0),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[76, 70])).
% 0.71/0.72 tff(78,plain,
% 0.71/0.72 ((~hskp29) | ndr1_0),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.71/0.72 tff(79,plain,
% 0.71/0.72 ((~hskp29) | ndr1_0),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[78, 70])).
% 0.71/0.72 tff(80,plain,
% 0.71/0.72 (~hskp29),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[79, 63])).
% 0.71/0.72 tff(81,plain,
% 0.71/0.72 ((ndr1_0 | (~hskp5)) <=> (ndr1_0 | (~hskp5))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(82,plain,
% 0.71/0.72 (((~hskp5) | ndr1_0) <=> (ndr1_0 | (~hskp5))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(83,axiom,((~hskp5) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause26')).
% 0.71/0.72 tff(84,plain,
% 0.71/0.72 (ndr1_0 | (~hskp5)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.71/0.72 tff(85,plain,
% 0.71/0.72 (ndr1_0 | (~hskp5)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[84, 81])).
% 0.71/0.72 tff(86,plain,
% 0.71/0.72 (~hskp5),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[85, 63])).
% 0.71/0.72 tff(87,plain,
% 0.71/0.72 ((hskp29 | hskp5 | hskp3) <=> (hskp29 | hskp5 | hskp3)),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(88,plain,
% 0.71/0.72 (((hskp29 | hskp5) | hskp3) <=> (hskp29 | hskp5 | hskp3)),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(89,axiom,((hskp29 | hskp5) | hskp3), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause37')).
% 0.71/0.72 tff(90,plain,
% 0.71/0.72 (hskp29 | hskp5 | hskp3),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.71/0.72 tff(91,plain,
% 0.71/0.72 (hskp29 | hskp5 | hskp3),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[90, 87])).
% 0.71/0.72 tff(92,plain,
% 0.71/0.72 (hskp29 | hskp5 | hskp3),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.71/0.72 tff(93,plain,
% 0.71/0.72 (hskp29 | hskp5 | hskp3),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[92, 87])).
% 0.71/0.72 tff(94,plain,
% 0.71/0.72 (hskp29 | hskp5 | hskp3),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[93, 87])).
% 0.71/0.72 tff(95,plain,
% 0.71/0.72 (hskp29 | hskp5 | hskp3),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.71/0.72 tff(96,plain,
% 0.71/0.72 (hskp29 | hskp5 | hskp3),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[95, 87])).
% 0.71/0.72 tff(97,plain,
% 0.71/0.72 (hskp29 | hskp5 | hskp3),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[96, 87])).
% 0.71/0.72 tff(98,plain,
% 0.71/0.72 ($false),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[97, 86, 80, 69])).
% 0.71/0.72 tff(99,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.71/0.72 tff(100,plain,
% 0.71/0.72 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | c1_1(a2149) | (~ndr1_0) | (~c3_1(a2149)) | (~c0_1(a2149)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2149) | (~ndr1_0) | (~c3_1(a2149)) | (~c0_1(a2149)))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(101,plain,
% 0.71/0.72 ((hskp11 | hskp10 | (~ndr1_0) | c1_1(a2149) | (~c3_1(a2149)) | (~c0_1(a2149))) <=> (hskp11 | hskp10 | c1_1(a2149) | (~ndr1_0) | (~c3_1(a2149)) | (~c0_1(a2149)))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(102,plain,
% 0.71/0.72 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2149) | (~c3_1(a2149)) | (~c0_1(a2149)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | c1_1(a2149) | (~ndr1_0) | (~c3_1(a2149)) | (~c0_1(a2149))))),
% 0.71/0.72 inference(monotonicity,[status(thm)],[101])).
% 0.71/0.72 tff(103,plain,
% 0.71/0.72 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2149) | (~c3_1(a2149)) | (~c0_1(a2149)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2149) | (~ndr1_0) | (~c3_1(a2149)) | (~c0_1(a2149)))),
% 0.71/0.72 inference(transitivity,[status(thm)],[102, 100])).
% 0.71/0.72 tff(104,plain,
% 0.71/0.72 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2149) | (~c3_1(a2149)) | (~c0_1(a2149)))),
% 0.71/0.72 inference(quant_inst,[status(thm)],[])).
% 0.71/0.72 tff(105,plain,
% 0.71/0.72 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2149) | (~ndr1_0) | (~c3_1(a2149)) | (~c0_1(a2149))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.71/0.72 tff(106,plain,
% 0.71/0.72 ($false),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[105, 99, 22, 33, 62, 51, 40, 32])).
% 0.71/0.72 tff(107,plain,((~hskp23) | hskp11 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.71/0.72 tff(108,plain,
% 0.71/0.72 (~hskp23),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[107, 33, 22])).
% 0.71/0.72 tff(109,plain,
% 0.71/0.72 ((hskp17 | hskp23 | hskp1) <=> (hskp17 | hskp23 | hskp1)),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(110,plain,
% 0.71/0.72 (((hskp17 | hskp23) | hskp1) <=> (hskp17 | hskp23 | hskp1)),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(111,axiom,((hskp17 | hskp23) | hskp1), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 0.71/0.72 tff(112,plain,
% 0.71/0.72 (hskp17 | hskp23 | hskp1),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.71/0.72 tff(113,plain,
% 0.71/0.72 (hskp17 | hskp23 | hskp1),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[112, 109])).
% 0.71/0.72 tff(114,plain,
% 0.71/0.72 (hskp17 | hskp23 | hskp1),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.71/0.72 tff(115,plain,
% 0.71/0.72 (hskp17 | hskp23 | hskp1),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[114, 109])).
% 0.71/0.72 tff(116,plain,
% 0.71/0.72 (hskp17 | hskp23 | hskp1),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[115, 109])).
% 0.71/0.72 tff(117,plain,
% 0.71/0.72 (hskp17 | hskp23 | hskp1),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.71/0.72 tff(118,plain,
% 0.71/0.72 (hskp17 | hskp23 | hskp1),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[117, 109])).
% 0.71/0.72 tff(119,plain,
% 0.71/0.72 (hskp17 | hskp23 | hskp1),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[118, 109])).
% 0.71/0.72 tff(120,plain,
% 0.71/0.72 (hskp17),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[119, 108, 11])).
% 0.71/0.72 tff(121,plain,
% 0.71/0.72 (((~hskp17) | (~c1_1(a2110))) <=> ((~hskp17) | (~c1_1(a2110)))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(122,plain,
% 0.71/0.72 (((~c1_1(a2110)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a2110)))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(123,axiom,((~c1_1(a2110)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 0.71/0.72 tff(124,plain,
% 0.71/0.72 ((~hskp17) | (~c1_1(a2110))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.71/0.72 tff(125,plain,
% 0.71/0.72 ((~hskp17) | (~c1_1(a2110))),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[124, 121])).
% 0.71/0.72 tff(126,plain,
% 0.71/0.72 (~c1_1(a2110)),
% 0.71/0.72 inference(unit_resolution,[status(thm)],[125, 120])).
% 0.71/0.72 tff(127,plain,
% 0.71/0.72 (((~hskp17) | c0_1(a2110)) <=> ((~hskp17) | c0_1(a2110))),
% 0.71/0.72 inference(rewrite,[status(thm)],[])).
% 0.71/0.72 tff(128,axiom,((~hskp17) | c0_1(a2110)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 0.71/0.72 tff(129,plain,
% 0.71/0.72 ((~hskp17) | c0_1(a2110)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.71/0.72 tff(130,plain,
% 0.71/0.72 ((~hskp17) | c0_1(a2110)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[129, 127])).
% 0.71/0.72 tff(131,plain,
% 0.71/0.72 ((~hskp17) | c0_1(a2110)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[130, 127])).
% 0.71/0.72 tff(132,plain,
% 0.71/0.72 ((~hskp17) | c0_1(a2110)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.71/0.72 tff(133,plain,
% 0.71/0.72 ((~hskp17) | c0_1(a2110)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[132, 127])).
% 0.71/0.72 tff(134,plain,
% 0.71/0.72 ((~hskp17) | c0_1(a2110)),
% 0.71/0.72 inference(modus_ponens,[status(thm)],[133, 127])).
% 0.71/0.72 tff(135,plain,
% 0.71/0.72 ((~hskp17) | c0_1(a2110)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.71/0.73 tff(136,plain,
% 0.71/0.73 ((~hskp17) | c0_1(a2110)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[135, 127])).
% 0.71/0.73 tff(137,plain,
% 0.71/0.73 (c0_1(a2110)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[136, 120])).
% 0.71/0.73 tff(138,plain,
% 0.71/0.73 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | c1_1(a2110) | (~ndr1_0) | (~c3_1(a2110)) | (~c0_1(a2110)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2110) | (~ndr1_0) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(139,plain,
% 0.71/0.73 ((hskp11 | hskp10 | (~ndr1_0) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110))) <=> (hskp11 | hskp10 | c1_1(a2110) | (~ndr1_0) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(140,plain,
% 0.71/0.73 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | c1_1(a2110) | (~ndr1_0) | (~c3_1(a2110)) | (~c0_1(a2110))))),
% 0.71/0.73 inference(monotonicity,[status(thm)],[139])).
% 0.71/0.73 tff(141,plain,
% 0.71/0.73 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2110) | (~ndr1_0) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.71/0.73 inference(transitivity,[status(thm)],[140, 138])).
% 0.71/0.73 tff(142,plain,
% 0.71/0.73 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.71/0.73 inference(quant_inst,[status(thm)],[])).
% 0.71/0.73 tff(143,plain,
% 0.71/0.73 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2110) | (~ndr1_0) | (~c3_1(a2110)) | (~c0_1(a2110))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.71/0.73 tff(144,plain,
% 0.71/0.73 (~c3_1(a2110)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[143, 99, 22, 33, 137, 126, 32])).
% 0.71/0.73 tff(145,assumption,(hskp17), introduced(assumption)).
% 0.71/0.73 tff(146,plain,
% 0.71/0.73 (~c1_1(a2110)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[125, 145])).
% 0.71/0.73 tff(147,plain,
% 0.71/0.73 (c0_1(a2110)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[136, 145])).
% 0.71/0.73 tff(148,plain,
% 0.71/0.73 (~c3_1(a2110)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[143, 99, 22, 33, 147, 146, 32])).
% 0.71/0.73 tff(149,plain,
% 0.71/0.73 (^[U: $i] : refl((hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.71/0.73 inference(bind,[status(th)],[])).
% 0.71/0.73 tff(150,plain,
% 0.71/0.73 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.71/0.73 inference(quant_intro,[status(thm)],[149])).
% 0.71/0.73 tff(151,plain,
% 0.71/0.73 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(152,plain,
% 0.71/0.73 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp8) <=> ((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp8))), rewrite(((hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp8) <=> (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp8) <=> (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.71/0.73 inference(bind,[status(th)],[])).
% 0.71/0.73 tff(153,plain,
% 0.71/0.73 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp8) <=> ![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.71/0.73 inference(quant_intro,[status(thm)],[152])).
% 0.71/0.73 tff(154,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp1) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 0.71/0.73 tff(155,plain,
% 0.71/0.73 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.71/0.73 tff(156,plain,
% 0.71/0.73 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.71/0.73 tff(157,plain,(
% 0.71/0.73 ![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.71/0.73 inference(skolemize,[status(sab)],[156])).
% 0.71/0.73 tff(158,plain,
% 0.71/0.73 (![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.71/0.73 tff(159,assumption,(~hskp8), introduced(assumption)).
% 0.71/0.73 tff(160,plain,
% 0.71/0.73 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | c1_1(a2110) | (~ndr1_0) | c3_1(a2110) | (~c0_1(a2110)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2110) | (~ndr1_0) | c3_1(a2110) | (~c0_1(a2110)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(161,plain,
% 0.71/0.73 ((hskp8 | hskp1 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c0_1(a2110))) <=> (hskp8 | hskp1 | c1_1(a2110) | (~ndr1_0) | c3_1(a2110) | (~c0_1(a2110)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(162,plain,
% 0.71/0.73 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c0_1(a2110)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | c1_1(a2110) | (~ndr1_0) | c3_1(a2110) | (~c0_1(a2110))))),
% 0.71/0.73 inference(monotonicity,[status(thm)],[161])).
% 0.71/0.73 tff(163,plain,
% 0.71/0.73 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c0_1(a2110)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2110) | (~ndr1_0) | c3_1(a2110) | (~c0_1(a2110)))),
% 0.71/0.73 inference(transitivity,[status(thm)],[162, 160])).
% 0.71/0.73 tff(164,plain,
% 0.71/0.73 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c0_1(a2110)))),
% 0.71/0.73 inference(quant_inst,[status(thm)],[])).
% 0.71/0.73 tff(165,plain,
% 0.71/0.73 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2110) | (~ndr1_0) | c3_1(a2110) | (~c0_1(a2110))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.71/0.73 tff(166,plain,
% 0.71/0.73 ($false),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[165, 99, 159, 11, 147, 146, 158, 148])).
% 0.71/0.73 tff(167,plain,((~hskp17) | hskp8 | hskp1 | hskp11 | hskp10), inference(lemma,lemma(discharge,[]))).
% 0.71/0.73 tff(168,plain,
% 0.71/0.73 (hskp8),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[167, 120, 11, 22, 33])).
% 0.71/0.73 tff(169,plain,
% 0.71/0.73 (((~hskp8) | (~c0_1(a2082))) <=> ((~hskp8) | (~c0_1(a2082)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(170,plain,
% 0.71/0.73 (((~c0_1(a2082)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a2082)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(171,axiom,((~c0_1(a2082)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 0.71/0.73 tff(172,plain,
% 0.71/0.73 ((~hskp8) | (~c0_1(a2082))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.71/0.73 tff(173,plain,
% 0.71/0.73 ((~hskp8) | (~c0_1(a2082))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[172, 169])).
% 0.71/0.73 tff(174,plain,
% 0.71/0.73 (~c0_1(a2082)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[173, 168])).
% 0.71/0.73 tff(175,plain,
% 0.71/0.73 (((~hskp8) | c2_1(a2082)) <=> ((~hskp8) | c2_1(a2082))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(176,axiom,((~hskp8) | c2_1(a2082)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 0.71/0.73 tff(177,plain,
% 0.71/0.73 ((~hskp8) | c2_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.71/0.73 tff(178,plain,
% 0.71/0.73 ((~hskp8) | c2_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[177, 175])).
% 0.71/0.73 tff(179,plain,
% 0.71/0.73 ((~hskp8) | c2_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[178, 175])).
% 0.71/0.73 tff(180,plain,
% 0.71/0.73 ((~hskp8) | c2_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.71/0.73 tff(181,plain,
% 0.71/0.73 ((~hskp8) | c2_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[180, 175])).
% 0.71/0.73 tff(182,plain,
% 0.71/0.73 ((~hskp8) | c2_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[181, 175])).
% 0.71/0.73 tff(183,plain,
% 0.71/0.73 ((~hskp8) | c2_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[182, 175])).
% 0.71/0.73 tff(184,plain,
% 0.71/0.73 ((~hskp8) | c2_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[183, 175])).
% 0.71/0.73 tff(185,plain,
% 0.71/0.73 (c2_1(a2082)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[184, 168])).
% 0.71/0.73 tff(186,plain,
% 0.71/0.73 (((~hskp8) | c1_1(a2082)) <=> ((~hskp8) | c1_1(a2082))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(187,axiom,((~hskp8) | c1_1(a2082)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 0.71/0.73 tff(188,plain,
% 0.71/0.73 ((~hskp8) | c1_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.71/0.73 tff(189,plain,
% 0.71/0.73 ((~hskp8) | c1_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[188, 186])).
% 0.71/0.73 tff(190,plain,
% 0.71/0.73 ((~hskp8) | c1_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[189, 186])).
% 0.71/0.73 tff(191,plain,
% 0.71/0.73 ((~hskp8) | c1_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.71/0.73 tff(192,plain,
% 0.71/0.73 ((~hskp8) | c1_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[191, 186])).
% 0.71/0.73 tff(193,plain,
% 0.71/0.73 ((~hskp8) | c1_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[192, 186])).
% 0.71/0.73 tff(194,plain,
% 0.71/0.73 ((~hskp8) | c1_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[193, 186])).
% 0.71/0.73 tff(195,plain,
% 0.71/0.73 ((~hskp8) | c1_1(a2082)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[194, 186])).
% 0.71/0.73 tff(196,plain,
% 0.71/0.73 (c1_1(a2082)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[195, 168])).
% 0.71/0.73 tff(197,plain,
% 0.71/0.73 (((~hskp17) | c2_1(a2110)) <=> ((~hskp17) | c2_1(a2110))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(198,axiom,((~hskp17) | c2_1(a2110)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 0.71/0.73 tff(199,plain,
% 0.71/0.73 ((~hskp17) | c2_1(a2110)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.71/0.73 tff(200,plain,
% 0.71/0.73 ((~hskp17) | c2_1(a2110)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[199, 197])).
% 0.71/0.73 tff(201,plain,
% 0.71/0.73 ((~hskp17) | c2_1(a2110)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[200, 197])).
% 0.71/0.73 tff(202,plain,
% 0.71/0.73 ((~hskp17) | c2_1(a2110)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[201, 197])).
% 0.71/0.73 tff(203,plain,
% 0.71/0.73 ((~hskp17) | c2_1(a2110)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[202, 197])).
% 0.71/0.73 tff(204,plain,
% 0.71/0.73 ((~hskp17) | c2_1(a2110)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[203, 197])).
% 0.71/0.73 tff(205,plain,
% 0.71/0.73 ((~hskp17) | c2_1(a2110)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.71/0.73 tff(206,plain,
% 0.71/0.73 ((~hskp17) | c2_1(a2110)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[205, 197])).
% 0.71/0.73 tff(207,plain,
% 0.71/0.73 (c2_1(a2110)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[206, 120])).
% 0.71/0.73 tff(208,plain,
% 0.71/0.73 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2110) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c3_1(a2110) | (~c2_1(a2110)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2110) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(209,plain,
% 0.71/0.73 ((hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082))) <=> (hskp11 | c1_1(a2110) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(210,plain,
% 0.71/0.73 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2110) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c3_1(a2110) | (~c2_1(a2110))))),
% 0.71/0.73 inference(monotonicity,[status(thm)],[209])).
% 0.71/0.73 tff(211,plain,
% 0.71/0.73 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2110) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.71/0.73 inference(transitivity,[status(thm)],[210, 208])).
% 0.71/0.73 tff(212,plain,
% 0.71/0.73 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.71/0.73 inference(quant_inst,[status(thm)],[])).
% 0.71/0.73 tff(213,plain,
% 0.71/0.73 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2110) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c3_1(a2110) | (~c2_1(a2110))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.71/0.73 tff(214,plain,
% 0.71/0.73 ($false),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[213, 99, 22, 207, 196, 185, 126, 174, 21, 144])).
% 0.71/0.73 tff(215,plain,(hskp10 | hskp11 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.71/0.73 tff(216,plain,
% 0.71/0.73 (hskp10),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[215, 22, 11])).
% 0.71/0.73 tff(217,plain,
% 0.71/0.73 (((~hskp10) | (~c3_1(a2087))) <=> ((~hskp10) | (~c3_1(a2087)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(218,plain,
% 0.71/0.73 (((~c3_1(a2087)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a2087)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(219,axiom,((~c3_1(a2087)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause115')).
% 0.71/0.73 tff(220,plain,
% 0.71/0.73 ((~hskp10) | (~c3_1(a2087))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.71/0.73 tff(221,plain,
% 0.71/0.73 ((~hskp10) | (~c3_1(a2087))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[220, 217])).
% 0.71/0.73 tff(222,plain,
% 0.71/0.73 (~c3_1(a2087)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[221, 216])).
% 0.71/0.73 tff(223,plain,
% 0.71/0.73 (((~hskp10) | (~c1_1(a2087))) <=> ((~hskp10) | (~c1_1(a2087)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(224,plain,
% 0.71/0.73 (((~c1_1(a2087)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a2087)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(225,axiom,((~c1_1(a2087)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 0.71/0.73 tff(226,plain,
% 0.71/0.73 ((~hskp10) | (~c1_1(a2087))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.71/0.73 tff(227,plain,
% 0.71/0.73 ((~hskp10) | (~c1_1(a2087))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[226, 223])).
% 0.71/0.73 tff(228,plain,
% 0.71/0.73 (~c1_1(a2087)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[227, 216])).
% 0.71/0.73 tff(229,plain,
% 0.71/0.73 (((~hskp10) | c2_1(a2087)) <=> ((~hskp10) | c2_1(a2087))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(230,axiom,((~hskp10) | c2_1(a2087)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 0.71/0.73 tff(231,plain,
% 0.71/0.73 ((~hskp10) | c2_1(a2087)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.71/0.73 tff(232,plain,
% 0.71/0.73 ((~hskp10) | c2_1(a2087)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[231, 229])).
% 0.71/0.73 tff(233,plain,
% 0.71/0.73 ((~hskp10) | c2_1(a2087)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[232, 229])).
% 0.71/0.73 tff(234,plain,
% 0.71/0.73 ((~hskp10) | c2_1(a2087)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[233, 229])).
% 0.71/0.73 tff(235,plain,
% 0.71/0.73 ((~hskp10) | c2_1(a2087)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[234, 229])).
% 0.71/0.73 tff(236,plain,
% 0.71/0.73 ((~hskp10) | c2_1(a2087)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[235, 229])).
% 0.71/0.73 tff(237,plain,
% 0.71/0.73 ((~hskp10) | c2_1(a2087)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[236, 229])).
% 0.71/0.73 tff(238,plain,
% 0.71/0.73 ((~hskp10) | c2_1(a2087)),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[237, 229])).
% 0.71/0.73 tff(239,plain,
% 0.71/0.73 (c2_1(a2087)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[238, 216])).
% 0.71/0.73 tff(240,assumption,(~c3_1(a2087)), introduced(assumption)).
% 0.71/0.73 tff(241,assumption,(~c1_1(a2087)), introduced(assumption)).
% 0.71/0.73 tff(242,plain,
% 0.71/0.73 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(243,plain,
% 0.71/0.73 ((hskp8 | hskp1 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087))) <=> (hskp8 | hskp1 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(244,plain,
% 0.71/0.73 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087))))),
% 0.71/0.73 inference(monotonicity,[status(thm)],[243])).
% 0.71/0.73 tff(245,plain,
% 0.71/0.73 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.71/0.73 inference(transitivity,[status(thm)],[244, 242])).
% 0.71/0.73 tff(246,plain,
% 0.71/0.73 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))),
% 0.71/0.73 inference(quant_inst,[status(thm)],[])).
% 0.71/0.73 tff(247,plain,
% 0.71/0.73 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.71/0.73 tff(248,plain,
% 0.71/0.73 (hskp8 | (~c0_1(a2087))),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[247, 99, 11, 241, 240, 158])).
% 0.71/0.73 tff(249,plain,
% 0.71/0.73 (~c0_1(a2087)),
% 0.71/0.73 inference(unit_resolution,[status(thm)],[248, 159])).
% 0.71/0.73 tff(250,plain,
% 0.71/0.73 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.71/0.73 inference(bind,[status(th)],[])).
% 0.71/0.73 tff(251,plain,
% 0.71/0.73 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.73 inference(quant_intro,[status(thm)],[250])).
% 0.71/0.73 tff(252,plain,
% 0.71/0.73 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(253,plain,
% 0.71/0.73 (^[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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.71/0.73 inference(bind,[status(th)],[])).
% 0.71/0.73 tff(254,plain,
% 0.71/0.73 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.73 inference(quant_intro,[status(thm)],[253])).
% 0.71/0.73 tff(255,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 0.71/0.73 tff(256,plain,
% 0.71/0.73 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.71/0.73 tff(257,plain,
% 0.71/0.73 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[256, 252])).
% 0.71/0.73 tff(258,plain,(
% 0.71/0.73 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.73 inference(skolemize,[status(sab)],[257])).
% 0.71/0.73 tff(259,plain,
% 0.71/0.73 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.73 inference(modus_ponens,[status(thm)],[258, 251])).
% 0.71/0.73 tff(260,assumption,(c2_1(a2087)), introduced(assumption)).
% 0.71/0.73 tff(261,plain,
% 0.71/0.73 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.71/0.73 inference(rewrite,[status(thm)],[])).
% 0.71/0.73 tff(262,plain,
% 0.71/0.73 ((hskp4 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c3_1(a2087) | c1_1(a2087) | c0_1(a2087)) <=> (hskp4 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(263,plain,
% 0.71/0.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c3_1(a2087) | c1_1(a2087) | c0_1(a2087))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.71/0.74 inference(monotonicity,[status(thm)],[262])).
% 0.71/0.74 tff(264,plain,
% 0.71/0.74 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c3_1(a2087) | c1_1(a2087) | c0_1(a2087))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.71/0.74 inference(transitivity,[status(thm)],[263, 261])).
% 0.71/0.74 tff(265,plain,
% 0.71/0.74 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c3_1(a2087) | c1_1(a2087) | c0_1(a2087))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(266,plain,
% 0.71/0.74 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.71/0.74 tff(267,plain,
% 0.71/0.74 (hskp4 | c0_1(a2087)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[266, 99, 260, 241, 240, 259])).
% 0.71/0.74 tff(268,plain,
% 0.71/0.74 (hskp4),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[267, 249])).
% 0.71/0.74 tff(269,plain,
% 0.71/0.74 (((~hskp4) | (~c2_1(a2074))) <=> ((~hskp4) | (~c2_1(a2074)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(270,plain,
% 0.71/0.74 (((~c2_1(a2074)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a2074)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(271,axiom,((~c2_1(a2074)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 0.71/0.74 tff(272,plain,
% 0.71/0.74 ((~hskp4) | (~c2_1(a2074))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.71/0.74 tff(273,plain,
% 0.71/0.74 ((~hskp4) | (~c2_1(a2074))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[272, 269])).
% 0.71/0.74 tff(274,plain,
% 0.71/0.74 (~c2_1(a2074)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[273, 268])).
% 0.71/0.74 tff(275,plain,
% 0.71/0.74 (((~hskp4) | c3_1(a2074)) <=> ((~hskp4) | c3_1(a2074))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(276,axiom,((~hskp4) | c3_1(a2074)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 0.71/0.74 tff(277,plain,
% 0.71/0.74 ((~hskp4) | c3_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.71/0.74 tff(278,plain,
% 0.71/0.74 ((~hskp4) | c3_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[277, 275])).
% 0.71/0.74 tff(279,plain,
% 0.71/0.74 ((~hskp4) | c3_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[278, 275])).
% 0.71/0.74 tff(280,plain,
% 0.71/0.74 ((~hskp4) | c3_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[279, 275])).
% 0.71/0.74 tff(281,plain,
% 0.71/0.74 ((~hskp4) | c3_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[280, 275])).
% 0.71/0.74 tff(282,plain,
% 0.71/0.74 ((~hskp4) | c3_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[281, 275])).
% 0.71/0.74 tff(283,plain,
% 0.71/0.74 ((~hskp4) | c3_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[282, 275])).
% 0.71/0.74 tff(284,plain,
% 0.71/0.74 ((~hskp4) | c3_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[283, 275])).
% 0.71/0.74 tff(285,plain,
% 0.71/0.74 (c3_1(a2074)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[284, 268])).
% 0.71/0.74 tff(286,plain,
% 0.71/0.74 (((~hskp4) | c1_1(a2074)) <=> ((~hskp4) | c1_1(a2074))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(287,axiom,((~hskp4) | c1_1(a2074)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 0.71/0.74 tff(288,plain,
% 0.71/0.74 ((~hskp4) | c1_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.71/0.74 tff(289,plain,
% 0.71/0.74 ((~hskp4) | c1_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[288, 286])).
% 0.71/0.74 tff(290,plain,
% 0.71/0.74 ((~hskp4) | c1_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[289, 286])).
% 0.71/0.74 tff(291,plain,
% 0.71/0.74 ((~hskp4) | c1_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[290, 286])).
% 0.71/0.74 tff(292,plain,
% 0.71/0.74 ((~hskp4) | c1_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[291, 286])).
% 0.71/0.74 tff(293,plain,
% 0.71/0.74 ((~hskp4) | c1_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[292, 286])).
% 0.71/0.74 tff(294,plain,
% 0.71/0.74 ((~hskp4) | c1_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[293, 286])).
% 0.71/0.74 tff(295,plain,
% 0.71/0.74 ((~hskp4) | c1_1(a2074)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[294, 286])).
% 0.71/0.74 tff(296,plain,
% 0.71/0.74 (c1_1(a2074)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[295, 268])).
% 0.71/0.74 tff(297,plain,
% 0.71/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(298,plain,
% 0.71/0.74 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087))) <=> (c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(299,plain,
% 0.71/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.71/0.74 inference(monotonicity,[status(thm)],[298])).
% 0.71/0.74 tff(300,plain,
% 0.71/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.71/0.74 inference(transitivity,[status(thm)],[299, 297])).
% 0.71/0.74 tff(301,plain,
% 0.71/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087)))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(302,plain,
% 0.71/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.71/0.74 tff(303,plain,
% 0.71/0.74 (~c0_1(a2074)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[302, 99, 260, 296, 285, 240, 274, 10, 249])).
% 0.71/0.74 tff(304,plain,
% 0.71/0.74 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(305,plain,
% 0.71/0.74 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[304])).
% 0.71/0.74 tff(306,plain,
% 0.71/0.74 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(307,plain,
% 0.71/0.74 (^[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)) | (~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))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(308,plain,
% 0.71/0.74 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[307])).
% 0.71/0.74 tff(309,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 0.71/0.74 tff(310,plain,
% 0.71/0.74 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.71/0.74 tff(311,plain,
% 0.71/0.74 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[310, 306])).
% 0.71/0.74 tff(312,plain,(
% 0.71/0.74 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.74 inference(skolemize,[status(sab)],[311])).
% 0.71/0.74 tff(313,plain,
% 0.71/0.74 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[312, 305])).
% 0.71/0.74 tff(314,plain,
% 0.71/0.74 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | c0_1(a2074) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | c0_1(a2074) | (~c2_1(a2087)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(315,plain,
% 0.71/0.74 ((hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074))) <=> (hskp8 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | c0_1(a2074) | (~c2_1(a2087)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(316,plain,
% 0.71/0.74 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | c0_1(a2074) | (~c2_1(a2087))))),
% 0.71/0.74 inference(monotonicity,[status(thm)],[315])).
% 0.71/0.74 tff(317,plain,
% 0.71/0.74 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | c0_1(a2074) | (~c2_1(a2087)))),
% 0.71/0.74 inference(transitivity,[status(thm)],[316, 314])).
% 0.71/0.74 tff(318,plain,
% 0.71/0.74 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074)))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(319,plain,
% 0.71/0.74 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | c0_1(a2074) | (~c2_1(a2087))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.71/0.74 tff(320,plain,
% 0.71/0.74 ($false),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[319, 99, 159, 260, 296, 241, 240, 274, 313, 303])).
% 0.71/0.74 tff(321,plain,(hskp8 | (~c2_1(a2087)) | c1_1(a2087) | c3_1(a2087) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.71/0.74 tff(322,plain,
% 0.71/0.74 (hskp8),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[321, 239, 228, 222, 11])).
% 0.71/0.74 tff(323,plain,
% 0.71/0.74 (~c0_1(a2082)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[173, 322])).
% 0.71/0.74 tff(324,plain,
% 0.71/0.74 (c2_1(a2082)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[184, 322])).
% 0.71/0.74 tff(325,plain,
% 0.71/0.74 (c1_1(a2082)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[195, 322])).
% 0.71/0.74 tff(326,plain,
% 0.71/0.74 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | (~c2_1(a2087)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(327,plain,
% 0.71/0.74 ((hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082))) <=> (hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | (~c2_1(a2087)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(328,plain,
% 0.71/0.74 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | (~c2_1(a2087))))),
% 0.71/0.74 inference(monotonicity,[status(thm)],[327])).
% 0.71/0.74 tff(329,plain,
% 0.71/0.74 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | (~c2_1(a2087)))),
% 0.71/0.74 inference(transitivity,[status(thm)],[328, 326])).
% 0.71/0.74 tff(330,plain,
% 0.71/0.74 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.71/0.74 inference(quant_inst,[status(thm)],[])).
% 0.71/0.74 tff(331,plain,
% 0.71/0.74 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | (~c2_1(a2087))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.71/0.74 tff(332,plain,
% 0.71/0.74 ($false),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[331, 99, 22, 239, 325, 324, 228, 222, 323, 21])).
% 0.71/0.74 tff(333,plain,(hskp11 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.71/0.74 tff(334,plain,
% 0.71/0.74 (hskp11),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[333, 11])).
% 0.71/0.74 tff(335,plain,
% 0.71/0.74 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(336,plain,
% 0.71/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[335])).
% 0.71/0.74 tff(337,plain,
% 0.71/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(338,plain,
% 0.71/0.74 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(339,plain,
% 0.71/0.74 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[338])).
% 0.71/0.74 tff(340,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 0.71/0.74 tff(341,plain,
% 0.71/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.71/0.74 tff(342,plain,
% 0.71/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[341, 337])).
% 0.71/0.74 tff(343,plain,(
% 0.71/0.74 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.74 inference(skolemize,[status(sab)],[342])).
% 0.71/0.74 tff(344,plain,
% 0.71/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[343, 336])).
% 0.71/0.74 tff(345,assumption,(hskp11), introduced(assumption)).
% 0.71/0.74 tff(346,plain,
% 0.71/0.74 (((~hskp11) | (~c3_1(a2093))) <=> ((~hskp11) | (~c3_1(a2093)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(347,plain,
% 0.71/0.74 (((~c3_1(a2093)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a2093)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(348,axiom,((~c3_1(a2093)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 0.71/0.74 tff(349,plain,
% 0.71/0.74 ((~hskp11) | (~c3_1(a2093))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.71/0.74 tff(350,plain,
% 0.71/0.74 ((~hskp11) | (~c3_1(a2093))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[349, 346])).
% 0.71/0.74 tff(351,plain,
% 0.71/0.74 (~c3_1(a2093)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[350, 345])).
% 0.71/0.74 tff(352,plain,
% 0.71/0.74 (((~hskp11) | (~c1_1(a2093))) <=> ((~hskp11) | (~c1_1(a2093)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(353,plain,
% 0.71/0.74 (((~c1_1(a2093)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a2093)))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(354,axiom,((~c1_1(a2093)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 0.71/0.74 tff(355,plain,
% 0.71/0.74 ((~hskp11) | (~c1_1(a2093))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.71/0.74 tff(356,plain,
% 0.71/0.74 ((~hskp11) | (~c1_1(a2093))),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[355, 352])).
% 0.71/0.74 tff(357,plain,
% 0.71/0.74 (~c1_1(a2093)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[356, 345])).
% 0.71/0.74 tff(358,plain,
% 0.71/0.74 (((~hskp11) | c0_1(a2093)) <=> ((~hskp11) | c0_1(a2093))),
% 0.71/0.74 inference(rewrite,[status(thm)],[])).
% 0.71/0.74 tff(359,axiom,((~hskp11) | c0_1(a2093)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 0.71/0.74 tff(360,plain,
% 0.71/0.74 ((~hskp11) | c0_1(a2093)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.71/0.74 tff(361,plain,
% 0.71/0.74 ((~hskp11) | c0_1(a2093)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[360, 358])).
% 0.71/0.74 tff(362,plain,
% 0.71/0.74 ((~hskp11) | c0_1(a2093)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[361, 358])).
% 0.71/0.74 tff(363,plain,
% 0.71/0.74 ((~hskp11) | c0_1(a2093)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[362, 358])).
% 0.71/0.74 tff(364,plain,
% 0.71/0.74 ((~hskp11) | c0_1(a2093)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[363, 358])).
% 0.71/0.74 tff(365,plain,
% 0.71/0.74 ((~hskp11) | c0_1(a2093)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[364, 358])).
% 0.71/0.74 tff(366,plain,
% 0.71/0.74 ((~hskp11) | c0_1(a2093)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[365, 358])).
% 0.71/0.74 tff(367,plain,
% 0.71/0.74 ((~hskp11) | c0_1(a2093)),
% 0.71/0.74 inference(modus_ponens,[status(thm)],[366, 358])).
% 0.71/0.74 tff(368,plain,
% 0.71/0.74 (c0_1(a2093)),
% 0.71/0.74 inference(unit_resolution,[status(thm)],[367, 345])).
% 0.71/0.74 tff(369,assumption,(~hskp29), introduced(assumption)).
% 0.71/0.74 tff(370,plain,
% 0.71/0.74 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.71/0.74 inference(bind,[status(th)],[])).
% 0.71/0.74 tff(371,plain,
% 0.71/0.74 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.71/0.74 inference(quant_intro,[status(thm)],[370])).
% 0.71/0.75 tff(372,plain,
% 0.71/0.75 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(373,plain,
% 0.71/0.75 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~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))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(374,plain,
% 0.71/0.75 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[373])).
% 0.71/0.75 tff(375,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 0.71/0.75 tff(376,plain,
% 0.71/0.75 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.71/0.75 tff(377,plain,
% 0.71/0.75 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[376, 372])).
% 0.71/0.75 tff(378,plain,(
% 0.71/0.75 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.71/0.75 inference(skolemize,[status(sab)],[377])).
% 0.71/0.75 tff(379,plain,
% 0.71/0.75 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[378, 371])).
% 0.71/0.75 tff(380,assumption,(~hskp5), introduced(assumption)).
% 0.71/0.75 tff(381,plain,
% 0.71/0.75 (hskp3),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[97, 380, 369])).
% 0.71/0.75 tff(382,plain,
% 0.71/0.75 (((~hskp3) | (~c3_1(a2072))) <=> ((~hskp3) | (~c3_1(a2072)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(383,plain,
% 0.71/0.75 (((~c3_1(a2072)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a2072)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(384,axiom,((~c3_1(a2072)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 0.71/0.75 tff(385,plain,
% 0.71/0.75 ((~hskp3) | (~c3_1(a2072))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.71/0.75 tff(386,plain,
% 0.71/0.75 ((~hskp3) | (~c3_1(a2072))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[385, 382])).
% 0.71/0.75 tff(387,plain,
% 0.71/0.75 (~c3_1(a2072)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[386, 381])).
% 0.71/0.75 tff(388,plain,
% 0.71/0.75 (((~hskp3) | (~c1_1(a2072))) <=> ((~hskp3) | (~c1_1(a2072)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(389,plain,
% 0.71/0.75 (((~c1_1(a2072)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a2072)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(390,axiom,((~c1_1(a2072)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 0.71/0.75 tff(391,plain,
% 0.71/0.75 ((~hskp3) | (~c1_1(a2072))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.71/0.75 tff(392,plain,
% 0.71/0.75 ((~hskp3) | (~c1_1(a2072))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[391, 388])).
% 0.71/0.75 tff(393,plain,
% 0.71/0.75 (~c1_1(a2072)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[392, 381])).
% 0.71/0.75 tff(394,plain,
% 0.71/0.75 (((~hskp3) | (~c0_1(a2072))) <=> ((~hskp3) | (~c0_1(a2072)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(395,plain,
% 0.71/0.75 (((~c0_1(a2072)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a2072)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(396,axiom,((~c0_1(a2072)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 0.71/0.75 tff(397,plain,
% 0.71/0.75 ((~hskp3) | (~c0_1(a2072))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.71/0.75 tff(398,plain,
% 0.71/0.75 ((~hskp3) | (~c0_1(a2072))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[397, 394])).
% 0.71/0.75 tff(399,plain,
% 0.71/0.75 (~c0_1(a2072)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[398, 381])).
% 0.71/0.75 tff(400,assumption,(~c2_1(a2072)), introduced(assumption)).
% 0.71/0.75 tff(401,plain,
% 0.71/0.75 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(402,plain,
% 0.71/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[401])).
% 0.71/0.75 tff(403,plain,
% 0.71/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(404,plain,
% 0.71/0.75 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V))), (((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W))), (((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W))), ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(405,plain,
% 0.71/0.75 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | 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)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[404])).
% 0.71/0.75 tff(406,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c1_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 0.71/0.75 tff(407,plain,
% 0.71/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.71/0.75 tff(408,plain,
% 0.71/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[407, 403])).
% 0.71/0.75 tff(409,plain,(
% 0.71/0.75 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.75 inference(skolemize,[status(sab)],[408])).
% 0.71/0.75 tff(410,plain,
% 0.71/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[409, 402])).
% 0.71/0.75 tff(411,assumption,(~c3_1(a2072)), introduced(assumption)).
% 0.71/0.75 tff(412,assumption,(~c1_1(a2072)), introduced(assumption)).
% 0.71/0.75 tff(413,assumption,(~c0_1(a2072)), introduced(assumption)).
% 0.71/0.75 tff(414,plain,
% 0.71/0.75 (^[U: $i] : refl((hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(415,plain,
% 0.71/0.75 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[414])).
% 0.71/0.75 tff(416,plain,
% 0.71/0.75 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(417,plain,
% 0.71/0.75 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp4) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp4))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp4) <=> (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp4) <=> (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(418,plain,
% 0.71/0.75 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp4) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[417])).
% 0.71/0.75 tff(419,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 0.71/0.75 tff(420,plain,
% 0.71/0.75 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[419, 418])).
% 0.71/0.75 tff(421,plain,
% 0.71/0.75 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[420, 416])).
% 0.71/0.75 tff(422,plain,(
% 0.71/0.75 ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.75 inference(skolemize,[status(sab)],[421])).
% 0.71/0.75 tff(423,plain,
% 0.71/0.75 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[422, 415])).
% 0.71/0.75 tff(424,plain,
% 0.71/0.75 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(425,plain,
% 0.71/0.75 ((hskp5 | hskp4 | (~ndr1_0) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072)) <=> (hskp5 | hskp4 | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(426,plain,
% 0.71/0.75 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072)))),
% 0.71/0.75 inference(monotonicity,[status(thm)],[425])).
% 0.71/0.75 tff(427,plain,
% 0.71/0.75 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072))),
% 0.71/0.75 inference(transitivity,[status(thm)],[426, 424])).
% 0.71/0.75 tff(428,plain,
% 0.71/0.75 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp5 | hskp4 | (~ndr1_0) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(429,plain,
% 0.71/0.75 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp5 | hskp4 | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[428, 427])).
% 0.71/0.75 tff(430,plain,
% 0.71/0.75 (hskp4 | c2_1(a2072)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[429, 99, 380, 413, 411, 423])).
% 0.71/0.75 tff(431,plain,
% 0.71/0.75 (hskp4),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[430, 400])).
% 0.71/0.75 tff(432,plain,
% 0.71/0.75 (~c2_1(a2074)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[273, 431])).
% 0.71/0.75 tff(433,plain,
% 0.71/0.75 (c1_1(a2074)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[295, 431])).
% 0.71/0.75 tff(434,plain,
% 0.71/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2074) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2074) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(435,plain,
% 0.71/0.75 (((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072)) <=> (c2_1(a2074) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(436,plain,
% 0.71/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2074) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074)))),
% 0.71/0.75 inference(monotonicity,[status(thm)],[435])).
% 0.71/0.75 tff(437,plain,
% 0.71/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2074) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.71/0.75 inference(transitivity,[status(thm)],[436, 434])).
% 0.71/0.75 tff(438,plain,
% 0.71/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(439,plain,
% 0.71/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2074) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074)),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.71/0.75 tff(440,plain,
% 0.71/0.75 (c0_1(a2074)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[439, 99, 433, 432, 413, 412, 411, 410, 400])).
% 0.71/0.75 tff(441,plain,
% 0.71/0.75 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(442,plain,
% 0.71/0.75 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[441])).
% 0.71/0.75 tff(443,plain,
% 0.71/0.75 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(444,plain,
% 0.71/0.75 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~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))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.71/0.75 inference(bind,[status(th)],[])).
% 0.71/0.75 tff(445,plain,
% 0.71/0.75 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.75 inference(quant_intro,[status(thm)],[444])).
% 0.71/0.75 tff(446,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 0.71/0.75 tff(447,plain,
% 0.71/0.75 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.71/0.75 tff(448,plain,
% 0.71/0.75 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[447, 443])).
% 0.71/0.75 tff(449,plain,(
% 0.71/0.75 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.75 inference(skolemize,[status(sab)],[448])).
% 0.71/0.75 tff(450,plain,
% 0.71/0.75 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[449, 442])).
% 0.71/0.75 tff(451,plain,
% 0.71/0.75 (c3_1(a2074)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[284, 431])).
% 0.71/0.75 tff(452,plain,
% 0.71/0.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(453,plain,
% 0.71/0.75 ((hskp5 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074))) <=> (hskp5 | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.71/0.75 inference(rewrite,[status(thm)],[])).
% 0.71/0.75 tff(454,plain,
% 0.71/0.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074))))),
% 0.71/0.75 inference(monotonicity,[status(thm)],[453])).
% 0.71/0.75 tff(455,plain,
% 0.71/0.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.71/0.75 inference(transitivity,[status(thm)],[454, 452])).
% 0.71/0.75 tff(456,plain,
% 0.71/0.75 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.71/0.75 inference(quant_inst,[status(thm)],[])).
% 0.71/0.75 tff(457,plain,
% 0.71/0.75 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074))),
% 0.71/0.75 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.71/0.75 tff(458,plain,
% 0.71/0.75 ($false),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[457, 99, 380, 433, 451, 432, 450, 440])).
% 0.71/0.75 tff(459,plain,(c2_1(a2072) | hskp5 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.75 tff(460,plain,
% 0.71/0.75 (c2_1(a2072)),
% 0.71/0.75 inference(unit_resolution,[status(thm)],[459, 380, 399, 393, 387])).
% 0.71/0.75 tff(461,plain,
% 0.71/0.75 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(462,plain,
% 0.71/0.76 ((hskp4 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072)) <=> (hskp4 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(463,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072))))),
% 0.71/0.76 inference(monotonicity,[status(thm)],[462])).
% 0.71/0.76 tff(464,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))),
% 0.71/0.76 inference(transitivity,[status(thm)],[463, 461])).
% 0.71/0.76 tff(465,plain,
% 0.71/0.76 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp4 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072))),
% 0.71/0.76 inference(quant_inst,[status(thm)],[])).
% 0.71/0.76 tff(466,plain,
% 0.71/0.76 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp4 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072))),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.71/0.76 tff(467,plain,
% 0.71/0.76 (hskp4 | (~c2_1(a2072))),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[466, 99, 399, 393, 387, 259])).
% 0.71/0.76 tff(468,plain,
% 0.71/0.76 (hskp4),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[467, 460])).
% 0.71/0.76 tff(469,plain,
% 0.71/0.76 (~c2_1(a2074)),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[273, 468])).
% 0.71/0.76 tff(470,plain,
% 0.71/0.76 (c3_1(a2074)),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[284, 468])).
% 0.71/0.76 tff(471,plain,
% 0.71/0.76 (c1_1(a2074)),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[295, 468])).
% 0.71/0.76 tff(472,plain,
% 0.71/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(473,plain,
% 0.71/0.76 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072))) <=> (c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(474,plain,
% 0.71/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074))))),
% 0.71/0.76 inference(monotonicity,[status(thm)],[473])).
% 0.71/0.76 tff(475,plain,
% 0.71/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.71/0.76 inference(transitivity,[status(thm)],[474, 472])).
% 0.71/0.76 tff(476,plain,
% 0.71/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))),
% 0.71/0.76 inference(quant_inst,[status(thm)],[])).
% 0.71/0.76 tff(477,plain,
% 0.71/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074))),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.71/0.76 tff(478,plain,
% 0.71/0.76 (~c0_1(a2074)),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[477, 99, 471, 470, 469, 399, 387, 10, 460])).
% 0.71/0.76 tff(479,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2074)) | c0_1(a2074))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(480,plain,
% 0.71/0.76 ((hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074))) <=> (hskp8 | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(481,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2074)) | c0_1(a2074)))),
% 0.71/0.76 inference(monotonicity,[status(thm)],[480])).
% 0.71/0.76 tff(482,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.71/0.76 inference(transitivity,[status(thm)],[481, 479])).
% 0.71/0.76 tff(483,plain,
% 0.71/0.76 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2074) | c2_1(a2074) | (~c1_1(a2074)))),
% 0.71/0.76 inference(quant_inst,[status(thm)],[])).
% 0.71/0.76 tff(484,plain,
% 0.71/0.76 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2074)) | c0_1(a2074)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[483, 482])).
% 0.71/0.76 tff(485,plain,
% 0.71/0.76 (hskp8),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[484, 99, 471, 469, 393, 387, 313, 460, 478])).
% 0.71/0.76 tff(486,plain,
% 0.71/0.76 (~c0_1(a2082)),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[173, 485])).
% 0.71/0.76 tff(487,plain,
% 0.71/0.76 (c2_1(a2082)),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[184, 485])).
% 0.71/0.76 tff(488,plain,
% 0.71/0.76 (c1_1(a2082)),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[195, 485])).
% 0.71/0.76 tff(489,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a2082) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a2082) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(490,plain,
% 0.71/0.76 ((hskp11 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082))) <=> (hskp11 | c0_1(a2082) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(491,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c0_1(a2082) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082))))),
% 0.71/0.76 inference(monotonicity,[status(thm)],[490])).
% 0.71/0.76 tff(492,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a2082) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.71/0.76 inference(transitivity,[status(thm)],[491, 489])).
% 0.71/0.76 tff(493,plain,
% 0.71/0.76 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2082) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.71/0.76 inference(quant_inst,[status(thm)],[])).
% 0.71/0.76 tff(494,plain,
% 0.71/0.76 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c0_1(a2082) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082))),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[493, 492])).
% 0.71/0.76 tff(495,plain,
% 0.71/0.76 (hskp11),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[494, 99, 488, 487, 486, 393, 387, 21, 460])).
% 0.71/0.76 tff(496,plain,
% 0.71/0.76 (~c3_1(a2093)),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[350, 495])).
% 0.71/0.76 tff(497,plain,
% 0.71/0.76 (~c1_1(a2093)),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[356, 495])).
% 0.71/0.76 tff(498,plain,
% 0.71/0.76 (c0_1(a2093)),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[367, 495])).
% 0.71/0.76 tff(499,plain,
% 0.71/0.76 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.71/0.76 inference(bind,[status(th)],[])).
% 0.71/0.76 tff(500,plain,
% 0.71/0.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.76 inference(quant_intro,[status(thm)],[499])).
% 0.71/0.76 tff(501,plain,
% 0.71/0.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(502,plain,
% 0.71/0.76 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.71/0.76 inference(bind,[status(th)],[])).
% 0.71/0.76 tff(503,plain,
% 0.71/0.76 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.76 inference(quant_intro,[status(thm)],[502])).
% 0.71/0.76 tff(504,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 0.71/0.76 tff(505,plain,
% 0.71/0.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.71/0.76 tff(506,plain,
% 0.71/0.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[505, 501])).
% 0.71/0.76 tff(507,plain,(
% 0.71/0.76 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.76 inference(skolemize,[status(sab)],[506])).
% 0.71/0.76 tff(508,plain,
% 0.71/0.76 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[507, 500])).
% 0.71/0.76 tff(509,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a2082) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a2082) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(510,plain,
% 0.71/0.76 ((hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2072) | c0_1(a2072) | (~c2_1(a2072))) <=> (hskp1 | c0_1(a2082) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(511,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2072) | c0_1(a2072) | (~c2_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c0_1(a2082) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082))))),
% 0.71/0.76 inference(monotonicity,[status(thm)],[510])).
% 0.71/0.76 tff(512,plain,
% 0.71/0.76 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2072) | c0_1(a2072) | (~c2_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a2082) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082)))),
% 0.71/0.76 inference(transitivity,[status(thm)],[511, 509])).
% 0.71/0.76 tff(513,plain,
% 0.71/0.76 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2072) | c0_1(a2072) | (~c2_1(a2072)))),
% 0.71/0.76 inference(quant_inst,[status(thm)],[])).
% 0.71/0.76 tff(514,plain,
% 0.71/0.76 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c0_1(a2082) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)) | (~c1_1(a2082)) | (~c2_1(a2082))),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[513, 512])).
% 0.71/0.76 tff(515,plain,
% 0.71/0.76 (hskp1),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[514, 99, 488, 487, 486, 399, 387, 508, 460])).
% 0.71/0.76 tff(516,plain,
% 0.71/0.76 (^[U: $i] : refl((hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.71/0.76 inference(bind,[status(th)],[])).
% 0.71/0.76 tff(517,plain,
% 0.71/0.76 (![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.76 inference(quant_intro,[status(thm)],[516])).
% 0.71/0.76 tff(518,plain,
% 0.71/0.76 (![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(519,plain,
% 0.71/0.76 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp5) <=> ((hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5))), rewrite(((hskp26 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp5) <=> (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.71/0.76 inference(bind,[status(th)],[])).
% 0.71/0.76 tff(520,plain,
% 0.71/0.76 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp5) <=> ![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.76 inference(quant_intro,[status(thm)],[519])).
% 0.71/0.76 tff(521,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp26) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause145')).
% 0.71/0.76 tff(522,plain,
% 0.71/0.76 (![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[521, 520])).
% 0.71/0.76 tff(523,plain,
% 0.71/0.76 (![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[522, 518])).
% 0.71/0.76 tff(524,plain,(
% 0.71/0.76 ![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.76 inference(skolemize,[status(sab)],[523])).
% 0.71/0.76 tff(525,plain,
% 0.71/0.76 (![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[524, 517])).
% 0.71/0.76 tff(526,assumption,(hskp1), introduced(assumption)).
% 0.71/0.76 tff(527,plain,
% 0.71/0.76 (((~hskp1) | c3_1(a2070)) <=> ((~hskp1) | c3_1(a2070))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(528,axiom,((~hskp1) | c3_1(a2070)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 0.71/0.76 tff(529,plain,
% 0.71/0.76 ((~hskp1) | c3_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.71/0.76 tff(530,plain,
% 0.71/0.76 ((~hskp1) | c3_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[529, 527])).
% 0.71/0.76 tff(531,plain,
% 0.71/0.76 ((~hskp1) | c3_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[530, 527])).
% 0.71/0.76 tff(532,plain,
% 0.71/0.76 ((~hskp1) | c3_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[531, 527])).
% 0.71/0.76 tff(533,plain,
% 0.71/0.76 ((~hskp1) | c3_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[532, 527])).
% 0.71/0.76 tff(534,plain,
% 0.71/0.76 ((~hskp1) | c3_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[533, 527])).
% 0.71/0.76 tff(535,plain,
% 0.71/0.76 ((~hskp1) | c3_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[534, 527])).
% 0.71/0.76 tff(536,plain,
% 0.71/0.76 ((~hskp1) | c3_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[535, 527])).
% 0.71/0.76 tff(537,plain,
% 0.71/0.76 (c3_1(a2070)),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[536, 526])).
% 0.71/0.76 tff(538,plain,
% 0.71/0.76 (((~hskp1) | c0_1(a2070)) <=> ((~hskp1) | c0_1(a2070))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(539,axiom,((~hskp1) | c0_1(a2070)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 0.71/0.76 tff(540,plain,
% 0.71/0.76 ((~hskp1) | c0_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[539, 538])).
% 0.71/0.76 tff(541,plain,
% 0.71/0.76 ((~hskp1) | c0_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[540, 538])).
% 0.71/0.76 tff(542,plain,
% 0.71/0.76 ((~hskp1) | c0_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[541, 538])).
% 0.71/0.76 tff(543,plain,
% 0.71/0.76 ((~hskp1) | c0_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[542, 538])).
% 0.71/0.76 tff(544,plain,
% 0.71/0.76 ((~hskp1) | c0_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[543, 538])).
% 0.71/0.76 tff(545,plain,
% 0.71/0.76 ((~hskp1) | c0_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[544, 538])).
% 0.71/0.76 tff(546,plain,
% 0.71/0.76 ((~hskp1) | c0_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[545, 538])).
% 0.71/0.76 tff(547,plain,
% 0.71/0.76 ((~hskp1) | c0_1(a2070)),
% 0.71/0.76 inference(modus_ponens,[status(thm)],[546, 538])).
% 0.71/0.76 tff(548,plain,
% 0.71/0.76 (c0_1(a2070)),
% 0.71/0.76 inference(unit_resolution,[status(thm)],[547, 526])).
% 0.71/0.76 tff(549,assumption,(~hskp26), introduced(assumption)).
% 0.71/0.76 tff(550,plain,
% 0.71/0.76 (((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp5 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp5 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(551,plain,
% 0.71/0.76 ((hskp26 | hskp5 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070))) <=> (hskp26 | hskp5 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))),
% 0.71/0.76 inference(rewrite,[status(thm)],[])).
% 0.71/0.76 tff(552,plain,
% 0.71/0.76 (((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp5 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp5 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070))))),
% 0.71/0.77 inference(monotonicity,[status(thm)],[551])).
% 0.71/0.77 tff(553,plain,
% 0.71/0.77 (((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp5 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp5 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))),
% 0.71/0.77 inference(transitivity,[status(thm)],[552, 550])).
% 0.71/0.77 tff(554,plain,
% 0.71/0.77 ((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp26 | hskp5 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))),
% 0.71/0.77 inference(quant_inst,[status(thm)],[])).
% 0.71/0.77 tff(555,plain,
% 0.71/0.77 ((~![U: $i] : (hskp26 | hskp5 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp26 | hskp5 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070))),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[554, 553])).
% 0.71/0.77 tff(556,plain,
% 0.71/0.77 (c1_1(a2070)),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[555, 99, 549, 380, 548, 537, 525])).
% 0.71/0.77 tff(557,plain,
% 0.71/0.77 (((~hskp1) | (~c2_1(a2070))) <=> ((~hskp1) | (~c2_1(a2070)))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(558,plain,
% 0.71/0.77 (((~c2_1(a2070)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a2070)))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(559,axiom,((~c2_1(a2070)) | (~hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 0.71/0.77 tff(560,plain,
% 0.71/0.77 ((~hskp1) | (~c2_1(a2070))),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.71/0.77 tff(561,plain,
% 0.71/0.77 ((~hskp1) | (~c2_1(a2070))),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[560, 557])).
% 0.71/0.77 tff(562,plain,
% 0.71/0.77 (~c2_1(a2070)),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[561, 526])).
% 0.71/0.77 tff(563,plain,
% 0.71/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(564,plain,
% 0.71/0.77 ((hskp5 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070))) <=> (hskp5 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(565,plain,
% 0.71/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070))))),
% 0.71/0.77 inference(monotonicity,[status(thm)],[564])).
% 0.71/0.77 tff(566,plain,
% 0.71/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.71/0.77 inference(transitivity,[status(thm)],[565, 563])).
% 0.71/0.77 tff(567,plain,
% 0.71/0.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.71/0.77 inference(quant_inst,[status(thm)],[])).
% 0.71/0.77 tff(568,plain,
% 0.71/0.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070))),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.71/0.77 tff(569,plain,
% 0.71/0.77 ($false),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[568, 99, 380, 548, 537, 562, 450, 556])).
% 0.71/0.77 tff(570,plain,((~hskp1) | hskp5 | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.71/0.77 tff(571,plain,
% 0.71/0.77 (hskp26),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[570, 515, 380])).
% 0.71/0.77 tff(572,plain,
% 0.71/0.77 (((~hskp26) | c3_1(a2069)) <=> ((~hskp26) | c3_1(a2069))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(573,axiom,((~hskp26) | c3_1(a2069)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 0.71/0.77 tff(574,plain,
% 0.71/0.77 ((~hskp26) | c3_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.71/0.77 tff(575,plain,
% 0.71/0.77 ((~hskp26) | c3_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[574, 572])).
% 0.71/0.77 tff(576,plain,
% 0.71/0.77 ((~hskp26) | c3_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[575, 572])).
% 0.71/0.77 tff(577,plain,
% 0.71/0.77 ((~hskp26) | c3_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[576, 572])).
% 0.71/0.77 tff(578,plain,
% 0.71/0.77 ((~hskp26) | c3_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[577, 572])).
% 0.71/0.77 tff(579,plain,
% 0.71/0.77 ((~hskp26) | c3_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[578, 572])).
% 0.71/0.77 tff(580,plain,
% 0.71/0.77 ((~hskp26) | c3_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[579, 572])).
% 0.71/0.77 tff(581,plain,
% 0.71/0.77 ((~hskp26) | c3_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[580, 572])).
% 0.71/0.77 tff(582,plain,
% 0.71/0.77 (c3_1(a2069)),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[581, 571])).
% 0.71/0.77 tff(583,plain,
% 0.71/0.77 (((~hskp26) | c2_1(a2069)) <=> ((~hskp26) | c2_1(a2069))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(584,axiom,((~hskp26) | c2_1(a2069)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 0.71/0.77 tff(585,plain,
% 0.71/0.77 ((~hskp26) | c2_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[584, 583])).
% 0.71/0.77 tff(586,plain,
% 0.71/0.77 ((~hskp26) | c2_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[585, 583])).
% 0.71/0.77 tff(587,plain,
% 0.71/0.77 ((~hskp26) | c2_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[586, 583])).
% 0.71/0.77 tff(588,plain,
% 0.71/0.77 ((~hskp26) | c2_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[587, 583])).
% 0.71/0.77 tff(589,plain,
% 0.71/0.77 ((~hskp26) | c2_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[588, 583])).
% 0.71/0.77 tff(590,plain,
% 0.71/0.77 ((~hskp26) | c2_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[589, 583])).
% 0.71/0.77 tff(591,plain,
% 0.71/0.77 ((~hskp26) | c2_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[590, 583])).
% 0.71/0.77 tff(592,plain,
% 0.71/0.77 ((~hskp26) | c2_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[591, 583])).
% 0.71/0.77 tff(593,plain,
% 0.71/0.77 (c2_1(a2069)),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[592, 571])).
% 0.71/0.77 tff(594,plain,
% 0.71/0.77 (((~hskp26) | c0_1(a2069)) <=> ((~hskp26) | c0_1(a2069))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(595,axiom,((~hskp26) | c0_1(a2069)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 0.71/0.77 tff(596,plain,
% 0.71/0.77 ((~hskp26) | c0_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[595, 594])).
% 0.71/0.77 tff(597,plain,
% 0.71/0.77 ((~hskp26) | c0_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[596, 594])).
% 0.71/0.77 tff(598,plain,
% 0.71/0.77 ((~hskp26) | c0_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[597, 594])).
% 0.71/0.77 tff(599,plain,
% 0.71/0.77 ((~hskp26) | c0_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[598, 594])).
% 0.71/0.77 tff(600,plain,
% 0.71/0.77 ((~hskp26) | c0_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[599, 594])).
% 0.71/0.77 tff(601,plain,
% 0.71/0.77 ((~hskp26) | c0_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[600, 594])).
% 0.71/0.77 tff(602,plain,
% 0.71/0.77 ((~hskp26) | c0_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[601, 594])).
% 0.71/0.77 tff(603,plain,
% 0.71/0.77 ((~hskp26) | c0_1(a2069)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[602, 594])).
% 0.71/0.77 tff(604,plain,
% 0.71/0.77 (c0_1(a2069)),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[603, 571])).
% 0.71/0.77 tff(605,plain,
% 0.71/0.77 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.71/0.77 inference(bind,[status(th)],[])).
% 0.71/0.77 tff(606,plain,
% 0.71/0.77 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.77 inference(quant_intro,[status(thm)],[605])).
% 0.71/0.77 tff(607,plain,
% 0.71/0.77 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(608,plain,
% 0.71/0.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp27))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.71/0.77 inference(bind,[status(th)],[])).
% 0.71/0.77 tff(609,plain,
% 0.71/0.77 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.77 inference(quant_intro,[status(thm)],[608])).
% 0.71/0.77 tff(610,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 0.71/0.77 tff(611,plain,
% 0.71/0.77 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.71/0.77 tff(612,plain,
% 0.71/0.77 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[611, 607])).
% 0.71/0.77 tff(613,plain,(
% 0.71/0.77 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.77 inference(skolemize,[status(sab)],[612])).
% 0.71/0.77 tff(614,plain,
% 0.71/0.77 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[613, 606])).
% 0.71/0.77 tff(615,plain,
% 0.71/0.77 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(616,plain,
% 0.71/0.77 ((hskp27 | (~ndr1_0) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072)) <=> (hskp27 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(617,plain,
% 0.71/0.77 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072))))),
% 0.71/0.77 inference(monotonicity,[status(thm)],[616])).
% 0.71/0.77 tff(618,plain,
% 0.71/0.77 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072)))),
% 0.71/0.77 inference(transitivity,[status(thm)],[617, 615])).
% 0.71/0.77 tff(619,plain,
% 0.71/0.77 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp27 | (~ndr1_0) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)) | c3_1(a2072) | c1_1(a2072) | c0_1(a2072))),
% 0.71/0.77 inference(quant_inst,[status(thm)],[])).
% 0.71/0.77 tff(620,plain,
% 0.71/0.77 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp27 | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | (~c2_1(a2072))),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.71/0.77 tff(621,plain,
% 0.71/0.77 (hskp27 | (~c2_1(a2072))),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[620, 99, 399, 393, 387, 614])).
% 0.71/0.77 tff(622,plain,
% 0.71/0.77 (hskp27),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[621, 460])).
% 0.71/0.77 tff(623,plain,
% 0.71/0.77 (((~hskp27) | c3_1(a2073)) <=> ((~hskp27) | c3_1(a2073))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(624,axiom,((~hskp27) | c3_1(a2073)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 0.71/0.77 tff(625,plain,
% 0.71/0.77 ((~hskp27) | c3_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[624, 623])).
% 0.71/0.77 tff(626,plain,
% 0.71/0.77 ((~hskp27) | c3_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[625, 623])).
% 0.71/0.77 tff(627,plain,
% 0.71/0.77 ((~hskp27) | c3_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[626, 623])).
% 0.71/0.77 tff(628,plain,
% 0.71/0.77 ((~hskp27) | c3_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[627, 623])).
% 0.71/0.77 tff(629,plain,
% 0.71/0.77 ((~hskp27) | c3_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[628, 623])).
% 0.71/0.77 tff(630,plain,
% 0.71/0.77 ((~hskp27) | c3_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[629, 623])).
% 0.71/0.77 tff(631,plain,
% 0.71/0.77 ((~hskp27) | c3_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[630, 623])).
% 0.71/0.77 tff(632,plain,
% 0.71/0.77 ((~hskp27) | c3_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[631, 623])).
% 0.71/0.77 tff(633,plain,
% 0.71/0.77 (c3_1(a2073)),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[632, 622])).
% 0.71/0.77 tff(634,plain,
% 0.71/0.77 (((~hskp27) | c1_1(a2073)) <=> ((~hskp27) | c1_1(a2073))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(635,axiom,((~hskp27) | c1_1(a2073)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 0.71/0.77 tff(636,plain,
% 0.71/0.77 ((~hskp27) | c1_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.71/0.77 tff(637,plain,
% 0.71/0.77 ((~hskp27) | c1_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[636, 634])).
% 0.71/0.77 tff(638,plain,
% 0.71/0.77 ((~hskp27) | c1_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[637, 634])).
% 0.71/0.77 tff(639,plain,
% 0.71/0.77 ((~hskp27) | c1_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[638, 634])).
% 0.71/0.77 tff(640,plain,
% 0.71/0.77 ((~hskp27) | c1_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[639, 634])).
% 0.71/0.77 tff(641,plain,
% 0.71/0.77 ((~hskp27) | c1_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[640, 634])).
% 0.71/0.77 tff(642,plain,
% 0.71/0.77 ((~hskp27) | c1_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[641, 634])).
% 0.71/0.77 tff(643,plain,
% 0.71/0.77 ((~hskp27) | c1_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[642, 634])).
% 0.71/0.77 tff(644,plain,
% 0.71/0.77 (c1_1(a2073)),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[643, 622])).
% 0.71/0.77 tff(645,plain,
% 0.71/0.77 (((~hskp27) | c0_1(a2073)) <=> ((~hskp27) | c0_1(a2073))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(646,axiom,((~hskp27) | c0_1(a2073)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 0.71/0.77 tff(647,plain,
% 0.71/0.77 ((~hskp27) | c0_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.71/0.77 tff(648,plain,
% 0.71/0.77 ((~hskp27) | c0_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[647, 645])).
% 0.71/0.77 tff(649,plain,
% 0.71/0.77 ((~hskp27) | c0_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[648, 645])).
% 0.71/0.77 tff(650,plain,
% 0.71/0.77 ((~hskp27) | c0_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[649, 645])).
% 0.71/0.77 tff(651,plain,
% 0.71/0.77 ((~hskp27) | c0_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[650, 645])).
% 0.71/0.77 tff(652,plain,
% 0.71/0.77 ((~hskp27) | c0_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[651, 645])).
% 0.71/0.77 tff(653,plain,
% 0.71/0.77 ((~hskp27) | c0_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[652, 645])).
% 0.71/0.77 tff(654,plain,
% 0.71/0.77 ((~hskp27) | c0_1(a2073)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[653, 645])).
% 0.71/0.77 tff(655,plain,
% 0.71/0.77 (c0_1(a2073)),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[654, 622])).
% 0.71/0.77 tff(656,plain,
% 0.71/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2093)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2093)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(657,plain,
% 0.71/0.77 (((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093))) <=> (c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2093)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(658,plain,
% 0.71/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2093)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))))),
% 0.71/0.77 inference(monotonicity,[status(thm)],[657])).
% 0.71/0.77 tff(659,plain,
% 0.71/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2093)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.71/0.77 inference(transitivity,[status(thm)],[658, 656])).
% 0.71/0.77 tff(660,plain,
% 0.71/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))),
% 0.71/0.77 inference(quant_inst,[status(thm)],[])).
% 0.71/0.77 tff(661,plain,
% 0.71/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2093)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[660, 659])).
% 0.71/0.77 tff(662,plain,
% 0.71/0.77 ($false),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[661, 99, 655, 644, 633, 604, 593, 582, 498, 497, 496, 344])).
% 0.71/0.77 tff(663,plain,(hskp5 | hskp29), inference(lemma,lemma(discharge,[]))).
% 0.71/0.77 tff(664,plain,
% 0.71/0.77 (hskp5),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[663, 369])).
% 0.71/0.77 tff(665,plain,
% 0.71/0.77 (((~hskp5) | c3_1(a2076)) <=> ((~hskp5) | c3_1(a2076))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(666,axiom,((~hskp5) | c3_1(a2076)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 0.71/0.77 tff(667,plain,
% 0.71/0.77 ((~hskp5) | c3_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[666, 665])).
% 0.71/0.77 tff(668,plain,
% 0.71/0.77 ((~hskp5) | c3_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[667, 665])).
% 0.71/0.77 tff(669,plain,
% 0.71/0.77 ((~hskp5) | c3_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[668, 665])).
% 0.71/0.77 tff(670,plain,
% 0.71/0.77 ((~hskp5) | c3_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[669, 665])).
% 0.71/0.77 tff(671,plain,
% 0.71/0.77 ((~hskp5) | c3_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[670, 665])).
% 0.71/0.77 tff(672,plain,
% 0.71/0.77 ((~hskp5) | c3_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[671, 665])).
% 0.71/0.77 tff(673,plain,
% 0.71/0.77 ((~hskp5) | c3_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[672, 665])).
% 0.71/0.77 tff(674,plain,
% 0.71/0.77 ((~hskp5) | c3_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[673, 665])).
% 0.71/0.77 tff(675,plain,
% 0.71/0.77 (c3_1(a2076)),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[674, 664])).
% 0.71/0.77 tff(676,plain,
% 0.71/0.77 (((~hskp5) | (~c0_1(a2076))) <=> ((~hskp5) | (~c0_1(a2076)))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(677,plain,
% 0.71/0.77 (((~c0_1(a2076)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a2076)))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(678,axiom,((~c0_1(a2076)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 0.71/0.77 tff(679,plain,
% 0.71/0.77 ((~hskp5) | (~c0_1(a2076))),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[678, 677])).
% 0.71/0.77 tff(680,plain,
% 0.71/0.77 ((~hskp5) | (~c0_1(a2076))),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[679, 676])).
% 0.71/0.77 tff(681,plain,
% 0.71/0.77 (~c0_1(a2076)),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[680, 664])).
% 0.71/0.77 tff(682,plain,
% 0.71/0.77 (((~hskp5) | c1_1(a2076)) <=> ((~hskp5) | c1_1(a2076))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(683,axiom,((~hskp5) | c1_1(a2076)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 0.71/0.77 tff(684,plain,
% 0.71/0.77 ((~hskp5) | c1_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[683, 682])).
% 0.71/0.77 tff(685,plain,
% 0.71/0.77 ((~hskp5) | c1_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[684, 682])).
% 0.71/0.77 tff(686,plain,
% 0.71/0.77 ((~hskp5) | c1_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[685, 682])).
% 0.71/0.77 tff(687,plain,
% 0.71/0.77 ((~hskp5) | c1_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[686, 682])).
% 0.71/0.77 tff(688,plain,
% 0.71/0.77 ((~hskp5) | c1_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[687, 682])).
% 0.71/0.77 tff(689,plain,
% 0.71/0.77 ((~hskp5) | c1_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[688, 682])).
% 0.71/0.77 tff(690,plain,
% 0.71/0.77 ((~hskp5) | c1_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[689, 682])).
% 0.71/0.77 tff(691,plain,
% 0.71/0.77 ((~hskp5) | c1_1(a2076)),
% 0.71/0.77 inference(modus_ponens,[status(thm)],[690, 682])).
% 0.71/0.77 tff(692,plain,
% 0.71/0.77 (c1_1(a2076)),
% 0.71/0.77 inference(unit_resolution,[status(thm)],[691, 664])).
% 0.71/0.77 tff(693,assumption,(~hskp3), introduced(assumption)).
% 0.71/0.77 tff(694,plain,
% 0.71/0.77 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.71/0.77 inference(bind,[status(th)],[])).
% 0.71/0.77 tff(695,plain,
% 0.71/0.77 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.77 inference(quant_intro,[status(thm)],[694])).
% 0.71/0.77 tff(696,plain,
% 0.71/0.77 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.77 inference(rewrite,[status(thm)],[])).
% 0.71/0.77 tff(697,plain,
% 0.71/0.77 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.71/0.77 inference(bind,[status(th)],[])).
% 0.71/0.77 tff(698,plain,
% 0.71/0.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.78 inference(quant_intro,[status(thm)],[697])).
% 0.71/0.78 tff(699,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 0.71/0.78 tff(700,plain,
% 0.71/0.78 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[699, 698])).
% 0.71/0.78 tff(701,plain,
% 0.71/0.78 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[700, 696])).
% 0.71/0.78 tff(702,plain,(
% 0.71/0.78 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.78 inference(skolemize,[status(sab)],[701])).
% 0.71/0.78 tff(703,plain,
% 0.71/0.78 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[702, 695])).
% 0.71/0.78 tff(704,plain,
% 0.71/0.78 (^[U: $i] : refl((hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.71/0.78 inference(bind,[status(th)],[])).
% 0.71/0.78 tff(705,plain,
% 0.71/0.78 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(quant_intro,[status(thm)],[704])).
% 0.71/0.78 tff(706,plain,
% 0.71/0.78 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(707,plain,
% 0.71/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.71/0.78 inference(bind,[status(th)],[])).
% 0.71/0.78 tff(708,plain,
% 0.71/0.78 (![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0) <=> ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(quant_intro,[status(thm)],[707])).
% 0.71/0.78 tff(709,axiom,(![U: $i] : (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 0.71/0.78 tff(710,plain,
% 0.71/0.78 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[709, 708])).
% 0.71/0.78 tff(711,plain,
% 0.71/0.78 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[710, 706])).
% 0.71/0.78 tff(712,plain,(
% 0.71/0.78 ![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(skolemize,[status(sab)],[711])).
% 0.71/0.78 tff(713,plain,
% 0.71/0.78 (![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[712, 705])).
% 0.71/0.78 tff(714,assumption,(~c0_1(a2076)), introduced(assumption)).
% 0.71/0.78 tff(715,assumption,(c3_1(a2076)), introduced(assumption)).
% 0.71/0.78 tff(716,assumption,(c1_1(a2076)), introduced(assumption)).
% 0.71/0.78 tff(717,plain,
% 0.71/0.78 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(718,plain,
% 0.71/0.78 ((hskp0 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076))) <=> (hskp0 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(719,plain,
% 0.71/0.78 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076))))),
% 0.71/0.78 inference(monotonicity,[status(thm)],[718])).
% 0.71/0.78 tff(720,plain,
% 0.71/0.78 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.71/0.78 inference(transitivity,[status(thm)],[719, 717])).
% 0.71/0.78 tff(721,plain,
% 0.71/0.78 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.71/0.78 inference(quant_inst,[status(thm)],[])).
% 0.71/0.78 tff(722,plain,
% 0.71/0.78 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[721, 720])).
% 0.71/0.78 tff(723,plain,
% 0.71/0.78 (hskp0),
% 0.71/0.78 inference(unit_resolution,[status(thm)],[722, 99, 716, 715, 714, 713])).
% 0.71/0.78 tff(724,plain,
% 0.71/0.78 (((~hskp0) | (~c2_1(a2068))) <=> ((~hskp0) | (~c2_1(a2068)))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(725,plain,
% 0.71/0.78 (((~c2_1(a2068)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a2068)))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(726,axiom,((~c2_1(a2068)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 0.71/0.78 tff(727,plain,
% 0.71/0.78 ((~hskp0) | (~c2_1(a2068))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[726, 725])).
% 0.71/0.78 tff(728,plain,
% 0.71/0.78 ((~hskp0) | (~c2_1(a2068))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[727, 724])).
% 0.71/0.78 tff(729,plain,
% 0.71/0.78 (~c2_1(a2068)),
% 0.71/0.78 inference(unit_resolution,[status(thm)],[728, 723])).
% 0.71/0.78 tff(730,plain,
% 0.71/0.78 (((~hskp0) | (~c0_1(a2068))) <=> ((~hskp0) | (~c0_1(a2068)))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(731,plain,
% 0.71/0.78 (((~c0_1(a2068)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a2068)))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(732,axiom,((~c0_1(a2068)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 0.71/0.78 tff(733,plain,
% 0.71/0.78 ((~hskp0) | (~c0_1(a2068))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[732, 731])).
% 0.71/0.78 tff(734,plain,
% 0.71/0.78 ((~hskp0) | (~c0_1(a2068))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[733, 730])).
% 0.71/0.78 tff(735,plain,
% 0.71/0.78 (~c0_1(a2068)),
% 0.71/0.78 inference(unit_resolution,[status(thm)],[734, 723])).
% 0.71/0.78 tff(736,plain,
% 0.71/0.78 (((~hskp0) | c3_1(a2068)) <=> ((~hskp0) | c3_1(a2068))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(737,axiom,((~hskp0) | c3_1(a2068)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 0.71/0.78 tff(738,plain,
% 0.71/0.78 ((~hskp0) | c3_1(a2068)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.71/0.78 tff(739,plain,
% 0.71/0.78 ((~hskp0) | c3_1(a2068)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[738, 736])).
% 0.71/0.78 tff(740,plain,
% 0.71/0.78 ((~hskp0) | c3_1(a2068)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[739, 736])).
% 0.71/0.78 tff(741,plain,
% 0.71/0.78 ((~hskp0) | c3_1(a2068)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[740, 736])).
% 0.71/0.78 tff(742,plain,
% 0.71/0.78 ((~hskp0) | c3_1(a2068)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[741, 736])).
% 0.71/0.78 tff(743,plain,
% 0.71/0.78 ((~hskp0) | c3_1(a2068)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[742, 736])).
% 0.71/0.78 tff(744,plain,
% 0.71/0.78 ((~hskp0) | c3_1(a2068)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[743, 736])).
% 0.71/0.78 tff(745,plain,
% 0.71/0.78 ((~hskp0) | c3_1(a2068)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[744, 736])).
% 0.71/0.78 tff(746,plain,
% 0.71/0.78 (c3_1(a2068)),
% 0.71/0.78 inference(unit_resolution,[status(thm)],[745, 723])).
% 0.71/0.78 tff(747,assumption,(~hskp4), introduced(assumption)).
% 0.71/0.78 tff(748,plain,
% 0.71/0.78 (^[U: $i] : refl((hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.71/0.78 inference(bind,[status(th)],[])).
% 0.71/0.78 tff(749,plain,
% 0.71/0.78 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(quant_intro,[status(thm)],[748])).
% 0.71/0.78 tff(750,plain,
% 0.71/0.78 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(751,plain,
% 0.71/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp28) | hskp4) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp4))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp28) | hskp4) <=> (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.71/0.78 inference(bind,[status(th)],[])).
% 0.71/0.78 tff(752,plain,
% 0.71/0.78 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp28) | hskp4) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(quant_intro,[status(thm)],[751])).
% 0.71/0.78 tff(753,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp28) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 0.71/0.78 tff(754,plain,
% 0.71/0.78 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[753, 752])).
% 0.71/0.78 tff(755,plain,
% 0.71/0.78 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[754, 750])).
% 0.71/0.78 tff(756,plain,(
% 0.71/0.78 ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(skolemize,[status(sab)],[755])).
% 0.71/0.78 tff(757,plain,
% 0.71/0.78 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[756, 749])).
% 0.71/0.78 tff(758,plain,
% 0.71/0.78 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp4 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp4 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(759,plain,
% 0.71/0.78 ((hskp28 | hskp4 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076))) <=> (hskp28 | hskp4 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(760,plain,
% 0.71/0.78 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp4 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076))))),
% 0.71/0.78 inference(monotonicity,[status(thm)],[759])).
% 0.71/0.78 tff(761,plain,
% 0.71/0.78 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp4 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.71/0.78 inference(transitivity,[status(thm)],[760, 758])).
% 0.71/0.78 tff(762,plain,
% 0.71/0.78 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp4 | (~ndr1_0) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.71/0.78 inference(quant_inst,[status(thm)],[])).
% 0.71/0.78 tff(763,plain,
% 0.71/0.78 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp4 | c0_1(a2076) | (~ndr1_0) | (~c3_1(a2076)) | (~c1_1(a2076))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[762, 761])).
% 0.71/0.78 tff(764,plain,
% 0.71/0.78 (hskp28 | hskp4),
% 0.71/0.78 inference(unit_resolution,[status(thm)],[763, 99, 716, 715, 714, 757])).
% 0.71/0.78 tff(765,plain,
% 0.71/0.78 (hskp28),
% 0.71/0.78 inference(unit_resolution,[status(thm)],[764, 747])).
% 0.71/0.78 tff(766,plain,
% 0.71/0.78 (((~hskp28) | c2_1(a2075)) <=> ((~hskp28) | c2_1(a2075))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(767,axiom,((~hskp28) | c2_1(a2075)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 0.71/0.78 tff(768,plain,
% 0.71/0.78 ((~hskp28) | c2_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[767, 766])).
% 0.71/0.78 tff(769,plain,
% 0.71/0.78 ((~hskp28) | c2_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[768, 766])).
% 0.71/0.78 tff(770,plain,
% 0.71/0.78 ((~hskp28) | c2_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[769, 766])).
% 0.71/0.78 tff(771,plain,
% 0.71/0.78 ((~hskp28) | c2_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[770, 766])).
% 0.71/0.78 tff(772,plain,
% 0.71/0.78 ((~hskp28) | c2_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[771, 766])).
% 0.71/0.78 tff(773,plain,
% 0.71/0.78 ((~hskp28) | c2_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[772, 766])).
% 0.71/0.78 tff(774,plain,
% 0.71/0.78 ((~hskp28) | c2_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[773, 766])).
% 0.71/0.78 tff(775,plain,
% 0.71/0.78 ((~hskp28) | c2_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[774, 766])).
% 0.71/0.78 tff(776,plain,
% 0.71/0.78 (c2_1(a2075)),
% 0.71/0.78 inference(unit_resolution,[status(thm)],[775, 765])).
% 0.71/0.78 tff(777,plain,
% 0.71/0.78 (((~hskp28) | c1_1(a2075)) <=> ((~hskp28) | c1_1(a2075))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(778,axiom,((~hskp28) | c1_1(a2075)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 0.71/0.78 tff(779,plain,
% 0.71/0.78 ((~hskp28) | c1_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[778, 777])).
% 0.71/0.78 tff(780,plain,
% 0.71/0.78 ((~hskp28) | c1_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[779, 777])).
% 0.71/0.78 tff(781,plain,
% 0.71/0.78 ((~hskp28) | c1_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[780, 777])).
% 0.71/0.78 tff(782,plain,
% 0.71/0.78 ((~hskp28) | c1_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[781, 777])).
% 0.71/0.78 tff(783,plain,
% 0.71/0.78 ((~hskp28) | c1_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[782, 777])).
% 0.71/0.78 tff(784,plain,
% 0.71/0.78 ((~hskp28) | c1_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[783, 777])).
% 0.71/0.78 tff(785,plain,
% 0.71/0.78 ((~hskp28) | c1_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[784, 777])).
% 0.71/0.78 tff(786,plain,
% 0.71/0.78 ((~hskp28) | c1_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[785, 777])).
% 0.71/0.78 tff(787,plain,
% 0.71/0.78 (c1_1(a2075)),
% 0.71/0.78 inference(unit_resolution,[status(thm)],[786, 765])).
% 0.71/0.78 tff(788,plain,
% 0.71/0.78 (((~hskp28) | c0_1(a2075)) <=> ((~hskp28) | c0_1(a2075))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(789,axiom,((~hskp28) | c0_1(a2075)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 0.71/0.78 tff(790,plain,
% 0.71/0.78 ((~hskp28) | c0_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.71/0.78 tff(791,plain,
% 0.71/0.78 ((~hskp28) | c0_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[790, 788])).
% 0.71/0.78 tff(792,plain,
% 0.71/0.78 ((~hskp28) | c0_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[791, 788])).
% 0.71/0.78 tff(793,plain,
% 0.71/0.78 ((~hskp28) | c0_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[792, 788])).
% 0.71/0.78 tff(794,plain,
% 0.71/0.78 ((~hskp28) | c0_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[793, 788])).
% 0.71/0.78 tff(795,plain,
% 0.71/0.78 ((~hskp28) | c0_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[794, 788])).
% 0.71/0.78 tff(796,plain,
% 0.71/0.78 ((~hskp28) | c0_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[795, 788])).
% 0.71/0.78 tff(797,plain,
% 0.71/0.78 ((~hskp28) | c0_1(a2075)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[796, 788])).
% 0.71/0.78 tff(798,plain,
% 0.71/0.78 (c0_1(a2075)),
% 0.71/0.78 inference(unit_resolution,[status(thm)],[797, 765])).
% 0.71/0.78 tff(799,plain,
% 0.71/0.78 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.71/0.78 inference(bind,[status(th)],[])).
% 0.71/0.78 tff(800,plain,
% 0.71/0.78 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.78 inference(quant_intro,[status(thm)],[799])).
% 0.71/0.78 tff(801,plain,
% 0.71/0.78 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(802,plain,
% 0.71/0.78 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.71/0.78 inference(bind,[status(th)],[])).
% 0.71/0.78 tff(803,plain,
% 0.71/0.78 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.78 inference(quant_intro,[status(thm)],[802])).
% 0.71/0.78 tff(804,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 0.71/0.78 tff(805,plain,
% 0.71/0.78 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[804, 803])).
% 0.71/0.78 tff(806,plain,
% 0.71/0.78 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[805, 801])).
% 0.71/0.78 tff(807,plain,(
% 0.71/0.78 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.78 inference(skolemize,[status(sab)],[806])).
% 0.71/0.78 tff(808,plain,
% 0.71/0.78 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[807, 800])).
% 0.71/0.78 tff(809,plain,
% 0.71/0.78 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(810,plain,
% 0.71/0.78 ((hskp4 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068))) <=> (hskp4 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.78 tff(811,plain,
% 0.71/0.78 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp4 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068)))),
% 0.71/0.78 inference(monotonicity,[status(thm)],[810])).
% 0.71/0.78 tff(812,plain,
% 0.71/0.78 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))),
% 0.71/0.78 inference(transitivity,[status(thm)],[811, 809])).
% 0.71/0.78 tff(813,plain,
% 0.71/0.78 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp4 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))),
% 0.71/0.78 inference(quant_inst,[status(thm)],[])).
% 0.71/0.78 tff(814,plain,
% 0.71/0.78 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp4 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068)),
% 0.71/0.78 inference(modus_ponens,[status(thm)],[813, 812])).
% 0.71/0.78 tff(815,plain,
% 0.71/0.78 (hskp4 | c1_1(a2068)),
% 0.71/0.78 inference(unit_resolution,[status(thm)],[814, 99, 746, 735, 729, 808])).
% 0.71/0.78 tff(816,plain,
% 0.71/0.78 (c1_1(a2068)),
% 0.71/0.78 inference(unit_resolution,[status(thm)],[815, 747])).
% 0.71/0.78 tff(817,assumption,(c1_1(a2068)), introduced(assumption)).
% 0.71/0.78 tff(818,assumption,(~c2_1(a2068)), introduced(assumption)).
% 0.71/0.78 tff(819,assumption,(c3_1(a2068)), introduced(assumption)).
% 0.71/0.78 tff(820,plain,
% 0.71/0.78 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2093)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2093)))),
% 0.71/0.78 inference(rewrite,[status(thm)],[])).
% 0.71/0.79 tff(821,plain,
% 0.71/0.79 ((hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093))) <=> (hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2093)))),
% 0.71/0.79 inference(rewrite,[status(thm)],[])).
% 0.71/0.79 tff(822,plain,
% 0.71/0.79 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2093))))),
% 0.71/0.79 inference(monotonicity,[status(thm)],[821])).
% 0.71/0.79 tff(823,plain,
% 0.71/0.79 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2093)))),
% 0.71/0.79 inference(transitivity,[status(thm)],[822, 820])).
% 0.71/0.79 tff(824,plain,
% 0.71/0.79 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093)))),
% 0.71/0.79 inference(quant_inst,[status(thm)],[])).
% 0.71/0.79 tff(825,plain,
% 0.71/0.79 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2093))),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[824, 823])).
% 0.71/0.79 tff(826,plain,
% 0.71/0.79 ($false),
% 0.71/0.79 inference(unit_resolution,[status(thm)],[825, 99, 693, 368, 819, 357, 351, 818, 379, 817])).
% 0.71/0.79 tff(827,plain,((~hskp11) | hskp3 | (~c3_1(a2068)) | c2_1(a2068) | (~c1_1(a2068))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.79 tff(828,plain,
% 0.71/0.79 (~hskp11),
% 0.71/0.79 inference(unit_resolution,[status(thm)],[827, 816, 746, 729, 693])).
% 0.71/0.79 tff(829,plain,
% 0.71/0.79 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.71/0.79 inference(bind,[status(th)],[])).
% 0.71/0.79 tff(830,plain,
% 0.71/0.79 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.71/0.79 inference(quant_intro,[status(thm)],[829])).
% 0.71/0.79 tff(831,plain,
% 0.71/0.79 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.71/0.79 inference(rewrite,[status(thm)],[])).
% 0.71/0.79 tff(832,plain,
% 0.71/0.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp11))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.71/0.79 inference(bind,[status(th)],[])).
% 0.71/0.79 tff(833,plain,
% 0.71/0.79 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.71/0.79 inference(quant_intro,[status(thm)],[832])).
% 0.71/0.79 tff(834,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 0.71/0.79 tff(835,plain,
% 0.71/0.79 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[834, 833])).
% 0.71/0.79 tff(836,plain,
% 0.71/0.79 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[835, 831])).
% 0.71/0.79 tff(837,plain,(
% 0.71/0.79 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.71/0.79 inference(skolemize,[status(sab)],[836])).
% 0.71/0.79 tff(838,plain,
% 0.71/0.79 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[837, 830])).
% 0.71/0.79 tff(839,plain,
% 0.71/0.79 (^[U: $i] : refl((hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.71/0.79 inference(bind,[status(th)],[])).
% 0.71/0.79 tff(840,plain,
% 0.71/0.79 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.79 inference(quant_intro,[status(thm)],[839])).
% 0.71/0.79 tff(841,plain,
% 0.71/0.79 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.79 inference(rewrite,[status(thm)],[])).
% 0.71/0.79 tff(842,plain,
% 0.71/0.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp7))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) | hskp4) <=> ((hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp4))), rewrite(((hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) | hskp4) <=> (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.71/0.79 inference(bind,[status(th)],[])).
% 0.71/0.79 tff(843,plain,
% 0.71/0.79 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) | hskp4) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.79 inference(quant_intro,[status(thm)],[842])).
% 0.71/0.79 tff(844,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp7) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 0.71/0.79 tff(845,plain,
% 0.71/0.79 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[844, 843])).
% 0.71/0.79 tff(846,plain,
% 0.71/0.79 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[845, 841])).
% 0.71/0.79 tff(847,plain,(
% 0.71/0.79 ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.79 inference(skolemize,[status(sab)],[846])).
% 0.71/0.79 tff(848,plain,
% 0.71/0.79 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[847, 840])).
% 0.71/0.79 tff(849,plain,
% 0.71/0.79 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)))),
% 0.71/0.79 inference(rewrite,[status(thm)],[])).
% 0.71/0.79 tff(850,plain,
% 0.71/0.79 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)))),
% 0.71/0.79 inference(quant_inst,[status(thm)],[])).
% 0.71/0.79 tff(851,plain,
% 0.71/0.79 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp7 | hskp4 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075))),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[850, 849])).
% 0.71/0.79 tff(852,plain,
% 0.71/0.79 (hskp7),
% 0.71/0.79 inference(unit_resolution,[status(thm)],[851, 99, 747, 798, 787, 776, 848])).
% 0.71/0.79 tff(853,plain,
% 0.71/0.79 (((~hskp7) | (~c3_1(a2079))) <=> ((~hskp7) | (~c3_1(a2079)))),
% 0.71/0.79 inference(rewrite,[status(thm)],[])).
% 0.71/0.79 tff(854,plain,
% 0.71/0.79 (((~c3_1(a2079)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a2079)))),
% 0.71/0.79 inference(rewrite,[status(thm)],[])).
% 0.71/0.79 tff(855,axiom,((~c3_1(a2079)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 0.71/0.79 tff(856,plain,
% 0.71/0.79 ((~hskp7) | (~c3_1(a2079))),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[855, 854])).
% 0.71/0.79 tff(857,plain,
% 0.71/0.79 ((~hskp7) | (~c3_1(a2079))),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[856, 853])).
% 0.71/0.79 tff(858,plain,
% 0.71/0.79 (~c3_1(a2079)),
% 0.71/0.79 inference(unit_resolution,[status(thm)],[857, 852])).
% 0.71/0.79 tff(859,plain,
% 0.71/0.79 (((~hskp7) | c0_1(a2079)) <=> ((~hskp7) | c0_1(a2079))),
% 0.71/0.79 inference(rewrite,[status(thm)],[])).
% 0.71/0.79 tff(860,axiom,((~hskp7) | c0_1(a2079)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 0.71/0.79 tff(861,plain,
% 0.71/0.79 ((~hskp7) | c0_1(a2079)),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[860, 859])).
% 0.71/0.79 tff(862,plain,
% 0.71/0.79 ((~hskp7) | c0_1(a2079)),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[861, 859])).
% 0.71/0.79 tff(863,plain,
% 0.71/0.79 ((~hskp7) | c0_1(a2079)),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[862, 859])).
% 0.71/0.79 tff(864,plain,
% 0.71/0.79 ((~hskp7) | c0_1(a2079)),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[863, 859])).
% 0.71/0.79 tff(865,plain,
% 0.71/0.79 ((~hskp7) | c0_1(a2079)),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[864, 859])).
% 0.71/0.79 tff(866,plain,
% 0.71/0.79 ((~hskp7) | c0_1(a2079)),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[865, 859])).
% 0.71/0.79 tff(867,plain,
% 0.71/0.79 ((~hskp7) | c0_1(a2079)),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[866, 859])).
% 0.71/0.79 tff(868,plain,
% 0.71/0.79 ((~hskp7) | c0_1(a2079)),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[867, 859])).
% 0.71/0.79 tff(869,plain,
% 0.71/0.79 (c0_1(a2079)),
% 0.71/0.79 inference(unit_resolution,[status(thm)],[868, 852])).
% 0.71/0.79 tff(870,plain,
% 0.71/0.79 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c3_1(a2079) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c2_1(a2079) | (~c0_1(a2079)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c3_1(a2079) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c2_1(a2079) | (~c0_1(a2079)))),
% 0.71/0.79 inference(rewrite,[status(thm)],[])).
% 0.71/0.79 tff(871,plain,
% 0.71/0.79 ((hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2079) | c2_1(a2079) | (~c0_1(a2079))) <=> (hskp11 | c3_1(a2079) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c2_1(a2079) | (~c0_1(a2079)))),
% 0.71/0.79 inference(rewrite,[status(thm)],[])).
% 0.71/0.79 tff(872,plain,
% 0.71/0.79 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2079) | c2_1(a2079) | (~c0_1(a2079)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c3_1(a2079) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c2_1(a2079) | (~c0_1(a2079))))),
% 0.71/0.79 inference(monotonicity,[status(thm)],[871])).
% 0.71/0.79 tff(873,plain,
% 0.71/0.79 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2079) | c2_1(a2079) | (~c0_1(a2079)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c3_1(a2079) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c2_1(a2079) | (~c0_1(a2079)))),
% 0.71/0.79 inference(transitivity,[status(thm)],[872, 870])).
% 0.71/0.79 tff(874,plain,
% 0.71/0.79 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2079) | c2_1(a2079) | (~c0_1(a2079)))),
% 0.71/0.79 inference(quant_inst,[status(thm)],[])).
% 0.71/0.79 tff(875,plain,
% 0.71/0.79 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c3_1(a2079) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c2_1(a2079) | (~c0_1(a2079))),
% 0.71/0.79 inference(modus_ponens,[status(thm)],[874, 873])).
% 0.71/0.79 tff(876,plain,
% 0.71/0.79 (hskp11 | c2_1(a2079)),
% 0.71/0.79 inference(unit_resolution,[status(thm)],[875, 99, 798, 787, 776, 869, 858, 838])).
% 0.71/0.79 tff(877,plain,
% 0.71/0.79 (c2_1(a2079)),
% 0.71/0.79 inference(unit_resolution,[status(thm)],[876, 828])).
% 0.71/0.79 tff(878,assumption,(c2_1(a2079)), introduced(assumption)).
% 0.71/0.79 tff(879,plain,
% 0.71/0.79 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.71/0.79 inference(bind,[status(th)],[])).
% 0.71/0.79 tff(880,plain,
% 0.71/0.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.71/0.79 inference(quant_intro,[status(thm)],[879])).
% 0.79/0.79 tff(881,plain,
% 0.79/0.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(882,plain,
% 0.79/0.79 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.79/0.79 inference(bind,[status(th)],[])).
% 0.79/0.79 tff(883,plain,
% 0.79/0.79 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.79 inference(quant_intro,[status(thm)],[882])).
% 0.79/0.79 tff(884,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 0.79/0.79 tff(885,plain,
% 0.79/0.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.79 inference(modus_ponens,[status(thm)],[884, 883])).
% 0.79/0.79 tff(886,plain,
% 0.79/0.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.79 inference(modus_ponens,[status(thm)],[885, 881])).
% 0.79/0.79 tff(887,plain,(
% 0.79/0.79 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.79 inference(skolemize,[status(sab)],[886])).
% 0.79/0.79 tff(888,plain,
% 0.79/0.79 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.79 inference(modus_ponens,[status(thm)],[887, 880])).
% 0.79/0.79 tff(889,assumption,(~c3_1(a2079)), introduced(assumption)).
% 0.79/0.79 tff(890,assumption,(c0_1(a2079)), introduced(assumption)).
% 0.79/0.79 tff(891,plain,
% 0.79/0.79 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | c3_1(a2079) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2079)) | (~c0_1(a2079)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp4 | c3_1(a2079) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2079)) | (~c0_1(a2079)))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(892,plain,
% 0.79/0.79 ((hskp4 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c0_1(a2079)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070))) <=> (hskp4 | c3_1(a2079) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2079)) | (~c0_1(a2079)))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(893,plain,
% 0.79/0.79 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c0_1(a2079)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | c3_1(a2079) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2079)) | (~c0_1(a2079))))),
% 0.79/0.79 inference(monotonicity,[status(thm)],[892])).
% 0.79/0.79 tff(894,plain,
% 0.79/0.79 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c0_1(a2079)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp4 | c3_1(a2079) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2079)) | (~c0_1(a2079)))),
% 0.79/0.79 inference(transitivity,[status(thm)],[893, 891])).
% 0.79/0.79 tff(895,plain,
% 0.79/0.79 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c0_1(a2079)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))),
% 0.79/0.79 inference(quant_inst,[status(thm)],[])).
% 0.79/0.79 tff(896,plain,
% 0.79/0.79 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp4 | c3_1(a2079) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2079)) | (~c0_1(a2079))),
% 0.79/0.79 inference(modus_ponens,[status(thm)],[895, 894])).
% 0.79/0.79 tff(897,plain,
% 0.79/0.79 ($false),
% 0.79/0.79 inference(unit_resolution,[status(thm)],[896, 99, 747, 890, 548, 537, 889, 562, 888, 878])).
% 0.79/0.79 tff(898,plain,((~hskp1) | hskp4 | (~c0_1(a2079)) | c3_1(a2079) | (~c2_1(a2079))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.79 tff(899,plain,
% 0.79/0.79 (~hskp1),
% 0.79/0.79 inference(unit_resolution,[status(thm)],[898, 747, 869, 858, 877])).
% 0.79/0.79 tff(900,assumption,(c2_1(a2075)), introduced(assumption)).
% 0.79/0.79 tff(901,assumption,(c1_1(a2075)), introduced(assumption)).
% 0.79/0.79 tff(902,assumption,(c0_1(a2075)), introduced(assumption)).
% 0.79/0.79 tff(903,plain,
% 0.79/0.79 (~hskp11),
% 0.79/0.79 inference(unit_resolution,[status(thm)],[827, 817, 746, 729, 693])).
% 0.79/0.79 tff(904,assumption,(~c0_1(a2068)), introduced(assumption)).
% 0.79/0.79 tff(905,assumption,(hskp20), introduced(assumption)).
% 0.79/0.79 tff(906,plain,
% 0.79/0.79 (((~hskp20) | (~c3_1(a2130))) <=> ((~hskp20) | (~c3_1(a2130)))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(907,plain,
% 0.79/0.79 (((~c3_1(a2130)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a2130)))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(908,axiom,((~c3_1(a2130)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 0.79/0.79 tff(909,plain,
% 0.79/0.79 ((~hskp20) | (~c3_1(a2130))),
% 0.79/0.79 inference(modus_ponens,[status(thm)],[908, 907])).
% 0.79/0.79 tff(910,plain,
% 0.79/0.79 ((~hskp20) | (~c3_1(a2130))),
% 0.79/0.79 inference(modus_ponens,[status(thm)],[909, 906])).
% 0.79/0.79 tff(911,plain,
% 0.79/0.79 (~c3_1(a2130)),
% 0.79/0.79 inference(unit_resolution,[status(thm)],[910, 905])).
% 0.79/0.79 tff(912,plain,
% 0.79/0.79 (((~hskp20) | (~c2_1(a2130))) <=> ((~hskp20) | (~c2_1(a2130)))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(913,plain,
% 0.79/0.79 (((~c2_1(a2130)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a2130)))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(914,axiom,((~c2_1(a2130)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 0.79/0.79 tff(915,plain,
% 0.79/0.79 ((~hskp20) | (~c2_1(a2130))),
% 0.79/0.79 inference(modus_ponens,[status(thm)],[914, 913])).
% 0.79/0.79 tff(916,plain,
% 0.79/0.79 ((~hskp20) | (~c2_1(a2130))),
% 0.79/0.79 inference(modus_ponens,[status(thm)],[915, 912])).
% 0.79/0.79 tff(917,plain,
% 0.79/0.79 (~c2_1(a2130)),
% 0.79/0.79 inference(unit_resolution,[status(thm)],[916, 905])).
% 0.79/0.79 tff(918,plain,
% 0.79/0.79 (((~hskp20) | (~c1_1(a2130))) <=> ((~hskp20) | (~c1_1(a2130)))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(919,plain,
% 0.79/0.79 (((~c1_1(a2130)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a2130)))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(920,axiom,((~c1_1(a2130)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 0.79/0.79 tff(921,plain,
% 0.79/0.79 ((~hskp20) | (~c1_1(a2130))),
% 0.79/0.79 inference(modus_ponens,[status(thm)],[920, 919])).
% 0.79/0.79 tff(922,plain,
% 0.79/0.79 ((~hskp20) | (~c1_1(a2130))),
% 0.79/0.79 inference(modus_ponens,[status(thm)],[921, 918])).
% 0.79/0.79 tff(923,plain,
% 0.79/0.79 (~c1_1(a2130)),
% 0.79/0.79 inference(unit_resolution,[status(thm)],[922, 905])).
% 0.79/0.79 tff(924,plain,
% 0.79/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2130) | c2_1(a2130) | c3_1(a2130) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c0_1(a2130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2130) | c2_1(a2130) | c3_1(a2130) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c0_1(a2130))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(925,plain,
% 0.79/0.79 (((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2130) | c1_1(a2130) | c2_1(a2130) | c2_1(a2130) | c1_1(a2130) | c0_1(a2130)) <=> (c1_1(a2130) | c2_1(a2130) | c3_1(a2130) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c0_1(a2130))),
% 0.79/0.79 inference(rewrite,[status(thm)],[])).
% 0.79/0.79 tff(926,plain,
% 0.79/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2130) | c1_1(a2130) | c2_1(a2130) | c2_1(a2130) | c1_1(a2130) | c0_1(a2130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2130) | c2_1(a2130) | c3_1(a2130) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c0_1(a2130)))),
% 0.79/0.79 inference(monotonicity,[status(thm)],[925])).
% 0.79/0.79 tff(927,plain,
% 0.79/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2130) | c1_1(a2130) | c2_1(a2130) | c2_1(a2130) | c1_1(a2130) | c0_1(a2130))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2130) | c2_1(a2130) | c3_1(a2130) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c0_1(a2130))),
% 0.79/0.79 inference(transitivity,[status(thm)],[926, 924])).
% 0.79/0.79 tff(928,plain,
% 0.79/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2130) | c1_1(a2130) | c2_1(a2130) | c2_1(a2130) | c1_1(a2130) | c0_1(a2130))),
% 0.79/0.79 inference(quant_inst,[status(thm)],[])).
% 0.79/0.79 tff(929,plain,
% 0.79/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2130) | c2_1(a2130) | c3_1(a2130) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c0_1(a2130)),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[928, 927])).
% 0.79/0.80 tff(930,plain,
% 0.79/0.80 (c0_1(a2130)),
% 0.79/0.80 inference(unit_resolution,[status(thm)],[929, 99, 923, 917, 911, 904, 818, 410, 817])).
% 0.79/0.80 tff(931,plain,
% 0.79/0.80 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c2_1(a2130) | c3_1(a2130) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c0_1(a2130)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a2130) | c3_1(a2130) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c0_1(a2130)))),
% 0.79/0.80 inference(rewrite,[status(thm)],[])).
% 0.79/0.80 tff(932,plain,
% 0.79/0.80 ((hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2130) | c2_1(a2130) | (~c0_1(a2130))) <=> (hskp11 | c2_1(a2130) | c3_1(a2130) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c0_1(a2130)))),
% 0.79/0.80 inference(rewrite,[status(thm)],[])).
% 0.79/0.80 tff(933,plain,
% 0.79/0.80 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2130) | c2_1(a2130) | (~c0_1(a2130)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | c2_1(a2130) | c3_1(a2130) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c0_1(a2130))))),
% 0.79/0.80 inference(monotonicity,[status(thm)],[932])).
% 0.79/0.80 tff(934,plain,
% 0.79/0.80 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2130) | c2_1(a2130) | (~c0_1(a2130)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a2130) | c3_1(a2130) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c0_1(a2130)))),
% 0.79/0.80 inference(transitivity,[status(thm)],[933, 931])).
% 0.79/0.80 tff(935,plain,
% 0.79/0.80 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp11 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c3_1(a2130) | c2_1(a2130) | (~c0_1(a2130)))),
% 0.79/0.80 inference(quant_inst,[status(thm)],[])).
% 0.79/0.80 tff(936,plain,
% 0.79/0.80 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp11 | c2_1(a2130) | c3_1(a2130) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c0_1(a2130))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[935, 934])).
% 0.79/0.80 tff(937,plain,
% 0.79/0.80 ($false),
% 0.79/0.80 inference(unit_resolution,[status(thm)],[936, 99, 22, 902, 901, 900, 917, 911, 838, 930])).
% 0.79/0.80 tff(938,plain,((~hskp20) | hskp11 | (~c0_1(a2075)) | (~c1_1(a2075)) | (~c2_1(a2075)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.80 tff(939,plain,
% 0.79/0.80 (~hskp20),
% 0.79/0.80 inference(unit_resolution,[status(thm)],[938, 903, 902, 901, 900, 735, 729, 817])).
% 0.79/0.80 tff(940,plain,
% 0.79/0.80 (^[V: $i, U: $i] : refl((hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.79/0.80 inference(bind,[status(th)],[])).
% 0.79/0.80 tff(941,plain,
% 0.79/0.80 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(quant_intro,[status(thm)],[940])).
% 0.79/0.80 tff(942,plain,
% 0.79/0.80 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(rewrite,[status(thm)],[])).
% 0.79/0.80 tff(943,plain,
% 0.79/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp26) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp26))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp26) <=> (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.79/0.80 inference(bind,[status(th)],[])).
% 0.79/0.80 tff(944,plain,
% 0.79/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp26) <=> ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(quant_intro,[status(thm)],[943])).
% 0.79/0.80 tff(945,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 0.79/0.80 tff(946,plain,
% 0.79/0.80 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.79/0.80 tff(947,plain,
% 0.79/0.80 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[946, 942])).
% 0.79/0.80 tff(948,plain,(
% 0.79/0.80 ![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(skolemize,[status(sab)],[947])).
% 0.79/0.80 tff(949,plain,
% 0.79/0.80 (![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[948, 941])).
% 0.79/0.80 tff(950,plain,
% 0.79/0.80 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2076)) | (~c3_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2076)) | (~c3_1(a2076)))),
% 0.79/0.80 inference(rewrite,[status(thm)],[])).
% 0.79/0.80 tff(951,plain,
% 0.79/0.80 ((hskp26 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c0_1(a2076) | (~c3_1(a2076)) | (~c2_1(a2076))) <=> (hskp26 | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2076)) | (~c3_1(a2076)))),
% 0.79/0.80 inference(rewrite,[status(thm)],[])).
% 0.79/0.80 tff(952,plain,
% 0.79/0.80 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c0_1(a2076) | (~c3_1(a2076)) | (~c2_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2076)) | (~c3_1(a2076))))),
% 0.79/0.80 inference(monotonicity,[status(thm)],[951])).
% 0.79/0.80 tff(953,plain,
% 0.79/0.80 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c0_1(a2076) | (~c3_1(a2076)) | (~c2_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2076)) | (~c3_1(a2076)))),
% 0.79/0.80 inference(transitivity,[status(thm)],[952, 950])).
% 0.79/0.80 tff(954,plain,
% 0.79/0.80 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c0_1(a2076) | (~c3_1(a2076)) | (~c2_1(a2076)))),
% 0.79/0.80 inference(quant_inst,[status(thm)],[])).
% 0.79/0.80 tff(955,plain,
% 0.79/0.80 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2076)) | (~c3_1(a2076))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[954, 953])).
% 0.79/0.80 tff(956,plain,
% 0.79/0.80 (hskp26 | (~c2_1(a2076))),
% 0.79/0.80 inference(unit_resolution,[status(thm)],[955, 99, 902, 901, 900, 715, 714, 949])).
% 0.79/0.80 tff(957,plain,
% 0.79/0.80 (~c2_1(a2076)),
% 0.79/0.80 inference(unit_resolution,[status(thm)],[956, 549])).
% 0.79/0.80 tff(958,plain,
% 0.79/0.80 (~hskp11),
% 0.79/0.80 inference(unit_resolution,[status(thm)],[827, 817, 819, 818, 693])).
% 0.79/0.80 tff(959,assumption,(~hskp20), introduced(assumption)).
% 0.79/0.80 tff(960,assumption,(~c2_1(a2076)), introduced(assumption)).
% 0.79/0.80 tff(961,assumption,(c3_1(a2087)), introduced(assumption)).
% 0.79/0.80 tff(962,plain,
% 0.79/0.80 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.79/0.80 inference(bind,[status(th)],[])).
% 0.79/0.80 tff(963,plain,
% 0.79/0.80 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(quant_intro,[status(thm)],[962])).
% 0.79/0.80 tff(964,plain,
% 0.79/0.80 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(rewrite,[status(thm)],[])).
% 0.79/0.80 tff(965,plain,
% 0.79/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.79/0.80 inference(bind,[status(th)],[])).
% 0.79/0.80 tff(966,plain,
% 0.79/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(quant_intro,[status(thm)],[965])).
% 0.79/0.80 tff(967,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 0.79/0.80 tff(968,plain,
% 0.79/0.80 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[967, 966])).
% 0.79/0.80 tff(969,plain,
% 0.79/0.80 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[968, 964])).
% 0.79/0.80 tff(970,plain,(
% 0.79/0.80 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(skolemize,[status(sab)],[969])).
% 0.79/0.80 tff(971,plain,
% 0.79/0.80 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[970, 963])).
% 0.79/0.80 tff(972,plain,
% 0.79/0.80 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp20 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp20 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2087)))),
% 0.79/0.80 inference(rewrite,[status(thm)],[])).
% 0.79/0.80 tff(973,plain,
% 0.79/0.80 ((hskp20 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087))) <=> (hskp20 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2087)))),
% 0.79/0.80 inference(rewrite,[status(thm)],[])).
% 0.79/0.80 tff(974,plain,
% 0.79/0.80 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp20 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2087))))),
% 0.79/0.80 inference(monotonicity,[status(thm)],[973])).
% 0.79/0.80 tff(975,plain,
% 0.79/0.80 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp20 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2087)))),
% 0.79/0.80 inference(transitivity,[status(thm)],[974, 972])).
% 0.79/0.80 tff(976,plain,
% 0.79/0.80 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)))),
% 0.79/0.80 inference(quant_inst,[status(thm)],[])).
% 0.79/0.80 tff(977,plain,
% 0.79/0.80 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp20 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c2_1(a2075)) | (~c1_1(a2075)) | (~c0_1(a2075)) | (~c2_1(a2087))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[976, 975])).
% 0.79/0.80 tff(978,plain,
% 0.79/0.80 ((~c3_1(a2087)) | (~c2_1(a2087))),
% 0.79/0.80 inference(unit_resolution,[status(thm)],[977, 99, 959, 902, 901, 900, 241, 971])).
% 0.79/0.80 tff(979,plain,
% 0.79/0.80 (~c2_1(a2087)),
% 0.79/0.80 inference(unit_resolution,[status(thm)],[978, 961])).
% 0.79/0.80 tff(980,plain,
% 0.79/0.80 (~hskp10),
% 0.79/0.80 inference(unit_resolution,[status(thm)],[221, 961])).
% 0.79/0.80 tff(981,plain,
% 0.79/0.80 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.79/0.80 inference(rewrite,[status(thm)],[])).
% 0.79/0.80 tff(982,plain,
% 0.79/0.80 ((hskp11 | hskp10 | (~ndr1_0) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087))) <=> (hskp11 | hskp10 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.79/0.80 inference(rewrite,[status(thm)],[])).
% 0.79/0.80 tff(983,plain,
% 0.79/0.80 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c0_1(a2087))))),
% 0.79/0.80 inference(monotonicity,[status(thm)],[982])).
% 0.79/0.80 tff(984,plain,
% 0.79/0.80 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.79/0.80 inference(transitivity,[status(thm)],[983, 981])).
% 0.79/0.80 tff(985,plain,
% 0.79/0.80 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)))),
% 0.79/0.80 inference(quant_inst,[status(thm)],[])).
% 0.79/0.80 tff(986,plain,
% 0.79/0.80 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | (~c0_1(a2087))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[985, 984])).
% 0.79/0.80 tff(987,plain,
% 0.79/0.80 (hskp10 | (~c3_1(a2087)) | (~c0_1(a2087))),
% 0.79/0.80 inference(unit_resolution,[status(thm)],[986, 99, 22, 241, 32])).
% 0.79/0.80 tff(988,plain,
% 0.79/0.80 (~c0_1(a2087)),
% 0.79/0.80 inference(unit_resolution,[status(thm)],[987, 980, 961])).
% 0.79/0.80 tff(989,plain,
% 0.79/0.80 (^[U: $i] : refl((hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.79/0.80 inference(bind,[status(th)],[])).
% 0.79/0.80 tff(990,plain,
% 0.79/0.80 (![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.79/0.80 inference(quant_intro,[status(thm)],[989])).
% 0.79/0.80 tff(991,plain,
% 0.79/0.80 (![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.79/0.80 inference(rewrite,[status(thm)],[])).
% 0.79/0.80 tff(992,plain,
% 0.79/0.80 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp1) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp1) <=> (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.79/0.80 inference(bind,[status(th)],[])).
% 0.79/0.80 tff(993,plain,
% 0.79/0.80 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp1) <=> ![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.79/0.80 inference(quant_intro,[status(thm)],[992])).
% 0.79/0.80 tff(994,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp1)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 0.79/0.80 tff(995,plain,
% 0.79/0.80 (![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[994, 993])).
% 0.79/0.80 tff(996,plain,
% 0.79/0.80 (![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[995, 991])).
% 0.79/0.80 tff(997,plain,(
% 0.79/0.80 ![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.79/0.80 inference(skolemize,[status(sab)],[996])).
% 0.79/0.80 tff(998,plain,
% 0.79/0.80 (![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.79/0.80 inference(modus_ponens,[status(thm)],[997, 990])).
% 0.79/0.80 tff(999,plain,
% 0.79/0.80 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | c2_1(a2087) | c1_1(a2087) | (~ndr1_0) | c0_1(a2087))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c2_1(a2087) | c1_1(a2087) | (~ndr1_0) | c0_1(a2087))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1000,plain,
% 0.79/0.81 ((hskp26 | hskp1 | (~ndr1_0) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087)) <=> (hskp26 | hskp1 | c2_1(a2087) | c1_1(a2087) | (~ndr1_0) | c0_1(a2087))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1001,plain,
% 0.79/0.81 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | c2_1(a2087) | c1_1(a2087) | (~ndr1_0) | c0_1(a2087)))),
% 0.79/0.81 inference(monotonicity,[status(thm)],[1000])).
% 0.79/0.81 tff(1002,plain,
% 0.79/0.81 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c2_1(a2087) | c1_1(a2087) | (~ndr1_0) | c0_1(a2087))),
% 0.79/0.81 inference(transitivity,[status(thm)],[1001, 999])).
% 0.79/0.81 tff(1003,plain,
% 0.79/0.81 ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(1004,plain,
% 0.79/0.81 ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c2_1(a2087) | c1_1(a2087) | (~ndr1_0) | c0_1(a2087)),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 0.79/0.81 tff(1005,plain,
% 0.79/0.81 (c2_1(a2087) | c0_1(a2087)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1004, 99, 549, 11, 241, 998])).
% 0.79/0.81 tff(1006,plain,
% 0.79/0.81 ($false),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1005, 988, 979])).
% 0.79/0.81 tff(1007,plain,((~c3_1(a2087)) | hskp26 | hskp1 | c1_1(a2087) | hskp11 | hskp20 | (~c0_1(a2075)) | (~c1_1(a2075)) | (~c2_1(a2075))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.81 tff(1008,plain,
% 0.79/0.81 (~c3_1(a2087)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1007, 241, 11, 549, 958, 959, 902, 901, 900])).
% 0.79/0.81 tff(1009,plain,
% 0.79/0.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2087)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1010,plain,
% 0.79/0.81 ((hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087))) <=> (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2087)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1011,plain,
% 0.79/0.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2087))))),
% 0.79/0.81 inference(monotonicity,[status(thm)],[1010])).
% 0.79/0.81 tff(1012,plain,
% 0.79/0.81 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2087)))),
% 0.79/0.81 inference(transitivity,[status(thm)],[1011, 1009])).
% 0.79/0.81 tff(1013,plain,
% 0.79/0.81 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(1014,plain,
% 0.79/0.81 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)) | (~c0_1(a2087))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 0.79/0.81 tff(1015,plain,
% 0.79/0.81 (~c0_1(a2087)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1014, 99, 693, 819, 241, 1008, 818, 379, 817])).
% 0.79/0.81 tff(1016,plain,
% 0.79/0.81 (hskp8 | c3_1(a2087) | (~c0_1(a2087))),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[247, 99, 11, 241, 158])).
% 0.79/0.81 tff(1017,plain,
% 0.79/0.81 (~c0_1(a2087)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1016, 240, 159])).
% 0.79/0.81 tff(1018,plain,
% 0.79/0.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2087)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1019,plain,
% 0.79/0.81 ((hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076))) <=> (hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2087)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1020,plain,
% 0.79/0.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2087))))),
% 0.79/0.81 inference(monotonicity,[status(thm)],[1019])).
% 0.79/0.81 tff(1021,plain,
% 0.79/0.81 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2087)))),
% 0.79/0.81 inference(transitivity,[status(thm)],[1020, 1018])).
% 0.79/0.81 tff(1022,plain,
% 0.79/0.81 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076)))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(1023,plain,
% 0.79/0.81 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2087))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 0.79/0.81 tff(1024,plain,
% 0.79/0.81 (hskp8 | c3_1(a2087) | (~c2_1(a2087))),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1023, 99, 716, 241, 714, 313, 960])).
% 0.79/0.81 tff(1025,plain,
% 0.79/0.81 (~c2_1(a2087)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1024, 240, 159])).
% 0.79/0.81 tff(1026,plain,
% 0.79/0.81 ($false),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1005, 1025, 1017])).
% 0.79/0.81 tff(1027,plain,(c3_1(a2087) | hskp26 | hskp1 | c1_1(a2087) | hskp8 | (~c1_1(a2076)) | c0_1(a2076) | c2_1(a2076)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.81 tff(1028,plain,
% 0.79/0.81 (hskp8),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1027, 1008, 11, 241, 549, 716, 714, 960])).
% 0.79/0.81 tff(1029,plain,
% 0.79/0.81 (~c0_1(a2082)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[173, 1028])).
% 0.79/0.81 tff(1030,plain,
% 0.79/0.81 (c2_1(a2082)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[184, 1028])).
% 0.79/0.81 tff(1031,plain,
% 0.79/0.81 (c1_1(a2082)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[195, 1028])).
% 0.79/0.81 tff(1032,plain,
% 0.79/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1033,plain,
% 0.79/0.81 ((hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087))) <=> (hskp1 | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1034,plain,
% 0.79/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.79/0.81 inference(monotonicity,[status(thm)],[1033])).
% 0.79/0.81 tff(1035,plain,
% 0.79/0.81 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.79/0.81 inference(transitivity,[status(thm)],[1034, 1032])).
% 0.79/0.81 tff(1036,plain,
% 0.79/0.81 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp1 | (~ndr1_0) | c0_1(a2082) | (~c2_1(a2082)) | (~c1_1(a2082)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(1037,plain,
% 0.79/0.81 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp1 | c3_1(a2087) | c0_1(a2082) | (~ndr1_0) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 0.79/0.81 tff(1038,plain,
% 0.79/0.81 (~c2_1(a2087)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1037, 99, 11, 1031, 1030, 1008, 1029, 508, 1015])).
% 0.79/0.81 tff(1039,plain,
% 0.79/0.81 ($false),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1005, 1038, 1015])).
% 0.79/0.81 tff(1040,plain,(c1_1(a2087) | hskp26 | hskp1 | hskp3 | (~c3_1(a2068)) | c2_1(a2068) | (~c1_1(a2068)) | (~c1_1(a2076)) | c0_1(a2076) | c2_1(a2076) | hskp20 | (~c0_1(a2075)) | (~c1_1(a2075)) | (~c2_1(a2075))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.81 tff(1041,plain,
% 0.79/0.81 (c1_1(a2087)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1040, 11, 549, 693, 819, 818, 817, 716, 714, 960, 959, 902, 901, 900])).
% 0.79/0.81 tff(1042,plain,
% 0.79/0.81 (~hskp10),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[227, 1041])).
% 0.79/0.81 tff(1043,plain,
% 0.79/0.81 (~hskp23),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[107, 1042, 958])).
% 0.79/0.81 tff(1044,plain,
% 0.79/0.81 (hskp17),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[119, 1043, 11])).
% 0.79/0.81 tff(1045,plain,
% 0.79/0.81 (~c1_1(a2110)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[125, 1044])).
% 0.79/0.81 tff(1046,plain,
% 0.79/0.81 (c0_1(a2110)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[136, 1044])).
% 0.79/0.81 tff(1047,plain,
% 0.79/0.81 (~c3_1(a2110)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[143, 99, 958, 1042, 1046, 1045, 32])).
% 0.79/0.81 tff(1048,plain,
% 0.79/0.81 (hskp8),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[167, 1044, 11, 958, 1042])).
% 0.79/0.81 tff(1049,plain,
% 0.79/0.81 (~c0_1(a2082)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[173, 1048])).
% 0.79/0.81 tff(1050,plain,
% 0.79/0.81 (c2_1(a2082)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[184, 1048])).
% 0.79/0.81 tff(1051,plain,
% 0.79/0.81 (c1_1(a2082)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[195, 1048])).
% 0.79/0.81 tff(1052,plain,
% 0.79/0.81 (c2_1(a2110)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[206, 1044])).
% 0.79/0.81 tff(1053,plain,
% 0.79/0.81 ($false),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[213, 99, 958, 1052, 1051, 1050, 1045, 1049, 21, 1047])).
% 0.79/0.81 tff(1054,plain,(hskp1 | hskp26 | hskp3 | (~c3_1(a2068)) | c2_1(a2068) | (~c1_1(a2068)) | (~c1_1(a2076)) | c0_1(a2076) | c2_1(a2076) | hskp20 | (~c0_1(a2075)) | (~c1_1(a2075)) | (~c2_1(a2075))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.81 tff(1055,plain,
% 0.79/0.81 ($false),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1054, 957, 549, 693, 746, 729, 817, 716, 714, 11, 939, 902, 901, 900])).
% 0.79/0.81 tff(1056,plain,(hskp26 | hskp3 | (~c1_1(a2068)) | (~c1_1(a2076)) | c0_1(a2076) | hskp1 | (~c0_1(a2075)) | (~c1_1(a2075)) | (~c2_1(a2075)) | (~c3_1(a2076))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.81 tff(1057,plain,
% 0.79/0.81 (hskp26),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1056, 816, 693, 716, 714, 899, 798, 787, 776, 715])).
% 0.79/0.81 tff(1058,plain,
% 0.79/0.81 (c3_1(a2069)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[581, 1057])).
% 0.79/0.81 tff(1059,plain,
% 0.79/0.81 (c2_1(a2069)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[592, 1057])).
% 0.79/0.81 tff(1060,plain,
% 0.79/0.81 (c0_1(a2069)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[603, 1057])).
% 0.79/0.81 tff(1061,plain,
% 0.79/0.81 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1062,plain,
% 0.79/0.81 ((hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068))) <=> (hskp10 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1063,plain,
% 0.79/0.81 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))))),
% 0.79/0.81 inference(monotonicity,[status(thm)],[1062])).
% 0.79/0.81 tff(1064,plain,
% 0.79/0.81 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.79/0.81 inference(transitivity,[status(thm)],[1063, 1061])).
% 0.79/0.81 tff(1065,plain,
% 0.79/0.81 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))),
% 0.79/0.81 inference(quant_inst,[status(thm)],[])).
% 0.79/0.81 tff(1066,plain,
% 0.79/0.81 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1065, 1064])).
% 0.79/0.81 tff(1067,plain,
% 0.79/0.81 (hskp10),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1066, 99, 1060, 1059, 1058, 746, 735, 729, 703])).
% 0.79/0.81 tff(1068,plain,
% 0.79/0.81 (~c3_1(a2087)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[221, 1067])).
% 0.79/0.81 tff(1069,plain,
% 0.79/0.81 (~c1_1(a2087)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[227, 1067])).
% 0.79/0.81 tff(1070,plain,
% 0.79/0.81 (c2_1(a2087)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[238, 1067])).
% 0.79/0.81 tff(1071,plain,
% 0.79/0.81 (c0_1(a2087)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[266, 99, 747, 1070, 1069, 1068, 259])).
% 0.79/0.81 tff(1072,plain,
% 0.79/0.81 ($false),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1014, 99, 693, 746, 1069, 1068, 729, 379, 816, 1071])).
% 0.79/0.81 tff(1073,plain,(hskp4 | hskp3 | (~c1_1(a2076)) | c0_1(a2076) | (~c3_1(a2076))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.81 tff(1074,plain,
% 0.79/0.81 (hskp4),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1073, 693, 692, 681, 675])).
% 0.79/0.81 tff(1075,plain,
% 0.79/0.81 (~c2_1(a2074)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[273, 1074])).
% 0.79/0.81 tff(1076,plain,
% 0.79/0.81 (hskp0),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[722, 99, 692, 675, 681, 713])).
% 0.79/0.81 tff(1077,plain,
% 0.79/0.81 (~c2_1(a2068)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[728, 1076])).
% 0.79/0.81 tff(1078,plain,
% 0.79/0.81 (~c0_1(a2068)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[734, 1076])).
% 0.79/0.81 tff(1079,plain,
% 0.79/0.81 (c3_1(a2068)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[745, 1076])).
% 0.79/0.81 tff(1080,assumption,(c1_1(a2070)), introduced(assumption)).
% 0.79/0.81 tff(1081,plain,
% 0.79/0.81 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 0.79/0.81 inference(bind,[status(th)],[])).
% 0.79/0.81 tff(1082,plain,
% 0.79/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.79/0.81 inference(quant_intro,[status(thm)],[1081])).
% 0.79/0.81 tff(1083,plain,
% 0.79/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.79/0.81 inference(rewrite,[status(thm)],[])).
% 0.79/0.81 tff(1084,plain,
% 0.79/0.81 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 0.79/0.81 inference(bind,[status(th)],[])).
% 0.79/0.81 tff(1085,plain,
% 0.79/0.81 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.79/0.81 inference(quant_intro,[status(thm)],[1084])).
% 0.79/0.81 tff(1086,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 0.79/0.81 tff(1087,plain,
% 0.79/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 0.79/0.81 tff(1088,plain,
% 0.79/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1087, 1083])).
% 0.79/0.81 tff(1089,plain,(
% 0.79/0.81 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.79/0.81 inference(skolemize,[status(sab)],[1088])).
% 0.79/0.81 tff(1090,plain,
% 0.79/0.81 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 0.79/0.81 inference(modus_ponens,[status(thm)],[1089, 1082])).
% 0.79/0.81 tff(1091,plain,
% 0.79/0.81 (hskp4),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[1073, 693, 716, 714, 715])).
% 0.79/0.81 tff(1092,plain,
% 0.79/0.81 (~c2_1(a2074)),
% 0.79/0.81 inference(unit_resolution,[status(thm)],[273, 1091])).
% 0.79/0.81 tff(1093,plain,
% 0.79/0.82 (c3_1(a2074)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[284, 1091])).
% 0.79/0.82 tff(1094,plain,
% 0.79/0.82 (c1_1(a2074)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[295, 1091])).
% 0.79/0.82 tff(1095,assumption,(~c2_1(a2074)), introduced(assumption)).
% 0.79/0.82 tff(1096,assumption,(c3_1(a2074)), introduced(assumption)).
% 0.79/0.82 tff(1097,assumption,(c1_1(a2074)), introduced(assumption)).
% 0.79/0.82 tff(1098,plain,
% 0.79/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2093)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2093)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1099,plain,
% 0.79/0.82 ((hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093))) <=> (hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2093)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1100,plain,
% 0.79/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2093))))),
% 0.79/0.82 inference(monotonicity,[status(thm)],[1099])).
% 0.79/0.82 tff(1101,plain,
% 0.79/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2093)))),
% 0.79/0.82 inference(transitivity,[status(thm)],[1100, 1098])).
% 0.79/0.82 tff(1102,plain,
% 0.79/0.82 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2093) | c1_1(a2093) | (~c0_1(a2093)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1103,plain,
% 0.79/0.82 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2093) | c3_1(a2093) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2093))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 0.79/0.82 tff(1104,plain,
% 0.79/0.82 ($false),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1103, 99, 693, 368, 1097, 1096, 357, 351, 1095, 379])).
% 0.79/0.82 tff(1105,plain,((~hskp11) | hskp3 | (~c1_1(a2074)) | (~c3_1(a2074)) | c2_1(a2074)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.82 tff(1106,plain,
% 0.79/0.82 (~hskp11),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1105, 693, 1094, 1093, 1092])).
% 0.79/0.82 tff(1107,plain,
% 0.79/0.82 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | (~c2_1(a2087)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1108,plain,
% 0.79/0.82 ((hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076))) <=> (hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | (~c2_1(a2087)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1109,plain,
% 0.79/0.82 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | (~c2_1(a2087))))),
% 0.79/0.82 inference(monotonicity,[status(thm)],[1108])).
% 0.79/0.82 tff(1110,plain,
% 0.79/0.82 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | (~c2_1(a2087)))),
% 0.79/0.82 inference(transitivity,[status(thm)],[1109, 1107])).
% 0.79/0.82 tff(1111,plain,
% 0.79/0.82 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1112,plain,
% 0.79/0.82 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2087) | c3_1(a2087) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | (~c2_1(a2087))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 0.79/0.82 tff(1113,plain,
% 0.79/0.82 (~c2_1(a2076)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1112, 99, 22, 239, 716, 228, 222, 714, 21])).
% 0.79/0.82 tff(1114,plain,
% 0.79/0.82 (hskp8),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1023, 99, 239, 716, 228, 222, 714, 313, 1113])).
% 0.79/0.82 tff(1115,plain,
% 0.79/0.82 (~c0_1(a2082)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[173, 1114])).
% 0.79/0.82 tff(1116,plain,
% 0.79/0.82 (c2_1(a2082)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[184, 1114])).
% 0.79/0.82 tff(1117,plain,
% 0.79/0.82 (c1_1(a2082)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[195, 1114])).
% 0.79/0.82 tff(1118,plain,
% 0.79/0.82 ($false),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[331, 99, 22, 239, 1117, 1116, 228, 222, 1115, 21])).
% 0.79/0.82 tff(1119,plain,(hskp11 | (~c1_1(a2076)) | c0_1(a2076) | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.79/0.82 tff(1120,plain,
% 0.79/0.82 (hskp1),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1119, 1106, 714, 716])).
% 0.79/0.82 tff(1121,plain,
% 0.79/0.82 (~c2_1(a2070)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[561, 1120])).
% 0.79/0.82 tff(1122,plain,
% 0.79/0.82 (^[U: $i] : refl((hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.79/0.82 inference(bind,[status(th)],[])).
% 0.79/0.82 tff(1123,plain,
% 0.79/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.82 inference(quant_intro,[status(thm)],[1122])).
% 0.79/0.82 tff(1124,plain,
% 0.79/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1125,plain,
% 0.79/0.82 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp22))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) <=> (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.79/0.82 inference(bind,[status(th)],[])).
% 0.79/0.82 tff(1126,plain,
% 0.79/0.82 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22) <=> ![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.82 inference(quant_intro,[status(thm)],[1125])).
% 0.79/0.82 tff(1127,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause141')).
% 0.79/0.82 tff(1128,plain,
% 0.79/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 0.79/0.82 tff(1129,plain,
% 0.79/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1128, 1124])).
% 0.79/0.82 tff(1130,plain,(
% 0.79/0.82 ![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.82 inference(skolemize,[status(sab)],[1129])).
% 0.79/0.82 tff(1131,plain,
% 0.79/0.82 (![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1130, 1123])).
% 0.79/0.82 tff(1132,plain,
% 0.79/0.82 (c0_1(a2070)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[547, 1120])).
% 0.79/0.82 tff(1133,plain,
% 0.79/0.82 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1134,plain,
% 0.79/0.82 ((hskp22 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070))) <=> (hskp22 | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1135,plain,
% 0.79/0.82 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070))))),
% 0.79/0.82 inference(monotonicity,[status(thm)],[1134])).
% 0.79/0.82 tff(1136,plain,
% 0.79/0.82 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.79/0.82 inference(transitivity,[status(thm)],[1135, 1133])).
% 0.79/0.82 tff(1137,plain,
% 0.79/0.82 ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1138,plain,
% 0.79/0.82 ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 0.79/0.82 tff(1139,plain,
% 0.79/0.82 (hskp22 | (~c1_1(a2070))),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1138, 99, 1132, 1121, 1131])).
% 0.79/0.82 tff(1140,plain,
% 0.79/0.82 (hskp22),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1139, 1080])).
% 0.79/0.82 tff(1141,plain,
% 0.79/0.82 (((~hskp22) | (~c0_1(a2140))) <=> ((~hskp22) | (~c0_1(a2140)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1142,plain,
% 0.79/0.82 (((~c0_1(a2140)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a2140)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1143,axiom,((~c0_1(a2140)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 0.79/0.82 tff(1144,plain,
% 0.79/0.82 ((~hskp22) | (~c0_1(a2140))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 0.79/0.82 tff(1145,plain,
% 0.79/0.82 ((~hskp22) | (~c0_1(a2140))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1144, 1141])).
% 0.79/0.82 tff(1146,plain,
% 0.79/0.82 (~c0_1(a2140)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1145, 1140])).
% 0.79/0.82 tff(1147,plain,
% 0.79/0.82 (((~hskp22) | c3_1(a2140)) <=> ((~hskp22) | c3_1(a2140))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1148,axiom,((~hskp22) | c3_1(a2140)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 0.79/0.82 tff(1149,plain,
% 0.79/0.82 ((~hskp22) | c3_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 0.79/0.82 tff(1150,plain,
% 0.79/0.82 ((~hskp22) | c3_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1149, 1147])).
% 0.79/0.82 tff(1151,plain,
% 0.79/0.82 ((~hskp22) | c3_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1150, 1147])).
% 0.79/0.82 tff(1152,plain,
% 0.79/0.82 ((~hskp22) | c3_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1151, 1147])).
% 0.79/0.82 tff(1153,plain,
% 0.79/0.82 ((~hskp22) | c3_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1152, 1147])).
% 0.79/0.82 tff(1154,plain,
% 0.79/0.82 ((~hskp22) | c3_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1153, 1147])).
% 0.79/0.82 tff(1155,plain,
% 0.79/0.82 ((~hskp22) | c3_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1154, 1147])).
% 0.79/0.82 tff(1156,plain,
% 0.79/0.82 ((~hskp22) | c3_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1155, 1147])).
% 0.79/0.82 tff(1157,plain,
% 0.79/0.82 (c3_1(a2140)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1156, 1140])).
% 0.79/0.82 tff(1158,plain,
% 0.79/0.82 (((~hskp22) | c2_1(a2140)) <=> ((~hskp22) | c2_1(a2140))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1159,axiom,((~hskp22) | c2_1(a2140)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 0.79/0.82 tff(1160,plain,
% 0.79/0.82 ((~hskp22) | c2_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1159, 1158])).
% 0.79/0.82 tff(1161,plain,
% 0.79/0.82 ((~hskp22) | c2_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1160, 1158])).
% 0.79/0.82 tff(1162,plain,
% 0.79/0.82 ((~hskp22) | c2_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1161, 1158])).
% 0.79/0.82 tff(1163,plain,
% 0.79/0.82 ((~hskp22) | c2_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1162, 1158])).
% 0.79/0.82 tff(1164,plain,
% 0.79/0.82 ((~hskp22) | c2_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1163, 1158])).
% 0.79/0.82 tff(1165,plain,
% 0.79/0.82 ((~hskp22) | c2_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1164, 1158])).
% 0.79/0.82 tff(1166,plain,
% 0.79/0.82 ((~hskp22) | c2_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1165, 1158])).
% 0.79/0.82 tff(1167,plain,
% 0.79/0.82 ((~hskp22) | c2_1(a2140)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1166, 1158])).
% 0.79/0.82 tff(1168,plain,
% 0.79/0.82 (c2_1(a2140)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1167, 1140])).
% 0.79/0.82 tff(1169,assumption,(~c0_1(a2140)), introduced(assumption)).
% 0.79/0.82 tff(1170,assumption,(hskp2), introduced(assumption)).
% 0.79/0.82 tff(1171,plain,
% 0.79/0.82 (((~hskp2) | c2_1(a2071)) <=> ((~hskp2) | c2_1(a2071))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1172,axiom,((~hskp2) | c2_1(a2071)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 0.79/0.82 tff(1173,plain,
% 0.79/0.82 ((~hskp2) | c2_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 0.79/0.82 tff(1174,plain,
% 0.79/0.82 ((~hskp2) | c2_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1173, 1171])).
% 0.79/0.82 tff(1175,plain,
% 0.79/0.82 ((~hskp2) | c2_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1174, 1171])).
% 0.79/0.82 tff(1176,plain,
% 0.79/0.82 ((~hskp2) | c2_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1175, 1171])).
% 0.79/0.82 tff(1177,plain,
% 0.79/0.82 ((~hskp2) | c2_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1176, 1171])).
% 0.79/0.82 tff(1178,plain,
% 0.79/0.82 ((~hskp2) | c2_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1177, 1171])).
% 0.79/0.82 tff(1179,plain,
% 0.79/0.82 ((~hskp2) | c2_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1178, 1171])).
% 0.79/0.82 tff(1180,plain,
% 0.79/0.82 ((~hskp2) | c2_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1179, 1171])).
% 0.79/0.82 tff(1181,plain,
% 0.79/0.82 (c2_1(a2071)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1180, 1170])).
% 0.79/0.82 tff(1182,plain,
% 0.79/0.82 (((~hskp2) | c0_1(a2071)) <=> ((~hskp2) | c0_1(a2071))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1183,axiom,((~hskp2) | c0_1(a2071)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 0.79/0.82 tff(1184,plain,
% 0.79/0.82 ((~hskp2) | c0_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 0.79/0.82 tff(1185,plain,
% 0.79/0.82 ((~hskp2) | c0_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1184, 1182])).
% 0.79/0.82 tff(1186,plain,
% 0.79/0.82 ((~hskp2) | c0_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1185, 1182])).
% 0.79/0.82 tff(1187,plain,
% 0.79/0.82 ((~hskp2) | c0_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1186, 1182])).
% 0.79/0.82 tff(1188,plain,
% 0.79/0.82 ((~hskp2) | c0_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1187, 1182])).
% 0.79/0.82 tff(1189,plain,
% 0.79/0.82 ((~hskp2) | c0_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1188, 1182])).
% 0.79/0.82 tff(1190,plain,
% 0.79/0.82 ((~hskp2) | c0_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1189, 1182])).
% 0.79/0.82 tff(1191,plain,
% 0.79/0.82 ((~hskp2) | c0_1(a2071)),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1190, 1182])).
% 0.79/0.82 tff(1192,plain,
% 0.79/0.82 (c0_1(a2071)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1191, 1170])).
% 0.79/0.82 tff(1193,assumption,(c3_1(a2140)), introduced(assumption)).
% 0.79/0.82 tff(1194,assumption,(c2_1(a2140)), introduced(assumption)).
% 0.79/0.82 tff(1195,plain,
% 0.79/0.82 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a2140) | (~ndr1_0) | (~c1_1(a2071)) | (~c2_1(a2071)) | (~c0_1(a2071)) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2140) | (~ndr1_0) | (~c1_1(a2071)) | (~c2_1(a2071)) | (~c0_1(a2071)) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1196,plain,
% 0.79/0.82 ((hskp26 | (~ndr1_0) | (~c2_1(a2071)) | (~c1_1(a2071)) | (~c0_1(a2071)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140))) <=> (hskp26 | c0_1(a2140) | (~ndr1_0) | (~c1_1(a2071)) | (~c2_1(a2071)) | (~c0_1(a2071)) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1197,plain,
% 0.79/0.82 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2071)) | (~c1_1(a2071)) | (~c0_1(a2071)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a2140) | (~ndr1_0) | (~c1_1(a2071)) | (~c2_1(a2071)) | (~c0_1(a2071)) | (~c3_1(a2140)) | (~c2_1(a2140))))),
% 0.79/0.82 inference(monotonicity,[status(thm)],[1196])).
% 0.79/0.82 tff(1198,plain,
% 0.79/0.82 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2071)) | (~c1_1(a2071)) | (~c0_1(a2071)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2140) | (~ndr1_0) | (~c1_1(a2071)) | (~c2_1(a2071)) | (~c0_1(a2071)) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.79/0.82 inference(transitivity,[status(thm)],[1197, 1195])).
% 0.79/0.82 tff(1199,plain,
% 0.79/0.82 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2071)) | (~c1_1(a2071)) | (~c0_1(a2071)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1200,plain,
% 0.79/0.82 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2140) | (~ndr1_0) | (~c1_1(a2071)) | (~c2_1(a2071)) | (~c0_1(a2071)) | (~c3_1(a2140)) | (~c2_1(a2140))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1199, 1198])).
% 0.79/0.82 tff(1201,plain,
% 0.79/0.82 (~c1_1(a2071)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1200, 99, 549, 1194, 1193, 1192, 1181, 1169, 949])).
% 0.79/0.82 tff(1202,plain,
% 0.79/0.82 (((~hskp2) | (~c3_1(a2071))) <=> ((~hskp2) | (~c3_1(a2071)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1203,plain,
% 0.79/0.82 (((~c3_1(a2071)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a2071)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1204,axiom,((~c3_1(a2071)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 0.79/0.82 tff(1205,plain,
% 0.79/0.82 ((~hskp2) | (~c3_1(a2071))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 0.79/0.82 tff(1206,plain,
% 0.79/0.82 ((~hskp2) | (~c3_1(a2071))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1205, 1202])).
% 0.79/0.82 tff(1207,plain,
% 0.79/0.82 (~c3_1(a2071)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1206, 1170])).
% 0.79/0.82 tff(1208,plain,
% 0.79/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a2074) | c3_1(a2071) | (~ndr1_0) | c1_1(a2071) | (~c0_1(a2071)) | (~c3_1(a2074)) | (~c1_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a2074) | c3_1(a2071) | (~ndr1_0) | c1_1(a2071) | (~c0_1(a2071)) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1209,plain,
% 0.79/0.82 ((hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2071) | c1_1(a2071) | (~c0_1(a2071))) <=> (hskp3 | c2_1(a2074) | c3_1(a2071) | (~ndr1_0) | c1_1(a2071) | (~c0_1(a2071)) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1210,plain,
% 0.79/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2071) | c1_1(a2071) | (~c0_1(a2071)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c2_1(a2074) | c3_1(a2071) | (~ndr1_0) | c1_1(a2071) | (~c0_1(a2071)) | (~c3_1(a2074)) | (~c1_1(a2074))))),
% 0.79/0.82 inference(monotonicity,[status(thm)],[1209])).
% 0.79/0.82 tff(1211,plain,
% 0.79/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2071) | c1_1(a2071) | (~c0_1(a2071)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a2074) | c3_1(a2071) | (~ndr1_0) | c1_1(a2071) | (~c0_1(a2071)) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.79/0.82 inference(transitivity,[status(thm)],[1210, 1208])).
% 0.79/0.82 tff(1212,plain,
% 0.79/0.82 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2071) | c1_1(a2071) | (~c0_1(a2071)))),
% 0.79/0.82 inference(quant_inst,[status(thm)],[])).
% 0.79/0.82 tff(1213,plain,
% 0.79/0.82 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c2_1(a2074) | c3_1(a2071) | (~ndr1_0) | c1_1(a2071) | (~c0_1(a2071)) | (~c3_1(a2074)) | (~c1_1(a2074))),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 0.79/0.82 tff(1214,plain,
% 0.79/0.82 ($false),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1213, 99, 693, 1097, 1096, 1192, 1095, 1207, 379, 1201])).
% 0.79/0.82 tff(1215,plain,((~hskp2) | hskp3 | (~c1_1(a2074)) | (~c3_1(a2074)) | c2_1(a2074) | hskp26 | (~c2_1(a2140)) | (~c3_1(a2140)) | c0_1(a2140)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.82 tff(1216,plain,
% 0.79/0.82 (~hskp2),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1215, 1168, 1094, 1093, 1092, 549, 693, 1157, 1146])).
% 0.79/0.82 tff(1217,plain,
% 0.79/0.82 ((hskp17 | hskp2) <=> (hskp17 | hskp2)),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1218,axiom,(hskp17 | hskp2), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.79/0.82 tff(1219,plain,
% 0.79/0.82 (hskp17 | hskp2),
% 0.79/0.82 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 0.79/0.82 tff(1220,plain,
% 0.79/0.82 (hskp17),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[1219, 1216])).
% 0.79/0.82 tff(1221,plain,
% 0.79/0.82 (~c1_1(a2110)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[125, 1220])).
% 0.79/0.82 tff(1222,plain,
% 0.79/0.82 (c0_1(a2110)),
% 0.79/0.82 inference(unit_resolution,[status(thm)],[136, 1220])).
% 0.79/0.82 tff(1223,plain,
% 0.79/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a2110) | c0_1(a2076) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2076)) | (~c1_1(a2076)) | (~c3_1(a2110)) | (~c0_1(a2110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a2110) | c0_1(a2076) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2076)) | (~c1_1(a2076)) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.79/0.82 inference(rewrite,[status(thm)],[])).
% 0.79/0.82 tff(1224,plain,
% 0.79/0.82 (((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076))) <=> (c1_1(a2110) | c0_1(a2076) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2076)) | (~c1_1(a2076)) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1225,plain,
% 0.79/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a2110) | c0_1(a2076) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2076)) | (~c1_1(a2076)) | (~c3_1(a2110)) | (~c0_1(a2110))))),
% 0.79/0.83 inference(monotonicity,[status(thm)],[1224])).
% 0.79/0.83 tff(1226,plain,
% 0.79/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a2110) | c0_1(a2076) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2076)) | (~c1_1(a2076)) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.79/0.83 inference(transitivity,[status(thm)],[1225, 1223])).
% 0.79/0.83 tff(1227,plain,
% 0.79/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2076) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1228,plain,
% 0.79/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a2110) | c0_1(a2076) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2076)) | (~c1_1(a2076)) | (~c3_1(a2110)) | (~c0_1(a2110))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 0.79/0.83 tff(1229,plain,
% 0.79/0.83 (~c3_1(a2110)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1228, 99, 1222, 716, 715, 1132, 1221, 714, 1121, 1090, 1080])).
% 0.79/0.83 tff(1230,plain,
% 0.79/0.83 (c2_1(a2110)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[206, 1220])).
% 0.79/0.83 tff(1231,plain,
% 0.79/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1232,plain,
% 0.79/0.83 ((hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076))) <=> (hskp11 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1233,plain,
% 0.79/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110))))),
% 0.79/0.83 inference(monotonicity,[status(thm)],[1232])).
% 0.79/0.83 tff(1234,plain,
% 0.79/0.83 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.79/0.83 inference(transitivity,[status(thm)],[1233, 1231])).
% 0.79/0.83 tff(1235,plain,
% 0.79/0.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | (~c1_1(a2076)) | (~c2_1(a2076)))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1236,plain,
% 0.79/0.83 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp11 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1235, 1234])).
% 0.79/0.83 tff(1237,plain,
% 0.79/0.83 (~c2_1(a2076)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1236, 99, 1106, 1230, 716, 1221, 714, 21, 1229])).
% 0.79/0.83 tff(1238,plain,
% 0.79/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1239,plain,
% 0.79/0.83 ((hskp8 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076))) <=> (hskp8 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1240,plain,
% 0.79/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110))))),
% 0.79/0.83 inference(monotonicity,[status(thm)],[1239])).
% 0.79/0.83 tff(1241,plain,
% 0.79/0.83 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110)))),
% 0.79/0.83 inference(transitivity,[status(thm)],[1240, 1238])).
% 0.79/0.83 tff(1242,plain,
% 0.79/0.83 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2110) | c3_1(a2110) | (~c2_1(a2110)) | c0_1(a2076) | c2_1(a2076) | (~c1_1(a2076)))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1243,plain,
% 0.79/0.83 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2110) | c0_1(a2076) | (~ndr1_0) | c2_1(a2076) | (~c1_1(a2076)) | c3_1(a2110) | (~c2_1(a2110))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1242, 1241])).
% 0.79/0.83 tff(1244,plain,
% 0.79/0.83 ($false),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1243, 99, 159, 1230, 716, 1221, 714, 313, 1237, 1229])).
% 0.79/0.83 tff(1245,plain,((~c1_1(a2070)) | hskp8 | (~c1_1(a2076)) | c0_1(a2076) | (~c3_1(a2076)) | hskp26 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.79/0.83 tff(1246,plain,
% 0.79/0.83 (~c1_1(a2070)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1245, 159, 716, 714, 715, 549, 693])).
% 0.79/0.83 tff(1247,plain,
% 0.79/0.83 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.79/0.83 inference(bind,[status(th)],[])).
% 0.79/0.83 tff(1248,plain,
% 0.79/0.83 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.83 inference(quant_intro,[status(thm)],[1247])).
% 0.79/0.83 tff(1249,plain,
% 0.79/0.83 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1250,plain,
% 0.79/0.83 (^[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(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.79/0.83 inference(bind,[status(th)],[])).
% 0.79/0.83 tff(1251,plain,
% 0.79/0.83 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.83 inference(quant_intro,[status(thm)],[1250])).
% 0.79/0.83 tff(1252,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 0.79/0.83 tff(1253,plain,
% 0.79/0.83 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 0.79/0.83 tff(1254,plain,
% 0.79/0.83 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1253, 1249])).
% 0.79/0.83 tff(1255,plain,(
% 0.79/0.83 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.83 inference(skolemize,[status(sab)],[1254])).
% 0.79/0.83 tff(1256,plain,
% 0.79/0.83 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1255, 1248])).
% 0.79/0.83 tff(1257,plain,
% 0.79/0.83 (^[U: $i] : refl((hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 0.79/0.83 inference(bind,[status(th)],[])).
% 0.79/0.83 tff(1258,plain,
% 0.79/0.83 (![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.79/0.83 inference(quant_intro,[status(thm)],[1257])).
% 0.79/0.83 tff(1259,plain,
% 0.79/0.83 (![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1260,plain,
% 0.79/0.83 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp18) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp18) <=> (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp18) <=> (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 0.79/0.83 inference(bind,[status(th)],[])).
% 0.79/0.83 tff(1261,plain,
% 0.79/0.83 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp18) <=> ![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.79/0.83 inference(quant_intro,[status(thm)],[1260])).
% 0.79/0.83 tff(1262,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 0.79/0.83 tff(1263,plain,
% 0.79/0.83 (![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 0.79/0.83 tff(1264,plain,
% 0.79/0.83 (![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1263, 1259])).
% 0.79/0.83 tff(1265,plain,(
% 0.79/0.83 ![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.79/0.83 inference(skolemize,[status(sab)],[1264])).
% 0.79/0.83 tff(1266,plain,
% 0.79/0.83 (![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1265, 1258])).
% 0.79/0.83 tff(1267,plain,
% 0.79/0.83 (c3_1(a2070)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[536, 1120])).
% 0.79/0.83 tff(1268,plain,
% 0.79/0.83 (((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070))) <=> ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp26 | hskp18 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1269,plain,
% 0.79/0.83 ((hskp26 | hskp18 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c3_1(a2070))) <=> (hskp26 | hskp18 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1270,plain,
% 0.79/0.83 (((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c3_1(a2070)))) <=> ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070)))),
% 0.79/0.83 inference(monotonicity,[status(thm)],[1269])).
% 0.79/0.83 tff(1271,plain,
% 0.79/0.83 (((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c3_1(a2070)))) <=> ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp26 | hskp18 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070))),
% 0.79/0.83 inference(transitivity,[status(thm)],[1270, 1268])).
% 0.79/0.83 tff(1272,plain,
% 0.79/0.83 ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c3_1(a2070)))),
% 0.79/0.83 inference(quant_inst,[status(thm)],[])).
% 0.79/0.83 tff(1273,plain,
% 0.79/0.83 ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp26 | hskp18 | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070)),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 0.79/0.83 tff(1274,plain,
% 0.79/0.83 (hskp26 | hskp18 | c1_1(a2070)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1273, 99, 1267, 1121, 1266])).
% 0.79/0.83 tff(1275,plain,
% 0.79/0.83 (hskp18),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1274, 1246, 549])).
% 0.79/0.83 tff(1276,plain,
% 0.79/0.83 (((~hskp18) | (~c3_1(a2116))) <=> ((~hskp18) | (~c3_1(a2116)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1277,plain,
% 0.79/0.83 (((~c3_1(a2116)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a2116)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1278,axiom,((~c3_1(a2116)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 0.79/0.83 tff(1279,plain,
% 0.79/0.83 ((~hskp18) | (~c3_1(a2116))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 0.79/0.83 tff(1280,plain,
% 0.79/0.83 ((~hskp18) | (~c3_1(a2116))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1279, 1276])).
% 0.79/0.83 tff(1281,plain,
% 0.79/0.83 (~c3_1(a2116)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1280, 1275])).
% 0.79/0.83 tff(1282,plain,
% 0.79/0.83 (((~hskp18) | (~c2_1(a2116))) <=> ((~hskp18) | (~c2_1(a2116)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1283,plain,
% 0.79/0.83 (((~c2_1(a2116)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a2116)))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1284,axiom,((~c2_1(a2116)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 0.79/0.83 tff(1285,plain,
% 0.79/0.83 ((~hskp18) | (~c2_1(a2116))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1284, 1283])).
% 0.79/0.83 tff(1286,plain,
% 0.79/0.83 ((~hskp18) | (~c2_1(a2116))),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1285, 1282])).
% 0.79/0.83 tff(1287,plain,
% 0.79/0.83 (~c2_1(a2116)),
% 0.79/0.83 inference(unit_resolution,[status(thm)],[1286, 1275])).
% 0.79/0.83 tff(1288,plain,
% 0.79/0.83 (((~hskp18) | c1_1(a2116)) <=> ((~hskp18) | c1_1(a2116))),
% 0.79/0.83 inference(rewrite,[status(thm)],[])).
% 0.79/0.83 tff(1289,axiom,((~hskp18) | c1_1(a2116)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 0.79/0.83 tff(1290,plain,
% 0.79/0.83 ((~hskp18) | c1_1(a2116)),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 0.79/0.83 tff(1291,plain,
% 0.79/0.83 ((~hskp18) | c1_1(a2116)),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1290, 1288])).
% 0.79/0.83 tff(1292,plain,
% 0.79/0.83 ((~hskp18) | c1_1(a2116)),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1291, 1288])).
% 0.79/0.83 tff(1293,plain,
% 0.79/0.83 ((~hskp18) | c1_1(a2116)),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1292, 1288])).
% 0.79/0.83 tff(1294,plain,
% 0.79/0.83 ((~hskp18) | c1_1(a2116)),
% 0.79/0.83 inference(modus_ponens,[status(thm)],[1293, 1288])).
% 0.79/0.83 tff(1295,plain,
% 0.79/0.84 ((~hskp18) | c1_1(a2116)),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1294, 1288])).
% 0.79/0.84 tff(1296,plain,
% 0.79/0.84 ((~hskp18) | c1_1(a2116)),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1295, 1288])).
% 0.79/0.84 tff(1297,plain,
% 0.79/0.84 ((~hskp18) | c1_1(a2116)),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1296, 1288])).
% 0.79/0.84 tff(1298,plain,
% 0.79/0.84 (c1_1(a2116)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1297, 1275])).
% 0.79/0.84 tff(1299,plain,
% 0.79/0.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a2116) | c3_1(a2116) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)) | (~c1_1(a2116)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a2116) | c3_1(a2116) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)) | (~c1_1(a2116)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1300,plain,
% 0.79/0.84 ((hskp8 | (~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070))) <=> (hskp8 | c2_1(a2116) | c3_1(a2116) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)) | (~c1_1(a2116)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1301,plain,
% 0.79/0.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp8 | c2_1(a2116) | c3_1(a2116) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)) | (~c1_1(a2116))))),
% 0.79/0.84 inference(monotonicity,[status(thm)],[1300])).
% 0.79/0.84 tff(1302,plain,
% 0.79/0.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a2116) | c3_1(a2116) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)) | (~c1_1(a2116)))),
% 0.79/0.84 inference(transitivity,[status(thm)],[1301, 1299])).
% 0.79/0.84 tff(1303,plain,
% 0.79/0.84 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(1304,plain,
% 0.79/0.84 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp8 | c2_1(a2116) | c3_1(a2116) | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)) | (~c1_1(a2116))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1303, 1302])).
% 0.79/0.84 tff(1305,plain,
% 0.79/0.84 ($false),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1304, 99, 159, 1298, 1132, 1267, 1287, 1281, 1256, 1246])).
% 0.79/0.84 tff(1306,plain,(hskp8 | hskp26 | (~c1_1(a2076)) | c0_1(a2076) | (~c3_1(a2076)) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.79/0.84 tff(1307,plain,
% 0.79/0.84 (hskp8),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1306, 549, 716, 714, 715, 693])).
% 0.79/0.84 tff(1308,plain,
% 0.79/0.84 (~c0_1(a2082)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[173, 1307])).
% 0.79/0.84 tff(1309,plain,
% 0.79/0.84 (c2_1(a2082)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[184, 1307])).
% 0.79/0.84 tff(1310,plain,
% 0.79/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2082) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2082) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1311,plain,
% 0.79/0.84 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082))) <=> (c0_1(a2082) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1312,plain,
% 0.79/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2082) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2082) | (~c2_1(a2082))))),
% 0.79/0.84 inference(monotonicity,[status(thm)],[1311])).
% 0.79/0.84 tff(1313,plain,
% 0.79/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2082) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.79/0.84 inference(transitivity,[status(thm)],[1312, 1310])).
% 0.79/0.84 tff(1314,plain,
% 0.79/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(1315,plain,
% 0.79/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2082) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2082) | (~c2_1(a2082))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 0.79/0.84 tff(1316,plain,
% 0.79/0.84 (c3_1(a2082)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1315, 99, 1309, 1094, 1093, 1132, 1267, 1308, 1092, 1121, 10])).
% 0.79/0.84 tff(1317,plain,
% 0.79/0.84 (c1_1(a2082)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[195, 1307])).
% 0.79/0.84 tff(1318,assumption,(c3_1(a2082)), introduced(assumption)).
% 0.79/0.84 tff(1319,assumption,(~c2_1(a2070)), introduced(assumption)).
% 0.79/0.84 tff(1320,assumption,(~c0_1(a2082)), introduced(assumption)).
% 0.79/0.84 tff(1321,assumption,(c0_1(a2070)), introduced(assumption)).
% 0.79/0.84 tff(1322,plain,
% 0.79/0.84 (hskp22 | (~c1_1(a2070))),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1138, 99, 1321, 1319, 1131])).
% 0.79/0.84 tff(1323,plain,
% 0.79/0.84 (hskp22),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1322, 1080])).
% 0.79/0.84 tff(1324,plain,
% 0.79/0.84 (~c0_1(a2140)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1145, 1323])).
% 0.79/0.84 tff(1325,plain,
% 0.79/0.84 (c3_1(a2140)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1156, 1323])).
% 0.79/0.84 tff(1326,plain,
% 0.79/0.84 (c2_1(a2140)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1167, 1323])).
% 0.79/0.84 tff(1327,plain,
% 0.79/0.84 (~hskp2),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1215, 1326, 1097, 1096, 1095, 549, 693, 1325, 1324])).
% 0.79/0.84 tff(1328,plain,
% 0.79/0.84 (hskp17),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1219, 1327])).
% 0.79/0.84 tff(1329,plain,
% 0.79/0.84 (~c1_1(a2110)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[125, 1328])).
% 0.79/0.84 tff(1330,assumption,(c1_1(a2082)), introduced(assumption)).
% 0.79/0.84 tff(1331,plain,
% 0.79/0.84 (c0_1(a2110)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[136, 1328])).
% 0.79/0.84 tff(1332,plain,
% 0.79/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a2110) | c0_1(a2082) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c3_1(a2110)) | (~c0_1(a2110)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a2110) | c0_1(a2082) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1333,plain,
% 0.79/0.84 (((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082))) <=> (c1_1(a2110) | c0_1(a2082) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1334,plain,
% 0.79/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a2110) | c0_1(a2082) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c3_1(a2110)) | (~c0_1(a2110))))),
% 0.79/0.84 inference(monotonicity,[status(thm)],[1333])).
% 0.79/0.84 tff(1335,plain,
% 0.79/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a2110) | c0_1(a2082) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c3_1(a2110)) | (~c0_1(a2110)))),
% 0.79/0.84 inference(transitivity,[status(thm)],[1334, 1332])).
% 0.79/0.84 tff(1336,plain,
% 0.79/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2110) | (~c3_1(a2110)) | (~c0_1(a2110)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082)))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(1337,plain,
% 0.79/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a2110) | c0_1(a2082) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c3_1(a2110)) | (~c0_1(a2110))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 0.79/0.84 tff(1338,plain,
% 0.79/0.84 (~c3_1(a2110)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1337, 99, 1331, 1330, 1321, 1329, 1320, 1319, 1090, 1318, 1080])).
% 0.79/0.84 tff(1339,assumption,(c2_1(a2082)), introduced(assumption)).
% 0.79/0.84 tff(1340,plain,
% 0.79/0.84 (c2_1(a2110)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[206, 1328])).
% 0.79/0.84 tff(1341,plain,
% 0.79/0.84 (~hskp11),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1105, 693, 1097, 1096, 1095])).
% 0.79/0.84 tff(1342,plain,
% 0.79/0.84 ($false),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[213, 99, 1341, 1340, 1330, 1339, 1329, 1320, 21, 1338])).
% 0.79/0.84 tff(1343,plain,((~c1_1(a2070)) | (~c1_1(a2082)) | (~c2_1(a2082)) | c0_1(a2082) | (~c0_1(a2070)) | c2_1(a2070) | (~c3_1(a2082)) | (~c1_1(a2074)) | (~c3_1(a2074)) | c2_1(a2074) | hskp26 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.79/0.84 tff(1344,plain,
% 0.79/0.84 (~c1_1(a2070)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1343, 1317, 1309, 1308, 1132, 1121, 1316, 1094, 1093, 1092, 549, 693])).
% 0.79/0.84 tff(1345,plain,
% 0.79/0.84 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1346,plain,
% 0.79/0.84 ((hskp11 | hskp10 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070))) <=> (hskp11 | hskp10 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1347,plain,
% 0.79/0.84 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070))))),
% 0.79/0.84 inference(monotonicity,[status(thm)],[1346])).
% 0.79/0.84 tff(1348,plain,
% 0.79/0.84 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070)))),
% 0.79/0.84 inference(transitivity,[status(thm)],[1347, 1345])).
% 0.79/0.84 tff(1349,plain,
% 0.79/0.84 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c1_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(1350,plain,
% 0.79/0.84 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp11 | hskp10 | (~ndr1_0) | (~c3_1(a2070)) | c1_1(a2070) | (~c0_1(a2070))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 0.79/0.84 tff(1351,plain,
% 0.79/0.84 (hskp10 | c1_1(a2070)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1350, 99, 1106, 1132, 1267, 32])).
% 0.79/0.84 tff(1352,plain,
% 0.79/0.84 (hskp10),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1351, 1344])).
% 0.79/0.84 tff(1353,plain,
% 0.79/0.84 (~c3_1(a2087)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[221, 1352])).
% 0.79/0.84 tff(1354,plain,
% 0.79/0.84 (~c1_1(a2087)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[227, 1352])).
% 0.79/0.84 tff(1355,plain,
% 0.79/0.84 (c2_1(a2087)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[238, 1352])).
% 0.79/0.84 tff(1356,plain,
% 0.79/0.84 ($false),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[331, 99, 1106, 1355, 1317, 1309, 1354, 1353, 1308, 21])).
% 0.79/0.84 tff(1357,plain,(hskp26 | hskp3 | (~c1_1(a2076)) | c0_1(a2076) | (~c3_1(a2076))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.84 tff(1358,plain,
% 0.79/0.84 (hskp26),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1357, 693, 692, 681, 675])).
% 0.79/0.84 tff(1359,plain,
% 0.79/0.84 (c3_1(a2069)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[581, 1358])).
% 0.79/0.84 tff(1360,plain,
% 0.79/0.84 (c2_1(a2069)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[592, 1358])).
% 0.79/0.84 tff(1361,plain,
% 0.79/0.84 (c0_1(a2069)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[603, 1358])).
% 0.79/0.84 tff(1362,plain,
% 0.79/0.84 (hskp10),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1066, 99, 1361, 1360, 1359, 1079, 1078, 1077, 703])).
% 0.79/0.84 tff(1363,plain,
% 0.79/0.84 (~c3_1(a2087)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[221, 1362])).
% 0.79/0.84 tff(1364,plain,
% 0.79/0.84 (~c1_1(a2087)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[227, 1362])).
% 0.79/0.84 tff(1365,plain,
% 0.79/0.84 (c3_1(a2074)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[284, 1074])).
% 0.79/0.84 tff(1366,plain,
% 0.79/0.84 (c1_1(a2074)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[295, 1074])).
% 0.79/0.84 tff(1367,plain,
% 0.79/0.84 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2087)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1368,plain,
% 0.79/0.84 ((hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087))) <=> (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2087)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1369,plain,
% 0.79/0.84 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2087))))),
% 0.79/0.84 inference(monotonicity,[status(thm)],[1368])).
% 0.79/0.84 tff(1370,plain,
% 0.79/0.84 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2087)))),
% 0.79/0.84 inference(transitivity,[status(thm)],[1369, 1367])).
% 0.79/0.84 tff(1371,plain,
% 0.79/0.84 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(1372,plain,
% 0.79/0.84 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2087))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1371, 1370])).
% 0.79/0.84 tff(1373,plain,
% 0.79/0.84 (~c0_1(a2087)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1372, 99, 693, 1366, 1365, 1364, 1363, 1075, 379])).
% 0.79/0.84 tff(1374,plain,
% 0.79/0.84 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.79/0.84 inference(bind,[status(th)],[])).
% 0.79/0.84 tff(1375,plain,
% 0.79/0.84 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.84 inference(quant_intro,[status(thm)],[1374])).
% 0.79/0.84 tff(1376,plain,
% 0.79/0.84 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1377,plain,
% 0.79/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp11))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.79/0.84 inference(bind,[status(th)],[])).
% 0.79/0.84 tff(1378,plain,
% 0.79/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.84 inference(quant_intro,[status(thm)],[1377])).
% 0.79/0.84 tff(1379,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 0.79/0.84 tff(1380,plain,
% 0.79/0.84 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1379, 1378])).
% 0.79/0.84 tff(1381,plain,
% 0.79/0.84 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1380, 1376])).
% 0.79/0.84 tff(1382,plain,(
% 0.79/0.84 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.84 inference(skolemize,[status(sab)],[1381])).
% 0.79/0.84 tff(1383,plain,
% 0.79/0.84 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1382, 1375])).
% 0.79/0.84 tff(1384,plain,
% 0.79/0.84 (~hskp11),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1105, 693, 1366, 1365, 1075])).
% 0.79/0.84 tff(1385,plain,
% 0.79/0.84 (hskp1),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1119, 1384, 681, 692])).
% 0.79/0.84 tff(1386,plain,
% 0.79/0.84 (~c2_1(a2070)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[561, 1385])).
% 0.79/0.84 tff(1387,plain,
% 0.79/0.84 (c0_1(a2070)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[547, 1385])).
% 0.79/0.84 tff(1388,plain,
% 0.79/0.84 (c2_1(a2087)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[238, 1362])).
% 0.79/0.84 tff(1389,plain,
% 0.79/0.84 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | c1_1(a2070) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp11 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | c1_1(a2070) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1390,plain,
% 0.79/0.84 ((hskp11 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c0_1(a2070)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087))) <=> (hskp11 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | c1_1(a2070) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1391,plain,
% 0.79/0.84 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c0_1(a2070)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | c1_1(a2070) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.79/0.84 inference(monotonicity,[status(thm)],[1390])).
% 0.79/0.84 tff(1392,plain,
% 0.79/0.84 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c0_1(a2070)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp11 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | c1_1(a2070) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.79/0.84 inference(transitivity,[status(thm)],[1391, 1389])).
% 0.79/0.84 tff(1393,plain,
% 0.79/0.84 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp11 | (~ndr1_0) | c2_1(a2070) | c1_1(a2070) | (~c0_1(a2070)) | c3_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.79/0.84 inference(quant_inst,[status(thm)],[])).
% 0.79/0.84 tff(1394,plain,
% 0.79/0.84 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp11 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | c1_1(a2070) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.79/0.84 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 0.79/0.84 tff(1395,plain,
% 0.79/0.84 (c1_1(a2070)),
% 0.79/0.84 inference(unit_resolution,[status(thm)],[1394, 99, 1384, 1388, 1387, 1363, 1386, 1383, 1373])).
% 0.79/0.84 tff(1396,plain,
% 0.79/0.84 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.79/0.84 inference(bind,[status(th)],[])).
% 0.79/0.84 tff(1397,plain,
% 0.79/0.84 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.84 inference(quant_intro,[status(thm)],[1396])).
% 0.79/0.84 tff(1398,plain,
% 0.79/0.84 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.84 inference(rewrite,[status(thm)],[])).
% 0.79/0.84 tff(1399,plain,
% 0.79/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.79/0.85 inference(bind,[status(th)],[])).
% 0.79/0.85 tff(1400,plain,
% 0.79/0.85 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.85 inference(quant_intro,[status(thm)],[1399])).
% 0.79/0.85 tff(1401,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 0.79/0.85 tff(1402,plain,
% 0.79/0.85 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.85 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 0.79/0.85 tff(1403,plain,
% 0.79/0.85 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.85 inference(modus_ponens,[status(thm)],[1402, 1398])).
% 0.79/0.85 tff(1404,plain,(
% 0.79/0.85 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.85 inference(skolemize,[status(sab)],[1403])).
% 0.79/0.85 tff(1405,plain,
% 0.79/0.85 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.79/0.85 inference(modus_ponens,[status(thm)],[1404, 1397])).
% 0.79/0.85 tff(1406,plain,
% 0.79/0.85 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c1_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(1407,plain,
% 0.79/0.85 ((hskp29 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087))) <=> (hskp29 | c1_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(1408,plain,
% 0.79/0.85 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c1_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.79/0.85 inference(monotonicity,[status(thm)],[1407])).
% 0.79/0.85 tff(1409,plain,
% 0.79/0.85 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.79/0.85 inference(transitivity,[status(thm)],[1408, 1406])).
% 0.79/0.85 tff(1410,plain,
% 0.79/0.85 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2070) | (~c1_1(a2070)) | (~c0_1(a2070)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.79/0.85 inference(quant_inst,[status(thm)],[])).
% 0.79/0.85 tff(1411,plain,
% 0.79/0.85 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c1_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.79/0.85 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 0.79/0.85 tff(1412,plain,
% 0.79/0.85 ((~c1_1(a2070)) | c0_1(a2087)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1411, 369, 99, 1388, 1387, 1364, 1386, 1405])).
% 0.79/0.85 tff(1413,plain,
% 0.79/0.85 ($false),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1412, 1395, 1373])).
% 0.79/0.85 tff(1414,plain,(hskp3 | hskp29), inference(lemma,lemma(discharge,[]))).
% 0.79/0.85 tff(1415,plain,
% 0.79/0.85 (hskp3),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1414, 369])).
% 0.79/0.85 tff(1416,plain,
% 0.79/0.85 (~c3_1(a2072)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[386, 1415])).
% 0.79/0.85 tff(1417,plain,
% 0.79/0.85 (~c0_1(a2072)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[398, 1415])).
% 0.79/0.85 tff(1418,plain,
% 0.79/0.85 (~c1_1(a2072)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[392, 1415])).
% 0.79/0.85 tff(1419,assumption,(~c1_1(a2068)), introduced(assumption)).
% 0.79/0.85 tff(1420,plain,
% 0.79/0.85 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(1421,plain,
% 0.79/0.85 ((hskp26 | hskp1 | (~ndr1_0) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072)) <=> (hskp26 | hskp1 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(1422,plain,
% 0.79/0.85 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072)))),
% 0.79/0.85 inference(monotonicity,[status(thm)],[1421])).
% 0.79/0.85 tff(1423,plain,
% 0.79/0.85 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072))),
% 0.79/0.85 inference(transitivity,[status(thm)],[1422, 1420])).
% 0.79/0.85 tff(1424,plain,
% 0.79/0.85 ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))),
% 0.79/0.85 inference(quant_inst,[status(thm)],[])).
% 0.79/0.85 tff(1425,plain,
% 0.79/0.85 ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072)),
% 0.79/0.85 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 0.79/0.85 tff(1426,plain,
% 0.79/0.85 (hskp26 | hskp1 | c0_1(a2072) | c2_1(a2072)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1425, 99, 412, 998])).
% 0.79/0.85 tff(1427,plain,
% 0.79/0.85 (c2_1(a2072)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1426, 549, 413, 11])).
% 0.79/0.85 tff(1428,plain,
% 0.79/0.85 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(1429,plain,
% 0.79/0.85 ((hskp26 | hskp1 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068)) <=> (hskp26 | hskp1 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(1430,plain,
% 0.79/0.85 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068)))),
% 0.79/0.85 inference(monotonicity,[status(thm)],[1429])).
% 0.79/0.85 tff(1431,plain,
% 0.79/0.85 (((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))) <=> ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068))),
% 0.79/0.85 inference(transitivity,[status(thm)],[1430, 1428])).
% 0.79/0.85 tff(1432,plain,
% 0.79/0.85 ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp1 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))),
% 0.79/0.85 inference(quant_inst,[status(thm)],[])).
% 0.79/0.85 tff(1433,plain,
% 0.79/0.85 ((~![U: $i] : (hskp26 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp1 | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068)),
% 0.79/0.85 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 0.79/0.85 tff(1434,plain,
% 0.79/0.85 (hskp26 | hskp1 | c1_1(a2068)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1433, 99, 904, 818, 998])).
% 0.79/0.85 tff(1435,plain,
% 0.79/0.85 (c1_1(a2068)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1434, 549, 11])).
% 0.79/0.85 tff(1436,plain,
% 0.79/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2072)))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(1437,plain,
% 0.79/0.85 ((hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068))) <=> (hskp8 | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2072)))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(1438,plain,
% 0.79/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2072))))),
% 0.79/0.85 inference(monotonicity,[status(thm)],[1437])).
% 0.79/0.85 tff(1439,plain,
% 0.79/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2072)))),
% 0.79/0.85 inference(transitivity,[status(thm)],[1438, 1436])).
% 0.79/0.85 tff(1440,plain,
% 0.79/0.85 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2072) | c3_1(a2072) | (~c2_1(a2072)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)))),
% 0.79/0.85 inference(quant_inst,[status(thm)],[])).
% 0.79/0.85 tff(1441,plain,
% 0.79/0.85 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2072))),
% 0.79/0.85 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 0.79/0.85 tff(1442,plain,
% 0.79/0.85 (hskp8 | (~c1_1(a2068)) | (~c2_1(a2072))),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1441, 99, 412, 411, 904, 818, 313])).
% 0.79/0.85 tff(1443,plain,
% 0.79/0.85 (hskp8),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1442, 1427, 1435])).
% 0.79/0.85 tff(1444,plain,
% 0.79/0.85 (~c0_1(a2082)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[173, 1443])).
% 0.79/0.85 tff(1445,plain,
% 0.79/0.85 (c2_1(a2082)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[184, 1443])).
% 0.79/0.85 tff(1446,plain,
% 0.79/0.85 (c1_1(a2082)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[195, 1443])).
% 0.79/0.85 tff(1447,plain,
% 0.79/0.85 ($false),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[514, 99, 11, 1446, 1445, 1444, 413, 411, 508, 1427])).
% 0.79/0.85 tff(1448,plain,(hskp26 | hskp1 | c0_1(a2072) | c3_1(a2072) | c1_1(a2072) | c0_1(a2068) | c2_1(a2068)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.85 tff(1449,plain,
% 0.79/0.85 (hskp26),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1448, 11, 413, 411, 412, 735, 729])).
% 0.79/0.85 tff(1450,plain,
% 0.79/0.85 (c3_1(a2069)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[581, 1449])).
% 0.79/0.85 tff(1451,plain,
% 0.79/0.85 (c2_1(a2069)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[592, 1449])).
% 0.79/0.85 tff(1452,plain,
% 0.79/0.85 (c0_1(a2069)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[603, 1449])).
% 0.79/0.85 tff(1453,plain,
% 0.79/0.85 (hskp10),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1066, 99, 1452, 1451, 1450, 746, 735, 729, 703])).
% 0.79/0.85 tff(1454,plain,
% 0.79/0.85 (~c3_1(a2087)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[221, 1453])).
% 0.79/0.85 tff(1455,plain,
% 0.79/0.85 (~c1_1(a2087)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[227, 1453])).
% 0.79/0.85 tff(1456,plain,
% 0.79/0.85 (c2_1(a2087)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[238, 1453])).
% 0.79/0.85 tff(1457,plain,
% 0.79/0.85 (hskp8 | c2_1(a2076)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1023, 99, 260, 716, 241, 240, 714, 313])).
% 0.79/0.85 tff(1458,plain,
% 0.79/0.85 (c2_1(a2076)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1457, 159])).
% 0.79/0.85 tff(1459,plain,
% 0.79/0.85 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.79/0.85 inference(bind,[status(th)],[])).
% 0.79/0.85 tff(1460,plain,
% 0.79/0.85 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.85 inference(quant_intro,[status(thm)],[1459])).
% 0.79/0.85 tff(1461,plain,
% 0.79/0.85 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(1462,plain,
% 0.79/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp8) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.79/0.85 inference(bind,[status(th)],[])).
% 0.79/0.85 tff(1463,plain,
% 0.79/0.85 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.85 inference(quant_intro,[status(thm)],[1462])).
% 0.79/0.85 tff(1464,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 0.79/0.85 tff(1465,plain,
% 0.79/0.85 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.85 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 0.79/0.85 tff(1466,plain,
% 0.79/0.85 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.85 inference(modus_ponens,[status(thm)],[1465, 1461])).
% 0.79/0.85 tff(1467,plain,(
% 0.79/0.85 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.85 inference(skolemize,[status(sab)],[1466])).
% 0.79/0.85 tff(1468,plain,
% 0.79/0.85 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.79/0.85 inference(modus_ponens,[status(thm)],[1467, 1460])).
% 0.79/0.85 tff(1469,plain,
% 0.79/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c2_1(a2076)) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c2_1(a2076)) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(1470,plain,
% 0.79/0.85 ((hskp8 | (~ndr1_0) | (~c3_1(a2076)) | (~c2_1(a2076)) | (~c1_1(a2076)) | c1_1(a2068) | c2_1(a2068) | (~c3_1(a2068))) <=> (hskp8 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c2_1(a2076)) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(1471,plain,
% 0.79/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a2076)) | (~c2_1(a2076)) | (~c1_1(a2076)) | c1_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c2_1(a2076)) | (~c3_1(a2076)) | (~c1_1(a2076))))),
% 0.79/0.85 inference(monotonicity,[status(thm)],[1470])).
% 0.79/0.85 tff(1472,plain,
% 0.79/0.85 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a2076)) | (~c2_1(a2076)) | (~c1_1(a2076)) | c1_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c2_1(a2076)) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.79/0.85 inference(transitivity,[status(thm)],[1471, 1469])).
% 0.79/0.85 tff(1473,plain,
% 0.79/0.85 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a2076)) | (~c2_1(a2076)) | (~c1_1(a2076)) | c1_1(a2068) | c2_1(a2068) | (~c3_1(a2068)))),
% 0.79/0.85 inference(quant_inst,[status(thm)],[])).
% 0.79/0.85 tff(1474,plain,
% 0.79/0.85 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp8 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c2_1(a2076)) | (~c3_1(a2076)) | (~c1_1(a2076))),
% 0.79/0.85 inference(modus_ponens,[status(thm)],[1473, 1472])).
% 0.79/0.85 tff(1475,plain,
% 0.79/0.85 (hskp8 | (~c2_1(a2076))),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1474, 99, 716, 715, 746, 729, 1468, 1419])).
% 0.79/0.85 tff(1476,plain,
% 0.79/0.85 ($false),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1475, 1458, 159])).
% 0.79/0.85 tff(1477,plain,(hskp8 | (~c1_1(a2076)) | (~c3_1(a2076)) | c1_1(a2068) | (~c2_1(a2087)) | c1_1(a2087) | c3_1(a2087) | c0_1(a2076)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.85 tff(1478,plain,
% 0.79/0.85 (hskp8),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1477, 1419, 715, 716, 1456, 1455, 1454, 714])).
% 0.79/0.85 tff(1479,plain,
% 0.79/0.85 (~c0_1(a2082)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[173, 1478])).
% 0.79/0.85 tff(1480,plain,
% 0.79/0.85 (c2_1(a2082)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[184, 1478])).
% 0.79/0.85 tff(1481,plain,
% 0.79/0.85 (c1_1(a2082)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[195, 1478])).
% 0.79/0.85 tff(1482,plain,
% 0.79/0.85 (~c2_1(a2072)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[514, 99, 11, 1481, 1480, 1479, 413, 411, 508])).
% 0.79/0.85 tff(1483,plain,
% 0.79/0.85 (c0_1(a2087)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1037, 99, 11, 1456, 1481, 1480, 1454, 1479, 508])).
% 0.79/0.85 tff(1484,plain,
% 0.79/0.85 (hskp4 | c1_1(a2068)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[814, 99, 819, 904, 818, 808])).
% 0.79/0.85 tff(1485,plain,
% 0.79/0.85 (c1_1(a2068)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1484, 747])).
% 0.79/0.85 tff(1486,plain,
% 0.79/0.85 (hskp4 | c0_1(a2072) | (~c2_1(a2072))),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[466, 99, 412, 411, 259])).
% 0.79/0.85 tff(1487,plain,
% 0.79/0.85 (~c2_1(a2072)),
% 0.79/0.85 inference(unit_resolution,[status(thm)],[1486, 413, 747])).
% 0.79/0.85 tff(1488,plain,
% 0.79/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c2_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c2_1(a2072))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(1489,plain,
% 0.79/0.85 (((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072)) <=> (c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c2_1(a2072))),
% 0.79/0.85 inference(rewrite,[status(thm)],[])).
% 0.79/0.85 tff(1490,plain,
% 0.79/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c2_1(a2072)))),
% 0.79/0.85 inference(monotonicity,[status(thm)],[1489])).
% 0.79/0.85 tff(1491,plain,
% 0.79/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c2_1(a2072))),
% 0.79/0.86 inference(transitivity,[status(thm)],[1490, 1488])).
% 0.79/0.86 tff(1492,plain,
% 0.79/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2068) | c0_1(a2068) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2072) | c1_1(a2072) | c0_1(a2072))),
% 0.79/0.86 inference(quant_inst,[status(thm)],[])).
% 0.79/0.86 tff(1493,plain,
% 0.79/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | c2_1(a2072)),
% 0.79/0.86 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 0.79/0.86 tff(1494,plain,
% 0.79/0.86 ($false),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[1493, 99, 413, 412, 411, 904, 818, 410, 1487, 817])).
% 0.79/0.86 tff(1495,plain,(c0_1(a2072) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)) | hskp4), inference(lemma,lemma(discharge,[]))).
% 0.79/0.86 tff(1496,plain,
% 0.79/0.86 (c0_1(a2072)),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[1495, 1485, 411, 904, 818, 412, 747])).
% 0.79/0.86 tff(1497,plain,
% 0.79/0.86 (~hskp3),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[398, 1496])).
% 0.79/0.86 tff(1498,plain,
% 0.79/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~c0_1(a2072)) | c1_1(a2072) | c3_1(a2072) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | (~c0_1(a2072)) | c1_1(a2072) | c3_1(a2072) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)))),
% 0.79/0.86 inference(rewrite,[status(thm)],[])).
% 0.79/0.86 tff(1499,plain,
% 0.79/0.86 ((hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | (~c0_1(a2072))) <=> (hskp3 | (~c0_1(a2072)) | c1_1(a2072) | c3_1(a2072) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)))),
% 0.79/0.86 inference(rewrite,[status(thm)],[])).
% 0.79/0.86 tff(1500,plain,
% 0.79/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | (~c0_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~c0_1(a2072)) | c1_1(a2072) | c3_1(a2072) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068))))),
% 0.79/0.86 inference(monotonicity,[status(thm)],[1499])).
% 0.79/0.86 tff(1501,plain,
% 0.79/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | (~c0_1(a2072)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | (~c0_1(a2072)) | c1_1(a2072) | c3_1(a2072) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068)))),
% 0.79/0.86 inference(transitivity,[status(thm)],[1500, 1498])).
% 0.79/0.86 tff(1502,plain,
% 0.79/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2068) | (~c3_1(a2068)) | (~c1_1(a2068)) | c3_1(a2072) | c1_1(a2072) | (~c0_1(a2072)))),
% 0.79/0.86 inference(quant_inst,[status(thm)],[])).
% 0.79/0.86 tff(1503,plain,
% 0.79/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | (~c0_1(a2072)) | c1_1(a2072) | c3_1(a2072) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2068))),
% 0.79/0.86 inference(modus_ponens,[status(thm)],[1502, 1501])).
% 0.79/0.86 tff(1504,plain,
% 0.79/0.86 (hskp3 | (~c0_1(a2072)) | c1_1(a2072) | (~c1_1(a2068))),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[1503, 99, 819, 411, 818, 379])).
% 0.79/0.86 tff(1505,plain,
% 0.79/0.86 ($false),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[1504, 1497, 1496, 412, 1485])).
% 0.79/0.86 tff(1506,plain,(hskp4 | c1_1(a2072) | (~c3_1(a2068)) | c3_1(a2072) | c2_1(a2068) | c0_1(a2068)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.86 tff(1507,plain,
% 0.79/0.86 (hskp4),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[1506, 412, 746, 411, 729, 735])).
% 0.79/0.86 tff(1508,plain,
% 0.79/0.86 (c3_1(a2074)),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[284, 1507])).
% 0.79/0.86 tff(1509,plain,
% 0.79/0.86 (c1_1(a2074)),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[295, 1507])).
% 0.79/0.86 tff(1510,plain,
% 0.79/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.79/0.86 inference(rewrite,[status(thm)],[])).
% 0.79/0.86 tff(1511,plain,
% 0.79/0.86 (((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2074)) | (~c3_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087))) <=> (c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.79/0.86 inference(rewrite,[status(thm)],[])).
% 0.79/0.86 tff(1512,plain,
% 0.79/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2074)) | (~c3_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))))),
% 0.79/0.86 inference(monotonicity,[status(thm)],[1511])).
% 0.79/0.86 tff(1513,plain,
% 0.79/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2074)) | (~c3_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.79/0.86 inference(transitivity,[status(thm)],[1512, 1510])).
% 0.79/0.86 tff(1514,plain,
% 0.79/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2074)) | (~c3_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))),
% 0.79/0.86 inference(quant_inst,[status(thm)],[])).
% 0.79/0.86 tff(1515,plain,
% 0.79/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))),
% 0.79/0.86 inference(modus_ponens,[status(thm)],[1514, 1513])).
% 0.79/0.86 tff(1516,plain,
% 0.79/0.86 ((~c0_1(a2074)) | (~c0_1(a2087))),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[1515, 99, 1452, 1451, 1450, 1509, 1508, 1455, 1454, 344])).
% 0.79/0.86 tff(1517,plain,
% 0.79/0.86 (~c0_1(a2074)),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[1516, 1483])).
% 0.79/0.86 tff(1518,plain,
% 0.79/0.86 (~c2_1(a2074)),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[273, 1507])).
% 0.79/0.86 tff(1519,plain,
% 0.79/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.79/0.86 inference(rewrite,[status(thm)],[])).
% 0.79/0.86 tff(1520,plain,
% 0.79/0.86 (((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068)) <=> (c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.79/0.86 inference(rewrite,[status(thm)],[])).
% 0.79/0.86 tff(1521,plain,
% 0.79/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074)))),
% 0.79/0.86 inference(monotonicity,[status(thm)],[1520])).
% 0.79/0.86 tff(1522,plain,
% 0.79/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.79/0.86 inference(transitivity,[status(thm)],[1521, 1519])).
% 0.79/0.86 tff(1523,plain,
% 0.79/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2074) | c0_1(a2074) | (~c1_1(a2074)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))),
% 0.79/0.86 inference(quant_inst,[status(thm)],[])).
% 0.79/0.86 tff(1524,plain,
% 0.79/0.86 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2074) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | (~c1_1(a2074)) | c0_1(a2074)),
% 0.79/0.86 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 0.79/0.86 tff(1525,plain,
% 0.79/0.86 (c1_1(a2068) | c2_1(a2072) | c0_1(a2074)),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[1524, 99, 1509, 1518, 412, 411, 735, 729, 410])).
% 0.79/0.86 tff(1526,plain,
% 0.79/0.86 ($false),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[1525, 1517, 1482, 1419])).
% 0.79/0.86 tff(1527,plain,(c1_1(a2068) | c1_1(a2072) | c3_1(a2072) | hskp1 | c0_1(a2072) | (~c3_1(a2076)) | (~c1_1(a2076)) | c0_1(a2076)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.86 tff(1528,plain,
% 0.79/0.86 (c1_1(a2068)),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[1527, 11, 411, 412, 413, 715, 716, 714])).
% 0.79/0.86 tff(1529,plain,
% 0.79/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2087)))),
% 0.79/0.86 inference(rewrite,[status(thm)],[])).
% 0.79/0.86 tff(1530,plain,
% 0.79/0.86 ((hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068))) <=> (hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2087)))),
% 0.79/0.86 inference(rewrite,[status(thm)],[])).
% 0.79/0.86 tff(1531,plain,
% 0.79/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2087))))),
% 0.79/0.86 inference(monotonicity,[status(thm)],[1530])).
% 0.79/0.86 tff(1532,plain,
% 0.79/0.86 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2087)))),
% 0.79/0.86 inference(transitivity,[status(thm)],[1531, 1529])).
% 0.79/0.86 tff(1533,plain,
% 0.79/0.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | (hskp8 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c2_1(a2087)) | c0_1(a2068) | c2_1(a2068) | (~c1_1(a2068)))),
% 0.79/0.86 inference(quant_inst,[status(thm)],[])).
% 0.79/0.86 tff(1534,plain,
% 0.79/0.86 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c1_1(V)))) | hskp8 | c1_1(a2087) | c3_1(a2087) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c1_1(a2068)) | (~c2_1(a2087))),
% 0.79/0.86 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 0.79/0.86 tff(1535,plain,
% 0.79/0.86 (hskp8 | (~c1_1(a2068))),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[1534, 99, 1456, 1455, 1454, 735, 729, 313])).
% 0.79/0.86 tff(1536,plain,
% 0.79/0.86 (hskp8),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[1535, 1528])).
% 0.79/0.86 tff(1537,plain,
% 0.79/0.86 (~c0_1(a2082)),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[173, 1536])).
% 0.79/0.86 tff(1538,plain,
% 0.79/0.86 (c2_1(a2082)),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[184, 1536])).
% 0.79/0.86 tff(1539,plain,
% 0.79/0.86 (c1_1(a2082)),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[195, 1536])).
% 0.79/0.86 tff(1540,plain,
% 0.79/0.86 (~c2_1(a2072)),
% 0.79/0.86 inference(unit_resolution,[status(thm)],[514, 99, 11, 1539, 1538, 1537, 413, 411, 508])).
% 0.79/0.86 tff(1541,plain,
% 0.79/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 0.79/0.86 inference(bind,[status(th)],[])).
% 0.79/0.86 tff(1542,plain,
% 0.79/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.79/0.86 inference(quant_intro,[status(thm)],[1541])).
% 0.79/0.86 tff(1543,plain,
% 0.79/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.79/0.86 inference(rewrite,[status(thm)],[])).
% 0.79/0.86 tff(1544,plain,
% 0.79/0.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 0.79/0.86 inference(bind,[status(th)],[])).
% 0.79/0.86 tff(1545,plain,
% 0.79/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.79/0.86 inference(quant_intro,[status(thm)],[1544])).
% 0.79/0.86 tff(1546,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 0.79/0.86 tff(1547,plain,
% 0.79/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.79/0.86 inference(modus_ponens,[status(thm)],[1546, 1545])).
% 0.79/0.86 tff(1548,plain,
% 0.79/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.79/0.86 inference(modus_ponens,[status(thm)],[1547, 1543])).
% 0.79/0.86 tff(1549,plain,(
% 0.79/0.86 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.79/0.86 inference(skolemize,[status(sab)],[1548])).
% 0.79/0.86 tff(1550,plain,
% 0.79/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 0.79/0.86 inference(modus_ponens,[status(thm)],[1549, 1542])).
% 0.79/0.86 tff(1551,plain,
% 0.79/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2087)))),
% 0.79/0.86 inference(rewrite,[status(thm)],[])).
% 0.79/0.86 tff(1552,plain,
% 0.79/0.86 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c2_1(a2087)) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072)) <=> (c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2087)))),
% 0.79/0.86 inference(rewrite,[status(thm)],[])).
% 0.79/0.86 tff(1553,plain,
% 0.79/0.86 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c2_1(a2087)) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2087))))),
% 0.79/0.87 inference(monotonicity,[status(thm)],[1552])).
% 0.79/0.87 tff(1554,plain,
% 0.79/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c2_1(a2087)) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2087)))),
% 0.79/0.87 inference(transitivity,[status(thm)],[1553, 1551])).
% 0.79/0.87 tff(1555,plain,
% 0.79/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c3_1(a2087) | c1_1(a2087) | (~c2_1(a2087)) | c2_1(a2072) | c0_1(a2072) | c3_1(a2072))),
% 0.79/0.87 inference(quant_inst,[status(thm)],[])).
% 0.79/0.87 tff(1556,plain,
% 0.79/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a2087) | c3_1(a2087) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2087))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1555, 1554])).
% 0.79/0.87 tff(1557,plain,
% 0.79/0.87 ($false),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[1556, 99, 1456, 1509, 1508, 1455, 1454, 1518, 413, 411, 1550, 1540])).
% 0.79/0.87 tff(1558,plain,(hskp1 | c0_1(a2072) | c3_1(a2072) | c1_1(a2072) | (~c3_1(a2076)) | (~c1_1(a2076)) | c0_1(a2076)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.87 tff(1559,plain,
% 0.79/0.87 (hskp1),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[1558, 413, 411, 412, 675, 692, 681])).
% 0.79/0.87 tff(1560,plain,
% 0.79/0.87 (~c2_1(a2070)),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[561, 1559])).
% 0.79/0.87 tff(1561,plain,
% 0.79/0.87 (hskp4),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[1506, 412, 1079, 411, 1077, 1078])).
% 0.79/0.87 tff(1562,plain,
% 0.79/0.87 (~c2_1(a2074)),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[273, 1561])).
% 0.79/0.87 tff(1563,plain,
% 0.79/0.87 (c3_1(a2070)),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[536, 1559])).
% 0.79/0.87 tff(1564,plain,
% 0.79/0.87 (c0_1(a2070)),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[547, 1559])).
% 0.79/0.87 tff(1565,plain,
% 0.79/0.87 (c3_1(a2074)),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[284, 1561])).
% 0.79/0.87 tff(1566,plain,
% 0.79/0.87 (c1_1(a2074)),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[295, 1561])).
% 0.79/0.87 tff(1567,plain,
% 0.79/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.79/0.87 inference(rewrite,[status(thm)],[])).
% 0.79/0.87 tff(1568,plain,
% 0.79/0.87 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072))) <=> (c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.79/0.87 inference(rewrite,[status(thm)],[])).
% 0.79/0.87 tff(1569,plain,
% 0.79/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074))))),
% 0.79/0.87 inference(monotonicity,[status(thm)],[1568])).
% 0.79/0.87 tff(1570,plain,
% 0.79/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.79/0.87 inference(transitivity,[status(thm)],[1569, 1567])).
% 0.79/0.87 tff(1571,plain,
% 0.79/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))),
% 0.79/0.87 inference(quant_inst,[status(thm)],[])).
% 0.79/0.87 tff(1572,plain,
% 0.79/0.87 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a2074) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)) | (~c3_1(a2074)) | (~c1_1(a2074))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 0.79/0.87 tff(1573,plain,
% 0.79/0.87 (~c2_1(a2072)),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[1572, 99, 1566, 1565, 1564, 1563, 1562, 413, 411, 1560, 10])).
% 0.79/0.87 tff(1574,plain,
% 0.79/0.87 (c0_1(a2074)),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[439, 99, 1566, 1562, 413, 412, 411, 410, 1573])).
% 0.79/0.87 tff(1575,plain,
% 0.79/0.87 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))),
% 0.79/0.87 inference(bind,[status(th)],[])).
% 0.79/0.87 tff(1576,plain,
% 0.79/0.87 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.87 inference(quant_intro,[status(thm)],[1575])).
% 0.79/0.87 tff(1577,plain,
% 0.79/0.87 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.87 inference(rewrite,[status(thm)],[])).
% 0.79/0.87 tff(1578,plain,
% 0.79/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~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)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp16))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))))),
% 0.79/0.87 inference(bind,[status(th)],[])).
% 0.79/0.87 tff(1579,plain,
% 0.79/0.87 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.87 inference(quant_intro,[status(thm)],[1578])).
% 0.79/0.87 tff(1580,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 0.79/0.87 tff(1581,plain,
% 0.79/0.87 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1580, 1579])).
% 0.79/0.87 tff(1582,plain,
% 0.79/0.87 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1581, 1577])).
% 0.79/0.87 tff(1583,plain,(
% 0.79/0.87 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.87 inference(skolemize,[status(sab)],[1582])).
% 0.79/0.87 tff(1584,plain,
% 0.79/0.87 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1583, 1576])).
% 0.79/0.87 tff(1585,plain,
% 0.79/0.87 (~c1_1(a2068)),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[1493, 99, 413, 412, 411, 1078, 1077, 410, 1573])).
% 0.79/0.87 tff(1586,plain,
% 0.79/0.87 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 0.79/0.87 inference(bind,[status(th)],[])).
% 0.79/0.87 tff(1587,plain,
% 0.79/0.87 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.79/0.87 inference(quant_intro,[status(thm)],[1586])).
% 0.79/0.87 tff(1588,plain,
% 0.79/0.87 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.79/0.87 inference(rewrite,[status(thm)],[])).
% 0.79/0.87 tff(1589,plain,
% 0.79/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 0.79/0.87 inference(bind,[status(th)],[])).
% 0.79/0.87 tff(1590,plain,
% 0.79/0.87 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.79/0.87 inference(quant_intro,[status(thm)],[1589])).
% 0.79/0.87 tff(1591,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 0.79/0.87 tff(1592,plain,
% 0.79/0.87 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 0.79/0.87 tff(1593,plain,
% 0.79/0.87 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1592, 1588])).
% 0.79/0.87 tff(1594,plain,(
% 0.79/0.87 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.79/0.87 inference(skolemize,[status(sab)],[1593])).
% 0.79/0.87 tff(1595,plain,
% 0.79/0.87 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1594, 1587])).
% 0.79/0.87 tff(1596,plain,
% 0.79/0.87 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a2076) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2076)) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a2076) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.79/0.87 inference(rewrite,[status(thm)],[])).
% 0.79/0.87 tff(1597,plain,
% 0.79/0.87 ((hskp15 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2076) | (~c1_1(a2076)) | (~c3_1(a2076))) <=> (hskp15 | c0_1(a2076) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.79/0.87 inference(rewrite,[status(thm)],[])).
% 0.79/0.87 tff(1598,plain,
% 0.79/0.87 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2076) | (~c1_1(a2076)) | (~c3_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | c0_1(a2076) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2076)) | (~c1_1(a2076))))),
% 0.79/0.87 inference(monotonicity,[status(thm)],[1597])).
% 0.79/0.87 tff(1599,plain,
% 0.79/0.87 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2076) | (~c1_1(a2076)) | (~c3_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a2076) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2076)) | (~c1_1(a2076)))),
% 0.79/0.87 inference(transitivity,[status(thm)],[1598, 1596])).
% 0.79/0.87 tff(1600,plain,
% 0.79/0.87 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp15 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)) | c0_1(a2076) | (~c1_1(a2076)) | (~c3_1(a2076)))),
% 0.79/0.87 inference(quant_inst,[status(thm)],[])).
% 0.79/0.87 tff(1601,plain,
% 0.79/0.87 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp15 | c0_1(a2076) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2076)) | (~c1_1(a2076))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 0.79/0.87 tff(1602,plain,
% 0.79/0.87 (hskp15 | c1_1(a2068)),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[1601, 99, 692, 675, 1079, 681, 1077, 1595])).
% 0.79/0.87 tff(1603,plain,
% 0.79/0.87 (hskp15),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[1602, 1585])).
% 0.79/0.87 tff(1604,plain,
% 0.79/0.87 (((~hskp15) | (~c3_1(a2099))) <=> ((~hskp15) | (~c3_1(a2099)))),
% 0.79/0.87 inference(rewrite,[status(thm)],[])).
% 0.79/0.87 tff(1605,plain,
% 0.79/0.87 (((~c3_1(a2099)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a2099)))),
% 0.79/0.87 inference(rewrite,[status(thm)],[])).
% 0.79/0.87 tff(1606,axiom,((~c3_1(a2099)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 0.79/0.87 tff(1607,plain,
% 0.79/0.87 ((~hskp15) | (~c3_1(a2099))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1606, 1605])).
% 0.79/0.87 tff(1608,plain,
% 0.79/0.87 ((~hskp15) | (~c3_1(a2099))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1607, 1604])).
% 0.79/0.87 tff(1609,plain,
% 0.79/0.87 (~c3_1(a2099)),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[1608, 1603])).
% 0.79/0.87 tff(1610,plain,
% 0.79/0.87 (((~hskp15) | (~c2_1(a2099))) <=> ((~hskp15) | (~c2_1(a2099)))),
% 0.79/0.87 inference(rewrite,[status(thm)],[])).
% 0.79/0.87 tff(1611,plain,
% 0.79/0.87 (((~c2_1(a2099)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a2099)))),
% 0.79/0.87 inference(rewrite,[status(thm)],[])).
% 0.79/0.87 tff(1612,axiom,((~c2_1(a2099)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 0.79/0.87 tff(1613,plain,
% 0.79/0.87 ((~hskp15) | (~c2_1(a2099))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1612, 1611])).
% 0.79/0.87 tff(1614,plain,
% 0.79/0.87 ((~hskp15) | (~c2_1(a2099))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1613, 1610])).
% 0.79/0.87 tff(1615,plain,
% 0.79/0.87 (~c2_1(a2099)),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[1614, 1603])).
% 0.79/0.87 tff(1616,plain,
% 0.79/0.87 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.79/0.87 inference(rewrite,[status(thm)],[])).
% 0.79/0.87 tff(1617,plain,
% 0.79/0.87 ((hskp22 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074))) <=> (hskp22 | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.79/0.87 inference(rewrite,[status(thm)],[])).
% 0.79/0.87 tff(1618,plain,
% 0.79/0.87 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074))))),
% 0.79/0.87 inference(monotonicity,[status(thm)],[1617])).
% 0.79/0.87 tff(1619,plain,
% 0.79/0.87 (((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.79/0.87 inference(transitivity,[status(thm)],[1618, 1616])).
% 0.79/0.87 tff(1620,plain,
% 0.79/0.87 ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp22 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.79/0.87 inference(quant_inst,[status(thm)],[])).
% 0.79/0.87 tff(1621,plain,
% 0.79/0.87 ((~![U: $i] : (hskp22 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp22 | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074))),
% 0.79/0.87 inference(modus_ponens,[status(thm)],[1620, 1619])).
% 0.79/0.87 tff(1622,plain,
% 0.79/0.87 (hskp22 | (~c0_1(a2074))),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[1621, 99, 1566, 1562, 1131])).
% 0.79/0.87 tff(1623,plain,
% 0.79/0.87 (hskp22),
% 0.79/0.87 inference(unit_resolution,[status(thm)],[1622, 1574])).
% 0.79/0.87 tff(1624,plain,
% 0.88/0.87 (~c0_1(a2140)),
% 0.88/0.87 inference(unit_resolution,[status(thm)],[1145, 1623])).
% 0.88/0.87 tff(1625,plain,
% 0.88/0.87 (((~hskp15) | c0_1(a2099)) <=> ((~hskp15) | c0_1(a2099))),
% 0.88/0.87 inference(rewrite,[status(thm)],[])).
% 0.88/0.87 tff(1626,axiom,((~hskp15) | c0_1(a2099)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 0.88/0.87 tff(1627,plain,
% 0.88/0.87 ((~hskp15) | c0_1(a2099)),
% 0.88/0.87 inference(modus_ponens,[status(thm)],[1626, 1625])).
% 0.88/0.87 tff(1628,plain,
% 0.88/0.87 ((~hskp15) | c0_1(a2099)),
% 0.88/0.87 inference(modus_ponens,[status(thm)],[1627, 1625])).
% 0.88/0.87 tff(1629,plain,
% 0.88/0.87 ((~hskp15) | c0_1(a2099)),
% 0.88/0.87 inference(modus_ponens,[status(thm)],[1628, 1625])).
% 0.88/0.87 tff(1630,plain,
% 0.88/0.87 ((~hskp15) | c0_1(a2099)),
% 0.88/0.87 inference(modus_ponens,[status(thm)],[1629, 1625])).
% 0.88/0.87 tff(1631,plain,
% 0.88/0.87 ((~hskp15) | c0_1(a2099)),
% 0.88/0.87 inference(modus_ponens,[status(thm)],[1630, 1625])).
% 0.88/0.87 tff(1632,plain,
% 0.88/0.87 ((~hskp15) | c0_1(a2099)),
% 0.88/0.87 inference(modus_ponens,[status(thm)],[1631, 1625])).
% 0.88/0.87 tff(1633,plain,
% 0.88/0.87 ((~hskp15) | c0_1(a2099)),
% 0.88/0.87 inference(modus_ponens,[status(thm)],[1632, 1625])).
% 0.88/0.87 tff(1634,plain,
% 0.88/0.87 ((~hskp15) | c0_1(a2099)),
% 0.88/0.87 inference(modus_ponens,[status(thm)],[1633, 1625])).
% 0.88/0.87 tff(1635,plain,
% 0.88/0.87 (c0_1(a2099)),
% 0.88/0.87 inference(unit_resolution,[status(thm)],[1634, 1603])).
% 0.88/0.87 tff(1636,plain,
% 0.88/0.87 (c3_1(a2140)),
% 0.88/0.87 inference(unit_resolution,[status(thm)],[1156, 1623])).
% 0.88/0.87 tff(1637,plain,
% 0.88/0.87 (c2_1(a2140)),
% 0.88/0.87 inference(unit_resolution,[status(thm)],[1167, 1623])).
% 0.88/0.87 tff(1638,plain,
% 0.88/0.87 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a2140) | c2_1(a2099) | c3_1(a2099) | (~ndr1_0) | (~c0_1(a2099)) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a2140) | c2_1(a2099) | c3_1(a2099) | (~ndr1_0) | (~c0_1(a2099)) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.88/0.87 inference(rewrite,[status(thm)],[])).
% 0.88/0.87 tff(1639,plain,
% 0.88/0.87 ((hskp16 | (~ndr1_0) | c2_1(a2099) | c3_1(a2099) | (~c0_1(a2099)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140))) <=> (hskp16 | c0_1(a2140) | c2_1(a2099) | c3_1(a2099) | (~ndr1_0) | (~c0_1(a2099)) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.88/0.87 inference(rewrite,[status(thm)],[])).
% 0.88/0.87 tff(1640,plain,
% 0.88/0.87 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a2099) | c3_1(a2099) | (~c0_1(a2099)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | c0_1(a2140) | c2_1(a2099) | c3_1(a2099) | (~ndr1_0) | (~c0_1(a2099)) | (~c3_1(a2140)) | (~c2_1(a2140))))),
% 0.88/0.87 inference(monotonicity,[status(thm)],[1639])).
% 0.88/0.87 tff(1641,plain,
% 0.88/0.87 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a2099) | c3_1(a2099) | (~c0_1(a2099)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a2140) | c2_1(a2099) | c3_1(a2099) | (~ndr1_0) | (~c0_1(a2099)) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.88/0.87 inference(transitivity,[status(thm)],[1640, 1638])).
% 0.88/0.87 tff(1642,plain,
% 0.88/0.87 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c2_1(a2099) | c3_1(a2099) | (~c0_1(a2099)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.88/0.87 inference(quant_inst,[status(thm)],[])).
% 0.88/0.87 tff(1643,plain,
% 0.88/0.87 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp16 | c0_1(a2140) | c2_1(a2099) | c3_1(a2099) | (~ndr1_0) | (~c0_1(a2099)) | (~c3_1(a2140)) | (~c2_1(a2140))),
% 0.88/0.87 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 0.88/0.87 tff(1644,plain,
% 0.88/0.87 (hskp16),
% 0.88/0.87 inference(unit_resolution,[status(thm)],[1643, 99, 1637, 1636, 1635, 1624, 1615, 1609, 1584])).
% 0.88/0.87 tff(1645,plain,
% 0.88/0.87 (((~hskp16) | (~c1_1(a2104))) <=> ((~hskp16) | (~c1_1(a2104)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1646,plain,
% 0.88/0.88 (((~c1_1(a2104)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a2104)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1647,axiom,((~c1_1(a2104)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 0.88/0.88 tff(1648,plain,
% 0.88/0.88 ((~hskp16) | (~c1_1(a2104))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1647, 1646])).
% 0.88/0.88 tff(1649,plain,
% 0.88/0.88 ((~hskp16) | (~c1_1(a2104))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1648, 1645])).
% 0.88/0.88 tff(1650,plain,
% 0.88/0.88 (~c1_1(a2104)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1649, 1644])).
% 0.88/0.88 tff(1651,plain,
% 0.88/0.88 (((~hskp16) | (~c0_1(a2104))) <=> ((~hskp16) | (~c0_1(a2104)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1652,plain,
% 0.88/0.88 (((~c0_1(a2104)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a2104)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1653,axiom,((~c0_1(a2104)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 0.88/0.88 tff(1654,plain,
% 0.88/0.88 ((~hskp16) | (~c0_1(a2104))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1653, 1652])).
% 0.88/0.88 tff(1655,plain,
% 0.88/0.88 ((~hskp16) | (~c0_1(a2104))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1654, 1651])).
% 0.88/0.88 tff(1656,plain,
% 0.88/0.88 (~c0_1(a2104)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1655, 1644])).
% 0.88/0.88 tff(1657,plain,
% 0.88/0.88 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2104) | c1_1(a2104) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c2_1(a2104)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2104) | c1_1(a2104) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c2_1(a2104)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1658,plain,
% 0.88/0.88 ((hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2104) | c0_1(a2104) | (~c2_1(a2104))) <=> (hskp29 | c0_1(a2104) | c1_1(a2104) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c2_1(a2104)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1659,plain,
% 0.88/0.88 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2104) | c0_1(a2104) | (~c2_1(a2104)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2104) | c1_1(a2104) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c2_1(a2104))))),
% 0.88/0.88 inference(monotonicity,[status(thm)],[1658])).
% 0.88/0.88 tff(1660,plain,
% 0.88/0.88 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2104) | c0_1(a2104) | (~c2_1(a2104)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2104) | c1_1(a2104) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c2_1(a2104)))),
% 0.88/0.88 inference(transitivity,[status(thm)],[1659, 1657])).
% 0.88/0.88 tff(1661,plain,
% 0.88/0.88 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2104) | c0_1(a2104) | (~c2_1(a2104)))),
% 0.88/0.88 inference(quant_inst,[status(thm)],[])).
% 0.88/0.88 tff(1662,plain,
% 0.88/0.88 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2104) | c1_1(a2104) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c2_1(a2104))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 0.88/0.88 tff(1663,plain,
% 0.88/0.88 (~c2_1(a2104)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1662, 369, 99, 1566, 1656, 1650, 1562, 1405, 1574])).
% 0.88/0.88 tff(1664,plain,
% 0.88/0.88 (((~hskp16) | c3_1(a2104)) <=> ((~hskp16) | c3_1(a2104))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1665,axiom,((~hskp16) | c3_1(a2104)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 0.88/0.88 tff(1666,plain,
% 0.88/0.88 ((~hskp16) | c3_1(a2104)),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 0.88/0.88 tff(1667,plain,
% 0.88/0.88 ((~hskp16) | c3_1(a2104)),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1666, 1664])).
% 0.88/0.88 tff(1668,plain,
% 0.88/0.88 ((~hskp16) | c3_1(a2104)),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1667, 1664])).
% 0.88/0.88 tff(1669,plain,
% 0.88/0.88 ((~hskp16) | c3_1(a2104)),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1668, 1664])).
% 0.88/0.88 tff(1670,plain,
% 0.88/0.88 ((~hskp16) | c3_1(a2104)),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1669, 1664])).
% 0.88/0.88 tff(1671,plain,
% 0.88/0.88 ((~hskp16) | c3_1(a2104)),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1670, 1664])).
% 0.88/0.88 tff(1672,plain,
% 0.88/0.88 ((~hskp16) | c3_1(a2104)),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1671, 1664])).
% 0.88/0.88 tff(1673,plain,
% 0.88/0.88 ((~hskp16) | c3_1(a2104)),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1672, 1664])).
% 0.88/0.88 tff(1674,plain,
% 0.88/0.88 (c3_1(a2104)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1673, 1644])).
% 0.88/0.88 tff(1675,plain,
% 0.88/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | c2_1(a2076) | (~c1_1(a2076)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | c2_1(a2076) | (~c1_1(a2076)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1676,plain,
% 0.88/0.88 (((~ndr1_0) | c2_1(a2076) | c0_1(a2076) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068)) <=> (c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | c2_1(a2076) | (~c1_1(a2076)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1677,plain,
% 0.88/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2076) | c0_1(a2076) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | c2_1(a2076) | (~c1_1(a2076))))),
% 0.88/0.88 inference(monotonicity,[status(thm)],[1676])).
% 0.88/0.88 tff(1678,plain,
% 0.88/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2076) | c0_1(a2076) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | c2_1(a2076) | (~c1_1(a2076)))),
% 0.88/0.88 inference(transitivity,[status(thm)],[1677, 1675])).
% 0.88/0.88 tff(1679,plain,
% 0.88/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2076) | c0_1(a2076) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2068) | c1_1(a2068) | c0_1(a2068))),
% 0.88/0.88 inference(quant_inst,[status(thm)],[])).
% 0.88/0.88 tff(1680,plain,
% 0.88/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | c1_1(a2068) | c2_1(a2072) | c2_1(a2076) | (~c1_1(a2076))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 0.88/0.88 tff(1681,plain,
% 0.88/0.88 ($false),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1680, 99, 716, 714, 412, 411, 904, 818, 410, 400, 960, 1419])).
% 0.88/0.88 tff(1682,plain,(c2_1(a2076) | (~c1_1(a2076)) | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | c0_1(a2068) | c2_1(a2068) | c2_1(a2072) | c1_1(a2068)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.88 tff(1683,plain,
% 0.88/0.88 (c2_1(a2076)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1682, 1573, 681, 412, 411, 1078, 1077, 692, 1585])).
% 0.88/0.88 tff(1684,plain,
% 0.88/0.88 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))),
% 0.88/0.88 inference(bind,[status(th)],[])).
% 0.88/0.88 tff(1685,plain,
% 0.88/0.88 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.88/0.88 inference(quant_intro,[status(thm)],[1684])).
% 0.88/0.88 tff(1686,plain,
% 0.88/0.88 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1687,plain,
% 0.88/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(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))) | 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))), (((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))))),
% 0.88/0.88 inference(bind,[status(th)],[])).
% 0.88/0.88 tff(1688,plain,
% 0.88/0.88 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.88/0.88 inference(quant_intro,[status(thm)],[1687])).
% 0.88/0.88 tff(1689,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c2_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 0.88/0.88 tff(1690,plain,
% 0.88/0.88 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 0.88/0.88 tff(1691,plain,
% 0.88/0.88 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1690, 1686])).
% 0.88/0.88 tff(1692,plain,(
% 0.88/0.88 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.88/0.88 inference(skolemize,[status(sab)],[1691])).
% 0.88/0.88 tff(1693,plain,
% 0.88/0.88 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1692, 1685])).
% 0.88/0.88 tff(1694,plain,
% 0.88/0.88 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp14 | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2076)) | (~c1_1(a2076)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp14 | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2076)) | (~c1_1(a2076)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1695,plain,
% 0.88/0.88 ((hskp14 | (~ndr1_0) | c0_1(a2076) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072)) <=> (hskp14 | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2076)) | (~c1_1(a2076)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1696,plain,
% 0.88/0.88 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp14 | (~ndr1_0) | c0_1(a2076) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp14 | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2076)) | (~c1_1(a2076))))),
% 0.88/0.88 inference(monotonicity,[status(thm)],[1695])).
% 0.88/0.88 tff(1697,plain,
% 0.88/0.88 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp14 | (~ndr1_0) | c0_1(a2076) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp14 | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2076)) | (~c1_1(a2076)))),
% 0.88/0.88 inference(transitivity,[status(thm)],[1696, 1694])).
% 0.88/0.88 tff(1698,plain,
% 0.88/0.88 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | (hskp14 | (~ndr1_0) | c0_1(a2076) | (~c2_1(a2076)) | (~c1_1(a2076)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072))),
% 0.88/0.88 inference(quant_inst,[status(thm)],[])).
% 0.88/0.88 tff(1699,plain,
% 0.88/0.88 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V))) | hskp14 | c0_1(a2076) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2076)) | (~c1_1(a2076))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 0.88/0.88 tff(1700,plain,
% 0.88/0.88 (hskp14 | c1_1(a2072) | c2_1(a2072) | (~c2_1(a2076))),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1699, 99, 692, 681, 411, 1693])).
% 0.88/0.88 tff(1701,plain,
% 0.88/0.88 (hskp14),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1700, 1683, 412, 1573])).
% 0.88/0.88 tff(1702,plain,
% 0.88/0.88 (((~hskp14) | (~c0_1(a2097))) <=> ((~hskp14) | (~c0_1(a2097)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1703,plain,
% 0.88/0.88 (((~c0_1(a2097)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a2097)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1704,axiom,((~c0_1(a2097)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 0.88/0.88 tff(1705,plain,
% 0.88/0.88 ((~hskp14) | (~c0_1(a2097))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1704, 1703])).
% 0.88/0.88 tff(1706,plain,
% 0.88/0.88 ((~hskp14) | (~c0_1(a2097))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1705, 1702])).
% 0.88/0.88 tff(1707,plain,
% 0.88/0.88 (~c0_1(a2097)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1706, 1701])).
% 0.88/0.88 tff(1708,plain,
% 0.88/0.88 (((~hskp14) | (~c2_1(a2097))) <=> ((~hskp14) | (~c2_1(a2097)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1709,plain,
% 0.88/0.88 (((~c2_1(a2097)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a2097)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1710,axiom,((~c2_1(a2097)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 0.88/0.88 tff(1711,plain,
% 0.88/0.88 ((~hskp14) | (~c2_1(a2097))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1710, 1709])).
% 0.88/0.88 tff(1712,plain,
% 0.88/0.88 ((~hskp14) | (~c2_1(a2097))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1711, 1708])).
% 0.88/0.88 tff(1713,plain,
% 0.88/0.88 (~c2_1(a2097)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1712, 1701])).
% 0.88/0.88 tff(1714,plain,
% 0.88/0.88 (((~hskp14) | (~c1_1(a2097))) <=> ((~hskp14) | (~c1_1(a2097)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1715,plain,
% 0.88/0.88 (((~c1_1(a2097)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a2097)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1716,axiom,((~c1_1(a2097)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 0.88/0.88 tff(1717,plain,
% 0.88/0.88 ((~hskp14) | (~c1_1(a2097))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 0.88/0.88 tff(1718,plain,
% 0.88/0.88 ((~hskp14) | (~c1_1(a2097))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1717, 1714])).
% 0.88/0.88 tff(1719,plain,
% 0.88/0.88 (~c1_1(a2097)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1718, 1701])).
% 0.88/0.88 tff(1720,plain,
% 0.88/0.88 (hskp8 | (~c2_1(a2076))),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1474, 99, 692, 675, 1079, 1077, 1468, 1585])).
% 0.88/0.88 tff(1721,plain,
% 0.88/0.88 (hskp8),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1720, 1683])).
% 0.88/0.88 tff(1722,plain,
% 0.88/0.88 (~c0_1(a2082)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[173, 1721])).
% 0.88/0.88 tff(1723,plain,
% 0.88/0.88 (c2_1(a2082)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[184, 1721])).
% 0.88/0.88 tff(1724,plain,
% 0.88/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2082) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2082) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1725,plain,
% 0.88/0.88 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082))) <=> (c0_1(a2082) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1726,plain,
% 0.88/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2082) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c3_1(a2082) | (~c2_1(a2082))))),
% 0.88/0.88 inference(monotonicity,[status(thm)],[1725])).
% 0.88/0.88 tff(1727,plain,
% 0.88/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2082) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.88/0.88 inference(transitivity,[status(thm)],[1726, 1724])).
% 0.88/0.88 tff(1728,plain,
% 0.88/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2074) | (~c3_1(a2074)) | (~c0_1(a2074)) | c0_1(a2082) | c3_1(a2082) | (~c2_1(a2082)))),
% 0.88/0.88 inference(quant_inst,[status(thm)],[])).
% 0.88/0.88 tff(1729,plain,
% 0.88/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2082) | c2_1(a2074) | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c3_1(a2082) | (~c2_1(a2082))),
% 0.88/0.88 inference(modus_ponens,[status(thm)],[1728, 1727])).
% 0.88/0.88 tff(1730,plain,
% 0.88/0.88 (c3_1(a2082)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1729, 99, 1723, 1566, 1565, 1722, 1562, 10, 1574])).
% 0.88/0.88 tff(1731,plain,
% 0.88/0.88 (c1_1(a2082)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[195, 1721])).
% 0.88/0.88 tff(1732,assumption,(~c0_1(a2097)), introduced(assumption)).
% 0.88/0.88 tff(1733,assumption,(~c2_1(a2097)), introduced(assumption)).
% 0.88/0.88 tff(1734,assumption,(~c1_1(a2097)), introduced(assumption)).
% 0.88/0.88 tff(1735,plain,
% 0.88/0.88 (hskp4),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1506, 412, 819, 411, 818, 904])).
% 0.88/0.88 tff(1736,plain,
% 0.88/0.88 (c3_1(a2074)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[284, 1735])).
% 0.88/0.88 tff(1737,plain,
% 0.88/0.88 (~c2_1(a2074)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[273, 1735])).
% 0.88/0.88 tff(1738,plain,
% 0.88/0.88 (c1_1(a2074)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[295, 1735])).
% 0.88/0.88 tff(1739,plain,
% 0.88/0.88 (c0_1(a2074)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[439, 99, 1738, 1737, 413, 412, 411, 410, 400])).
% 0.88/0.88 tff(1740,plain,
% 0.88/0.88 (~c1_1(a2068)),
% 0.88/0.88 inference(unit_resolution,[status(thm)],[1493, 99, 413, 412, 411, 904, 818, 410, 400])).
% 0.88/0.88 tff(1741,plain,
% 0.88/0.88 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.88/0.88 inference(bind,[status(th)],[])).
% 0.88/0.88 tff(1742,plain,
% 0.88/0.88 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/0.88 inference(quant_intro,[status(thm)],[1741])).
% 0.88/0.88 tff(1743,plain,
% 0.88/0.88 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/0.88 inference(rewrite,[status(thm)],[])).
% 0.88/0.88 tff(1744,plain,
% 0.88/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.88/0.89 inference(bind,[status(th)],[])).
% 0.88/0.89 tff(1745,plain,
% 0.88/0.89 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/0.89 inference(quant_intro,[status(thm)],[1744])).
% 0.88/0.89 tff(1746,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 0.88/0.89 tff(1747,plain,
% 0.88/0.89 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 0.88/0.89 tff(1748,plain,
% 0.88/0.89 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1747, 1743])).
% 0.88/0.89 tff(1749,plain,(
% 0.88/0.89 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/0.89 inference(skolemize,[status(sab)],[1748])).
% 0.88/0.89 tff(1750,plain,
% 0.88/0.89 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1749, 1742])).
% 0.88/0.89 tff(1751,plain,
% 0.88/0.89 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1752,plain,
% 0.88/0.89 ((hskp7 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2068) | c0_1(a2068) | (~c3_1(a2068))) <=> (hskp7 | c0_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1753,plain,
% 0.88/0.89 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074))))),
% 0.88/0.89 inference(monotonicity,[status(thm)],[1752])).
% 0.88/0.89 tff(1754,plain,
% 0.88/0.89 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.88/0.89 inference(transitivity,[status(thm)],[1753, 1751])).
% 0.88/0.89 tff(1755,plain,
% 0.88/0.89 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))),
% 0.88/0.89 inference(quant_inst,[status(thm)],[])).
% 0.88/0.89 tff(1756,plain,
% 0.88/0.89 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c0_1(a2074))),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1755, 1754])).
% 0.88/0.89 tff(1757,plain,
% 0.88/0.89 (hskp7),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1756, 99, 1738, 1736, 819, 904, 1750, 1740, 1739])).
% 0.88/0.89 tff(1758,plain,
% 0.88/0.89 (((~hskp7) | c1_1(a2079)) <=> ((~hskp7) | c1_1(a2079))),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1759,axiom,((~hskp7) | c1_1(a2079)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 0.88/0.89 tff(1760,plain,
% 0.88/0.89 ((~hskp7) | c1_1(a2079)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 0.88/0.89 tff(1761,plain,
% 0.88/0.89 ((~hskp7) | c1_1(a2079)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1760, 1758])).
% 0.88/0.89 tff(1762,plain,
% 0.88/0.89 ((~hskp7) | c1_1(a2079)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1761, 1758])).
% 0.88/0.89 tff(1763,plain,
% 0.88/0.89 ((~hskp7) | c1_1(a2079)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1762, 1758])).
% 0.88/0.89 tff(1764,plain,
% 0.88/0.89 ((~hskp7) | c1_1(a2079)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1763, 1758])).
% 0.88/0.89 tff(1765,plain,
% 0.88/0.89 ((~hskp7) | c1_1(a2079)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1764, 1758])).
% 0.88/0.89 tff(1766,plain,
% 0.88/0.89 ((~hskp7) | c1_1(a2079)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1765, 1758])).
% 0.88/0.89 tff(1767,plain,
% 0.88/0.89 ((~hskp7) | c1_1(a2079)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1766, 1758])).
% 0.88/0.89 tff(1768,plain,
% 0.88/0.89 (c1_1(a2079)),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1767, 1757])).
% 0.88/0.89 tff(1769,plain,
% 0.88/0.89 (~c3_1(a2079)),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[857, 1757])).
% 0.88/0.89 tff(1770,assumption,(c0_1(a2074)), introduced(assumption)).
% 0.88/0.89 tff(1771,assumption,(c1_1(a2079)), introduced(assumption)).
% 0.88/0.89 tff(1772,plain,
% 0.88/0.89 (~c2_1(a2087)),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1556, 99, 1097, 1096, 241, 240, 1095, 413, 411, 1550, 400])).
% 0.88/0.89 tff(1773,plain,
% 0.88/0.89 (~hskp10),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[238, 1772])).
% 0.88/0.89 tff(1774,plain,
% 0.88/0.89 (hskp22 | (~c0_1(a2074))),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1621, 99, 1097, 1095, 1131])).
% 0.88/0.89 tff(1775,plain,
% 0.88/0.89 (hskp22),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1774, 1770])).
% 0.88/0.89 tff(1776,plain,
% 0.88/0.89 (~c0_1(a2140)),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1145, 1775])).
% 0.88/0.89 tff(1777,plain,
% 0.88/0.89 (c3_1(a2140)),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1156, 1775])).
% 0.88/0.89 tff(1778,plain,
% 0.88/0.89 (c2_1(a2140)),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1167, 1775])).
% 0.88/0.89 tff(1779,assumption,(~hskp12), introduced(assumption)).
% 0.88/0.89 tff(1780,plain,
% 0.88/0.89 ((hskp24 | hskp12 | hskp10) <=> (hskp24 | hskp12 | hskp10)),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1781,plain,
% 0.88/0.89 (((hskp24 | hskp12) | hskp10) <=> (hskp24 | hskp12 | hskp10)),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1782,plain,
% 0.88/0.89 ((hskp24 | hskp12) <=> (hskp24 | hskp12)),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1783,plain,
% 0.88/0.89 (((hskp24 | hskp12) | hskp10) <=> ((hskp24 | hskp12) | hskp10)),
% 0.88/0.89 inference(monotonicity,[status(thm)],[1782])).
% 0.88/0.89 tff(1784,plain,
% 0.88/0.89 (((hskp24 | hskp12) | hskp10) <=> (hskp24 | hskp12 | hskp10)),
% 0.88/0.89 inference(transitivity,[status(thm)],[1783, 1781])).
% 0.88/0.89 tff(1785,axiom,((hskp24 | hskp12) | hskp10), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 0.88/0.89 tff(1786,plain,
% 0.88/0.89 (hskp24 | hskp12 | hskp10),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1785, 1784])).
% 0.88/0.89 tff(1787,plain,
% 0.88/0.89 (hskp24 | hskp12 | hskp10),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1786, 1780])).
% 0.88/0.89 tff(1788,plain,
% 0.88/0.89 (hskp24 | hskp12 | hskp10),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1787, 1780])).
% 0.88/0.89 tff(1789,plain,
% 0.88/0.89 (hskp24 | hskp12 | hskp10),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1788, 1780])).
% 0.88/0.89 tff(1790,plain,
% 0.88/0.89 (hskp24 | hskp12 | hskp10),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1789, 1780])).
% 0.88/0.89 tff(1791,plain,
% 0.88/0.89 (hskp24 | hskp12 | hskp10),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1790, 1780])).
% 0.88/0.89 tff(1792,plain,
% 0.88/0.89 (hskp24 | hskp12 | hskp10),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1791, 1780])).
% 0.88/0.89 tff(1793,plain,
% 0.88/0.89 (hskp24 | hskp12 | hskp10),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1792, 1780])).
% 0.88/0.89 tff(1794,plain,
% 0.88/0.89 (hskp24),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1793, 1779, 33])).
% 0.88/0.89 tff(1795,plain,
% 0.88/0.89 (((~hskp24) | c2_1(a2160)) <=> ((~hskp24) | c2_1(a2160))),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1796,axiom,((~hskp24) | c2_1(a2160)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 0.88/0.89 tff(1797,plain,
% 0.88/0.89 ((~hskp24) | c2_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1796, 1795])).
% 0.88/0.89 tff(1798,plain,
% 0.88/0.89 ((~hskp24) | c2_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1797, 1795])).
% 0.88/0.89 tff(1799,plain,
% 0.88/0.89 ((~hskp24) | c2_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1798, 1795])).
% 0.88/0.89 tff(1800,plain,
% 0.88/0.89 ((~hskp24) | c2_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1799, 1795])).
% 0.88/0.89 tff(1801,plain,
% 0.88/0.89 ((~hskp24) | c2_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1800, 1795])).
% 0.88/0.89 tff(1802,plain,
% 0.88/0.89 ((~hskp24) | c2_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1801, 1795])).
% 0.88/0.89 tff(1803,plain,
% 0.88/0.89 ((~hskp24) | c2_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1802, 1795])).
% 0.88/0.89 tff(1804,plain,
% 0.88/0.89 ((~hskp24) | c2_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1803, 1795])).
% 0.88/0.89 tff(1805,plain,
% 0.88/0.89 (c2_1(a2160)),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1804, 1794])).
% 0.88/0.89 tff(1806,plain,
% 0.88/0.89 (((~hskp24) | c1_1(a2160)) <=> ((~hskp24) | c1_1(a2160))),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1807,axiom,((~hskp24) | c1_1(a2160)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 0.88/0.89 tff(1808,plain,
% 0.88/0.89 ((~hskp24) | c1_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1807, 1806])).
% 0.88/0.89 tff(1809,plain,
% 0.88/0.89 ((~hskp24) | c1_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1808, 1806])).
% 0.88/0.89 tff(1810,plain,
% 0.88/0.89 ((~hskp24) | c1_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1809, 1806])).
% 0.88/0.89 tff(1811,plain,
% 0.88/0.89 ((~hskp24) | c1_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1810, 1806])).
% 0.88/0.89 tff(1812,plain,
% 0.88/0.89 ((~hskp24) | c1_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1811, 1806])).
% 0.88/0.89 tff(1813,plain,
% 0.88/0.89 ((~hskp24) | c1_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1812, 1806])).
% 0.88/0.89 tff(1814,plain,
% 0.88/0.89 ((~hskp24) | c1_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1813, 1806])).
% 0.88/0.89 tff(1815,plain,
% 0.88/0.89 ((~hskp24) | c1_1(a2160)),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1814, 1806])).
% 0.88/0.89 tff(1816,plain,
% 0.88/0.89 (c1_1(a2160)),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1815, 1794])).
% 0.88/0.89 tff(1817,plain,
% 0.88/0.89 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)) | (~c1_1(a2160)) | (~c2_1(a2160)) | (~c0_1(a2160)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)) | (~c1_1(a2160)) | (~c2_1(a2160)) | (~c0_1(a2160)))),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1818,plain,
% 0.88/0.89 ((hskp26 | (~ndr1_0) | (~c2_1(a2160)) | (~c1_1(a2160)) | (~c0_1(a2160)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140))) <=> (hskp26 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)) | (~c1_1(a2160)) | (~c2_1(a2160)) | (~c0_1(a2160)))),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1819,plain,
% 0.88/0.89 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2160)) | (~c1_1(a2160)) | (~c0_1(a2160)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)) | (~c1_1(a2160)) | (~c2_1(a2160)) | (~c0_1(a2160))))),
% 0.88/0.89 inference(monotonicity,[status(thm)],[1818])).
% 0.88/0.89 tff(1820,plain,
% 0.88/0.89 (((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2160)) | (~c1_1(a2160)) | (~c0_1(a2160)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)) | (~c1_1(a2160)) | (~c2_1(a2160)) | (~c0_1(a2160)))),
% 0.88/0.89 inference(transitivity,[status(thm)],[1819, 1817])).
% 0.88/0.89 tff(1821,plain,
% 0.88/0.89 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | (hskp26 | (~ndr1_0) | (~c2_1(a2160)) | (~c1_1(a2160)) | (~c0_1(a2160)) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.88/0.89 inference(quant_inst,[status(thm)],[])).
% 0.88/0.89 tff(1822,plain,
% 0.88/0.89 ((~![V: $i, U: $i] : (hskp26 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))) | hskp26 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)) | (~c1_1(a2160)) | (~c2_1(a2160)) | (~c0_1(a2160))),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1821, 1820])).
% 0.88/0.89 tff(1823,plain,
% 0.88/0.89 (~c0_1(a2160)),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1822, 99, 549, 1816, 1805, 1778, 1777, 1776, 949])).
% 0.88/0.89 tff(1824,plain,
% 0.88/0.89 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.88/0.89 inference(bind,[status(th)],[])).
% 0.88/0.89 tff(1825,plain,
% 0.88/0.89 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.88/0.89 inference(quant_intro,[status(thm)],[1824])).
% 0.88/0.89 tff(1826,plain,
% 0.88/0.89 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1827,plain,
% 0.88/0.89 (^[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)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.88/0.89 inference(bind,[status(th)],[])).
% 0.88/0.89 tff(1828,plain,
% 0.88/0.89 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.88/0.89 inference(quant_intro,[status(thm)],[1827])).
% 0.88/0.89 tff(1829,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(U)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 0.88/0.89 tff(1830,plain,
% 0.88/0.89 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 0.88/0.89 tff(1831,plain,
% 0.88/0.89 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1830, 1826])).
% 0.88/0.89 tff(1832,plain,(
% 0.88/0.89 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.88/0.89 inference(skolemize,[status(sab)],[1831])).
% 0.88/0.89 tff(1833,plain,
% 0.88/0.89 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1832, 1825])).
% 0.88/0.89 tff(1834,plain,
% 0.88/0.89 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c3_1(a2079) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c1_1(a2079)) | (~c2_1(a2079)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c3_1(a2079) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c1_1(a2079)) | (~c2_1(a2079)))),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1835,plain,
% 0.88/0.89 ((hskp12 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c1_1(a2079)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074))) <=> (hskp12 | c3_1(a2079) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c1_1(a2079)) | (~c2_1(a2079)))),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1836,plain,
% 0.88/0.89 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c1_1(a2079)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | c3_1(a2079) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c1_1(a2079)) | (~c2_1(a2079))))),
% 0.88/0.89 inference(monotonicity,[status(thm)],[1835])).
% 0.88/0.89 tff(1837,plain,
% 0.88/0.89 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c1_1(a2079)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c3_1(a2079) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c1_1(a2079)) | (~c2_1(a2079)))),
% 0.88/0.89 inference(transitivity,[status(thm)],[1836, 1834])).
% 0.88/0.89 tff(1838,plain,
% 0.88/0.89 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp12 | (~ndr1_0) | c3_1(a2079) | (~c2_1(a2079)) | (~c1_1(a2079)) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)))),
% 0.88/0.89 inference(quant_inst,[status(thm)],[])).
% 0.88/0.89 tff(1839,plain,
% 0.88/0.89 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp12 | c3_1(a2079) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | (~c1_1(a2079)) | (~c2_1(a2079))),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1838, 1837])).
% 0.88/0.89 tff(1840,plain,
% 0.88/0.89 (hskp12 | (~c2_1(a2079))),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1839, 99, 1771, 1097, 889, 1095, 1833, 1770])).
% 0.88/0.89 tff(1841,plain,
% 0.88/0.89 (~c2_1(a2079)),
% 0.88/0.89 inference(unit_resolution,[status(thm)],[1840, 1779])).
% 0.88/0.89 tff(1842,plain,
% 0.88/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.88/0.89 inference(bind,[status(th)],[])).
% 0.88/0.89 tff(1843,plain,
% 0.88/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.88/0.89 inference(quant_intro,[status(thm)],[1842])).
% 0.88/0.89 tff(1844,plain,
% 0.88/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.88/0.89 inference(rewrite,[status(thm)],[])).
% 0.88/0.89 tff(1845,plain,
% 0.88/0.89 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.88/0.89 inference(bind,[status(th)],[])).
% 0.88/0.89 tff(1846,plain,
% 0.88/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.88/0.89 inference(quant_intro,[status(thm)],[1845])).
% 0.88/0.89 tff(1847,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 0.88/0.89 tff(1848,plain,
% 0.88/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1847, 1846])).
% 0.88/0.89 tff(1849,plain,
% 0.88/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1848, 1844])).
% 0.88/0.89 tff(1850,plain,(
% 0.88/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.88/0.89 inference(skolemize,[status(sab)],[1849])).
% 0.88/0.89 tff(1851,plain,
% 0.88/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.88/0.89 inference(modus_ponens,[status(thm)],[1850, 1843])).
% 0.88/0.89 tff(1852,plain,
% 0.88/0.89 (((~hskp24) | (~c3_1(a2160))) <=> ((~hskp24) | (~c3_1(a2160)))),
% 0.88/0.90 inference(rewrite,[status(thm)],[])).
% 0.88/0.90 tff(1853,plain,
% 0.88/0.90 (((~c3_1(a2160)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a2160)))),
% 0.88/0.90 inference(rewrite,[status(thm)],[])).
% 0.88/0.90 tff(1854,axiom,((~c3_1(a2160)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 0.88/0.90 tff(1855,plain,
% 0.88/0.90 ((~hskp24) | (~c3_1(a2160))),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 0.88/0.90 tff(1856,plain,
% 0.88/0.90 ((~hskp24) | (~c3_1(a2160))),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1855, 1852])).
% 0.88/0.90 tff(1857,plain,
% 0.88/0.90 (~c3_1(a2160)),
% 0.88/0.90 inference(unit_resolution,[status(thm)],[1856, 1794])).
% 0.88/0.90 tff(1858,plain,
% 0.88/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a2160) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2079)) | c2_1(a2079) | c0_1(a2160) | (~c1_1(a2160)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a2160) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2079)) | c2_1(a2079) | c0_1(a2160) | (~c1_1(a2160)))),
% 0.88/0.90 inference(rewrite,[status(thm)],[])).
% 0.88/0.90 tff(1859,plain,
% 0.88/0.90 (((~ndr1_0) | c2_1(a2079) | c3_1(a2079) | (~c1_1(a2079)) | c3_1(a2160) | c0_1(a2160) | (~c1_1(a2160)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068))) <=> (c3_1(a2160) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2079)) | c2_1(a2079) | c0_1(a2160) | (~c1_1(a2160)))),
% 0.88/0.90 inference(rewrite,[status(thm)],[])).
% 0.88/0.90 tff(1860,plain,
% 0.88/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2079) | c3_1(a2079) | (~c1_1(a2079)) | c3_1(a2160) | c0_1(a2160) | (~c1_1(a2160)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c3_1(a2160) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2079)) | c2_1(a2079) | c0_1(a2160) | (~c1_1(a2160))))),
% 0.88/0.90 inference(monotonicity,[status(thm)],[1859])).
% 0.88/0.90 tff(1861,plain,
% 0.88/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2079) | c3_1(a2079) | (~c1_1(a2079)) | c3_1(a2160) | c0_1(a2160) | (~c1_1(a2160)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a2160) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2079)) | c2_1(a2079) | c0_1(a2160) | (~c1_1(a2160)))),
% 0.88/0.90 inference(transitivity,[status(thm)],[1860, 1858])).
% 0.88/0.90 tff(1862,plain,
% 0.88/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2079) | c3_1(a2079) | (~c1_1(a2079)) | c3_1(a2160) | c0_1(a2160) | (~c1_1(a2160)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))),
% 0.88/0.90 inference(quant_inst,[status(thm)],[])).
% 0.88/0.90 tff(1863,plain,
% 0.88/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c3_1(a2160) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | (~c1_1(a2079)) | c2_1(a2079) | c0_1(a2160) | (~c1_1(a2160))),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 0.88/0.90 tff(1864,plain,
% 0.88/0.90 ($false),
% 0.88/0.90 inference(unit_resolution,[status(thm)],[1863, 99, 1816, 1771, 819, 1857, 889, 904, 818, 1851, 1841, 1823])).
% 0.88/0.90 tff(1865,plain,(hskp12 | (~c1_1(a2079)) | (~c3_1(a2068)) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | hskp26 | hskp10 | (~c1_1(a2074)) | c2_1(a2074) | (~c0_1(a2074))), inference(lemma,lemma(discharge,[]))).
% 0.88/0.90 tff(1866,plain,
% 0.88/0.90 (hskp12),
% 0.88/0.90 inference(unit_resolution,[status(thm)],[1865, 1773, 819, 889, 904, 818, 549, 1771, 1097, 1095, 1770])).
% 0.88/0.90 tff(1867,plain,
% 0.88/0.90 (((~hskp12) | (~c2_1(a2095))) <=> ((~hskp12) | (~c2_1(a2095)))),
% 0.88/0.90 inference(rewrite,[status(thm)],[])).
% 0.88/0.90 tff(1868,plain,
% 0.88/0.90 (((~c2_1(a2095)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a2095)))),
% 0.88/0.90 inference(rewrite,[status(thm)],[])).
% 0.88/0.90 tff(1869,axiom,((~c2_1(a2095)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 0.88/0.90 tff(1870,plain,
% 0.88/0.90 ((~hskp12) | (~c2_1(a2095))),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1869, 1868])).
% 0.88/0.90 tff(1871,plain,
% 0.88/0.90 ((~hskp12) | (~c2_1(a2095))),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1870, 1867])).
% 0.88/0.90 tff(1872,plain,
% 0.88/0.90 (~c2_1(a2095)),
% 0.88/0.90 inference(unit_resolution,[status(thm)],[1871, 1866])).
% 0.88/0.90 tff(1873,plain,
% 0.88/0.90 (((~hskp12) | (~c0_1(a2095))) <=> ((~hskp12) | (~c0_1(a2095)))),
% 0.88/0.90 inference(rewrite,[status(thm)],[])).
% 0.88/0.90 tff(1874,plain,
% 0.88/0.90 (((~c0_1(a2095)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a2095)))),
% 0.88/0.90 inference(rewrite,[status(thm)],[])).
% 0.88/0.90 tff(1875,axiom,((~c0_1(a2095)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 0.88/0.90 tff(1876,plain,
% 0.88/0.90 ((~hskp12) | (~c0_1(a2095))),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1875, 1874])).
% 0.88/0.90 tff(1877,plain,
% 0.88/0.90 ((~hskp12) | (~c0_1(a2095))),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1876, 1873])).
% 0.88/0.90 tff(1878,plain,
% 0.88/0.90 (~c0_1(a2095)),
% 0.88/0.90 inference(unit_resolution,[status(thm)],[1877, 1866])).
% 0.88/0.90 tff(1879,plain,
% 0.88/0.90 (((~hskp12) | c1_1(a2095)) <=> ((~hskp12) | c1_1(a2095))),
% 0.88/0.90 inference(rewrite,[status(thm)],[])).
% 0.88/0.90 tff(1880,axiom,((~hskp12) | c1_1(a2095)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 0.88/0.90 tff(1881,plain,
% 0.88/0.90 ((~hskp12) | c1_1(a2095)),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1880, 1879])).
% 0.88/0.90 tff(1882,plain,
% 0.88/0.90 ((~hskp12) | c1_1(a2095)),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1881, 1879])).
% 0.88/0.90 tff(1883,plain,
% 0.88/0.90 ((~hskp12) | c1_1(a2095)),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1882, 1879])).
% 0.88/0.90 tff(1884,plain,
% 0.88/0.90 ((~hskp12) | c1_1(a2095)),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1883, 1879])).
% 0.88/0.90 tff(1885,plain,
% 0.88/0.90 ((~hskp12) | c1_1(a2095)),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1884, 1879])).
% 0.88/0.90 tff(1886,plain,
% 0.88/0.90 ((~hskp12) | c1_1(a2095)),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1885, 1879])).
% 0.88/0.90 tff(1887,plain,
% 0.88/0.90 ((~hskp12) | c1_1(a2095)),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1886, 1879])).
% 0.88/0.90 tff(1888,plain,
% 0.88/0.90 ((~hskp12) | c1_1(a2095)),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1887, 1879])).
% 0.88/0.90 tff(1889,plain,
% 0.88/0.90 (c1_1(a2095)),
% 0.88/0.90 inference(unit_resolution,[status(thm)],[1888, 1866])).
% 0.88/0.90 tff(1890,plain,
% 0.88/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2095)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2095)))),
% 0.88/0.90 inference(rewrite,[status(thm)],[])).
% 0.88/0.90 tff(1891,plain,
% 0.88/0.90 (((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2087) | c1_1(a2087) | c2_1(a2087) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097)) <=> (c2_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2095)))),
% 0.88/0.90 inference(rewrite,[status(thm)],[])).
% 0.88/0.90 tff(1892,plain,
% 0.88/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2087) | c1_1(a2087) | c2_1(a2087) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2095))))),
% 0.88/0.90 inference(monotonicity,[status(thm)],[1891])).
% 0.88/0.90 tff(1893,plain,
% 0.88/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2087) | c1_1(a2087) | c2_1(a2087) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2095)))),
% 0.88/0.90 inference(transitivity,[status(thm)],[1892, 1890])).
% 0.88/0.90 tff(1894,plain,
% 0.88/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2087) | c1_1(a2087) | c2_1(a2087) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097))),
% 0.88/0.90 inference(quant_inst,[status(thm)],[])).
% 0.88/0.90 tff(1895,plain,
% 0.88/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2095))),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1894, 1893])).
% 0.88/0.90 tff(1896,plain,
% 0.88/0.90 ($false),
% 0.88/0.90 inference(unit_resolution,[status(thm)],[1895, 99, 1889, 1772, 1732, 1734, 1733, 1878, 1872, 241, 240, 410])).
% 0.88/0.90 tff(1897,plain,(c3_1(a2087) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c1_1(a2087) | (~c3_1(a2068)) | c3_1(a2079) | c0_1(a2068) | c2_1(a2068) | hskp26 | (~c1_1(a2079)) | (~c1_1(a2074)) | c2_1(a2074) | (~c0_1(a2074)) | (~c3_1(a2074)) | c0_1(a2072) | c3_1(a2072) | c2_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.88/0.90 tff(1898,plain,
% 0.88/0.90 (c3_1(a2087)),
% 0.88/0.90 inference(unit_resolution,[status(thm)],[1897, 241, 1734, 1733, 1732, 819, 1769, 904, 818, 549, 1768, 1738, 1737, 1739, 1736, 413, 411, 400])).
% 0.88/0.90 tff(1899,plain,
% 0.88/0.90 (((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))) <=> ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp26 | hskp18 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))),
% 0.88/0.90 inference(rewrite,[status(thm)],[])).
% 0.88/0.90 tff(1900,plain,
% 0.88/0.90 ((hskp26 | hskp18 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068))) <=> (hskp26 | hskp18 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))),
% 0.88/0.90 inference(rewrite,[status(thm)],[])).
% 0.88/0.90 tff(1901,plain,
% 0.88/0.90 (((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)))) <=> ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068)))),
% 0.88/0.90 inference(monotonicity,[status(thm)],[1900])).
% 0.88/0.90 tff(1902,plain,
% 0.88/0.90 (((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)))) <=> ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp26 | hskp18 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068))),
% 0.88/0.90 inference(transitivity,[status(thm)],[1901, 1899])).
% 0.88/0.90 tff(1903,plain,
% 0.88/0.90 ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp26 | hskp18 | (~ndr1_0) | c2_1(a2068) | c1_1(a2068) | (~c3_1(a2068)))),
% 0.88/0.90 inference(quant_inst,[status(thm)],[])).
% 0.88/0.90 tff(1904,plain,
% 0.88/0.90 ((~![U: $i] : (hskp26 | hskp18 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp26 | hskp18 | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c1_1(a2068)),
% 0.88/0.90 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 0.88/0.90 tff(1905,plain,
% 0.88/0.90 (hskp26 | hskp18 | c1_1(a2068)),
% 0.88/0.90 inference(unit_resolution,[status(thm)],[1904, 99, 819, 818, 1266])).
% 0.88/0.90 tff(1906,plain,
% 0.88/0.90 (hskp18),
% 0.88/0.90 inference(unit_resolution,[status(thm)],[1905, 549, 1740])).
% 0.90/0.90 tff(1907,plain,
% 0.90/0.90 (~c3_1(a2116)),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1280, 1906])).
% 0.90/0.90 tff(1908,plain,
% 0.90/0.90 (~c2_1(a2116)),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1286, 1906])).
% 0.90/0.90 tff(1909,plain,
% 0.90/0.90 (c1_1(a2116)),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1297, 1906])).
% 0.90/0.90 tff(1910,plain,
% 0.90/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a2116) | c3_1(a2116) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c0_1(a2116) | (~c1_1(a2116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2116) | c3_1(a2116) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c0_1(a2116) | (~c1_1(a2116)))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1911,plain,
% 0.90/0.90 (((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c3_1(a2116) | c0_1(a2116) | (~c1_1(a2116)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068))) <=> (c2_1(a2116) | c3_1(a2116) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c0_1(a2116) | (~c1_1(a2116)))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1912,plain,
% 0.90/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c3_1(a2116) | c0_1(a2116) | (~c1_1(a2116)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a2116) | c3_1(a2116) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c0_1(a2116) | (~c1_1(a2116))))),
% 0.90/0.90 inference(monotonicity,[status(thm)],[1911])).
% 0.90/0.90 tff(1913,plain,
% 0.90/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c3_1(a2116) | c0_1(a2116) | (~c1_1(a2116)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2116) | c3_1(a2116) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c0_1(a2116) | (~c1_1(a2116)))),
% 0.90/0.90 inference(transitivity,[status(thm)],[1912, 1910])).
% 0.90/0.90 tff(1914,plain,
% 0.90/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c3_1(a2116) | c0_1(a2116) | (~c1_1(a2116)) | c2_1(a2068) | c0_1(a2068) | (~c3_1(a2068)))),
% 0.90/0.90 inference(quant_inst,[status(thm)],[])).
% 0.90/0.90 tff(1915,plain,
% 0.90/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2116) | c3_1(a2116) | c0_1(a2068) | c2_1(a2068) | (~ndr1_0) | (~c3_1(a2068)) | c0_1(a2116) | (~c1_1(a2116))),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 0.90/0.90 tff(1916,plain,
% 0.90/0.90 (c0_1(a2116)),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1915, 99, 1909, 819, 1908, 1907, 904, 818, 1851])).
% 0.90/0.90 tff(1917,plain,
% 0.90/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | c0_1(a2082) | (~ndr1_0) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c0_1(a2087)) | (~c1_1(a2116)) | (~c0_1(a2116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | c0_1(a2082) | (~ndr1_0) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c0_1(a2087)) | (~c1_1(a2116)) | (~c0_1(a2116)))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1918,plain,
% 0.90/0.90 (((~ndr1_0) | c2_1(a2116) | (~c1_1(a2116)) | (~c0_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082))) <=> (c2_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | c0_1(a2082) | (~ndr1_0) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c0_1(a2087)) | (~c1_1(a2116)) | (~c0_1(a2116)))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1919,plain,
% 0.90/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2116) | (~c1_1(a2116)) | (~c0_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | c0_1(a2082) | (~ndr1_0) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c0_1(a2087)) | (~c1_1(a2116)) | (~c0_1(a2116))))),
% 0.90/0.90 inference(monotonicity,[status(thm)],[1918])).
% 0.90/0.90 tff(1920,plain,
% 0.90/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2116) | (~c1_1(a2116)) | (~c0_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | c0_1(a2082) | (~ndr1_0) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c0_1(a2087)) | (~c1_1(a2116)) | (~c0_1(a2116)))),
% 0.90/0.90 inference(transitivity,[status(thm)],[1919, 1917])).
% 0.90/0.90 tff(1921,plain,
% 0.90/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2116) | (~c1_1(a2116)) | (~c0_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c0_1(a2087)) | c0_1(a2082) | (~c3_1(a2082)) | (~c1_1(a2082)))),
% 0.90/0.90 inference(quant_inst,[status(thm)],[])).
% 0.90/0.90 tff(1922,plain,
% 0.90/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | c0_1(a2082) | (~ndr1_0) | (~c3_1(a2082)) | (~c1_1(a2082)) | (~c0_1(a2087)) | (~c1_1(a2116)) | (~c0_1(a2116))),
% 0.90/0.90 inference(modus_ponens,[status(thm)],[1921, 1920])).
% 0.90/0.90 tff(1923,plain,
% 0.90/0.90 ((~c3_1(a2087)) | (~c0_1(a2087))),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1922, 99, 1909, 1330, 1908, 241, 1320, 1090, 1318, 1916])).
% 0.90/0.90 tff(1924,plain,
% 0.90/0.90 (~c0_1(a2087)),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1923, 1898])).
% 0.90/0.90 tff(1925,plain,
% 0.90/0.90 (~hskp10),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[221, 1898])).
% 0.90/0.90 tff(1926,plain,
% 0.90/0.90 (hskp12),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1865, 1925, 819, 1769, 904, 818, 549, 1768, 1738, 1737, 1739])).
% 0.90/0.90 tff(1927,plain,
% 0.90/0.90 (~c2_1(a2095)),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1871, 1926])).
% 0.90/0.90 tff(1928,plain,
% 0.90/0.90 (~c0_1(a2095)),
% 0.90/0.90 inference(unit_resolution,[status(thm)],[1877, 1926])).
% 0.90/0.90 tff(1929,plain,
% 0.90/0.90 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.90/0.90 inference(bind,[status(th)],[])).
% 0.90/0.90 tff(1930,plain,
% 0.90/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.90/0.90 inference(quant_intro,[status(thm)],[1929])).
% 0.90/0.90 tff(1931,plain,
% 0.90/0.90 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.90/0.90 inference(rewrite,[status(thm)],[])).
% 0.90/0.90 tff(1932,plain,
% 0.90/0.90 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.90/0.91 inference(bind,[status(th)],[])).
% 0.90/0.91 tff(1933,plain,
% 0.90/0.91 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.90/0.91 inference(quant_intro,[status(thm)],[1932])).
% 0.90/0.91 tff(1934,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 0.90/0.91 tff(1935,plain,
% 0.90/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1934, 1933])).
% 0.90/0.91 tff(1936,plain,
% 0.90/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1935, 1931])).
% 0.90/0.91 tff(1937,plain,(
% 0.90/0.91 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.90/0.91 inference(skolemize,[status(sab)],[1936])).
% 0.90/0.91 tff(1938,plain,
% 0.90/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1937, 1930])).
% 0.90/0.91 tff(1939,plain,
% 0.90/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a2116) | c3_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)) | (~c1_1(a2116)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2116) | c3_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)) | (~c1_1(a2116)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1940,plain,
% 0.90/0.91 (((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)) | c1_1(a2087) | c0_1(a2087) | (~c3_1(a2087))) <=> (c2_1(a2116) | c3_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)) | (~c1_1(a2116)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1941,plain,
% 0.90/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)) | c1_1(a2087) | c0_1(a2087) | (~c3_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a2116) | c3_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)) | (~c1_1(a2116))))),
% 0.90/0.91 inference(monotonicity,[status(thm)],[1940])).
% 0.90/0.91 tff(1942,plain,
% 0.90/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)) | c1_1(a2087) | c0_1(a2087) | (~c3_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2116) | c3_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)) | (~c1_1(a2116)))),
% 0.90/0.91 inference(transitivity,[status(thm)],[1941, 1939])).
% 0.90/0.91 tff(1943,plain,
% 0.90/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a2116) | c3_1(a2116) | (~c1_1(a2116)) | c1_1(a2087) | (~c3_1(a2087)) | (~c2_1(a2087)) | c1_1(a2087) | c0_1(a2087) | (~c3_1(a2087)))),
% 0.90/0.91 inference(quant_inst,[status(thm)],[])).
% 0.90/0.91 tff(1944,plain,
% 0.90/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a2116) | c3_1(a2116) | c1_1(a2087) | (~c3_1(a2087)) | (~ndr1_0) | c0_1(a2087) | (~c2_1(a2087)) | (~c1_1(a2116))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1943, 1942])).
% 0.90/0.91 tff(1945,plain,
% 0.90/0.91 ((~c3_1(a2087)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1944, 99, 1909, 1908, 1907, 241, 1938])).
% 0.90/0.91 tff(1946,plain,
% 0.90/0.91 (~c2_1(a2087)),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1945, 1898, 1924])).
% 0.90/0.91 tff(1947,plain,
% 0.90/0.91 (c1_1(a2095)),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1888, 1926])).
% 0.90/0.91 tff(1948,plain,
% 0.90/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2087) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | c0_1(a2087) | (~c1_1(a2095)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2087) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | c0_1(a2087) | (~c1_1(a2095)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1949,plain,
% 0.90/0.91 (((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087)) <=> (c2_1(a2087) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | c0_1(a2087) | (~c1_1(a2095)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1950,plain,
% 0.90/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2087) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | c0_1(a2087) | (~c1_1(a2095))))),
% 0.90/0.91 inference(monotonicity,[status(thm)],[1949])).
% 0.90/0.91 tff(1951,plain,
% 0.90/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2087) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | c0_1(a2087) | (~c1_1(a2095)))),
% 0.90/0.91 inference(transitivity,[status(thm)],[1950, 1948])).
% 0.90/0.91 tff(1952,plain,
% 0.90/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2087) | c1_1(a2087) | c0_1(a2087))),
% 0.90/0.91 inference(quant_inst,[status(thm)],[])).
% 0.90/0.91 tff(1953,plain,
% 0.90/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2087) | c0_1(a2095) | c2_1(a2095) | c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | c0_1(a2087) | (~c1_1(a2095))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1952, 1951])).
% 0.90/0.91 tff(1954,plain,
% 0.90/0.91 ($false),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1953, 99, 1947, 1946, 1928, 1927, 241, 412, 411, 410, 400, 1924])).
% 0.90/0.91 tff(1955,plain,(c1_1(a2087) | c1_1(a2072) | c3_1(a2072) | c2_1(a2072) | (~c3_1(a2068)) | c0_1(a2068) | c2_1(a2068) | hskp26 | (~c1_1(a2082)) | c0_1(a2082) | (~c3_1(a2082)) | c1_1(a2097) | c2_1(a2097) | c0_1(a2097) | c0_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.91 tff(1956,plain,
% 0.90/0.91 (c1_1(a2087)),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1955, 549, 411, 400, 819, 904, 818, 412, 1330, 1320, 1318, 1734, 1733, 1732, 413])).
% 0.90/0.91 tff(1957,assumption,(hskp12), introduced(assumption)).
% 0.90/0.91 tff(1958,plain,
% 0.90/0.91 (~c2_1(a2095)),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1871, 1957])).
% 0.90/0.91 tff(1959,plain,
% 0.90/0.91 (~c0_1(a2095)),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1877, 1957])).
% 0.90/0.91 tff(1960,plain,
% 0.90/0.91 (c1_1(a2095)),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1888, 1957])).
% 0.90/0.91 tff(1961,plain,
% 0.90/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2095)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2095)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1962,plain,
% 0.90/0.91 (((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097)) <=> (c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2095)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1963,plain,
% 0.90/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2095))))),
% 0.90/0.91 inference(monotonicity,[status(thm)],[1962])).
% 0.90/0.91 tff(1964,plain,
% 0.90/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2095)))),
% 0.90/0.91 inference(transitivity,[status(thm)],[1963, 1961])).
% 0.90/0.91 tff(1965,plain,
% 0.90/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a2095) | c0_1(a2095) | (~c1_1(a2095)) | c3_1(a2072) | c1_1(a2072) | c2_1(a2072) | c2_1(a2097) | c1_1(a2097) | c0_1(a2097))),
% 0.90/0.91 inference(quant_inst,[status(thm)],[])).
% 0.90/0.91 tff(1966,plain,
% 0.90/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c3_1(V) | c1_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c0_1(a2095) | c2_1(a2095) | c1_1(a2072) | c3_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c1_1(a2095))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1965, 1964])).
% 0.90/0.91 tff(1967,plain,
% 0.90/0.91 ($false),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1966, 99, 1960, 1732, 1734, 1733, 1959, 1958, 412, 411, 410, 400])).
% 0.90/0.91 tff(1968,plain,((~hskp12) | c0_1(a2097) | c1_1(a2097) | c2_1(a2097) | c1_1(a2072) | c3_1(a2072) | c2_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.91 tff(1969,plain,
% 0.90/0.91 (~hskp12),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1968, 1732, 1734, 1733, 412, 411, 400])).
% 0.90/0.91 tff(1970,plain,
% 0.90/0.91 (hskp10),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1865, 549, 819, 1769, 904, 818, 1969, 1768, 1738, 1737, 1739])).
% 0.90/0.91 tff(1971,plain,
% 0.90/0.91 ($false),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[227, 1970, 1956])).
% 0.90/0.91 tff(1972,plain,(hskp26 | (~c3_1(a2068)) | c0_1(a2068) | c2_1(a2068) | c3_1(a2072) | c2_1(a2072) | c1_1(a2072) | (~c1_1(a2082)) | c0_1(a2082) | (~c3_1(a2082)) | c1_1(a2097) | c2_1(a2097) | c0_1(a2097) | c0_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.90/0.91 tff(1973,plain,
% 0.90/0.91 (hskp26),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1972, 1573, 1078, 1077, 411, 1079, 412, 1731, 1722, 1730, 1719, 1713, 1707, 413])).
% 0.90/0.91 tff(1974,plain,
% 0.90/0.91 (c3_1(a2069)),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[581, 1973])).
% 0.90/0.91 tff(1975,plain,
% 0.90/0.91 (c2_1(a2069)),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[592, 1973])).
% 0.90/0.91 tff(1976,plain,
% 0.90/0.91 (c0_1(a2069)),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[603, 1973])).
% 0.90/0.91 tff(1977,plain,
% 0.90/0.91 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a2104) | (~ndr1_0) | (~c3_1(a2104)) | c2_1(a2104) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2104) | (~ndr1_0) | (~c3_1(a2104)) | c2_1(a2104) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1978,plain,
% 0.90/0.91 ((hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2104) | c2_1(a2104) | (~c3_1(a2104))) <=> (hskp10 | c0_1(a2104) | (~ndr1_0) | (~c3_1(a2104)) | c2_1(a2104) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1979,plain,
% 0.90/0.91 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2104) | c2_1(a2104) | (~c3_1(a2104)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a2104) | (~ndr1_0) | (~c3_1(a2104)) | c2_1(a2104) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))))),
% 0.90/0.91 inference(monotonicity,[status(thm)],[1978])).
% 0.90/0.91 tff(1980,plain,
% 0.90/0.91 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2104) | c2_1(a2104) | (~c3_1(a2104)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2104) | (~ndr1_0) | (~c3_1(a2104)) | c2_1(a2104) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.90/0.91 inference(transitivity,[status(thm)],[1979, 1977])).
% 0.90/0.91 tff(1981,plain,
% 0.90/0.91 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c0_1(a2104) | c2_1(a2104) | (~c3_1(a2104)))),
% 0.90/0.91 inference(quant_inst,[status(thm)],[])).
% 0.90/0.91 tff(1982,plain,
% 0.90/0.91 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2104) | (~ndr1_0) | (~c3_1(a2104)) | c2_1(a2104) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 0.90/0.91 tff(1983,plain,
% 0.90/0.91 (hskp10),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[1982, 99, 1976, 1975, 1974, 1674, 1656, 703, 1663])).
% 0.90/0.91 tff(1984,plain,
% 0.90/0.91 (~c3_1(a2087)),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[221, 1983])).
% 0.90/0.91 tff(1985,plain,
% 0.90/0.91 (~c1_1(a2087)),
% 0.90/0.91 inference(unit_resolution,[status(thm)],[227, 1983])).
% 0.90/0.91 tff(1986,plain,
% 0.90/0.91 (^[U: $i] : refl((hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 0.90/0.91 inference(bind,[status(th)],[])).
% 0.90/0.91 tff(1987,plain,
% 0.90/0.91 (![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/0.91 inference(quant_intro,[status(thm)],[1986])).
% 0.90/0.91 tff(1988,plain,
% 0.90/0.91 (![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1989,plain,
% 0.90/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp29) <=> ((hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp29))), rewrite(((hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp29) <=> (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp29) <=> (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 0.90/0.91 inference(bind,[status(th)],[])).
% 0.90/0.91 tff(1990,plain,
% 0.90/0.91 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp29) <=> ![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/0.91 inference(quant_intro,[status(thm)],[1989])).
% 0.90/0.91 tff(1991,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 0.90/0.91 tff(1992,plain,
% 0.90/0.91 (![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 0.90/0.91 tff(1993,plain,
% 0.90/0.91 (![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1992, 1988])).
% 0.90/0.91 tff(1994,plain,(
% 0.90/0.91 ![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/0.91 inference(skolemize,[status(sab)],[1993])).
% 0.90/0.91 tff(1995,plain,
% 0.90/0.91 (![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 0.90/0.91 inference(modus_ponens,[status(thm)],[1994, 1987])).
% 0.90/0.91 tff(1996,plain,
% 0.90/0.91 (((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp27 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp29 | hskp27 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1997,plain,
% 0.90/0.91 ((hskp29 | hskp27 | (~ndr1_0) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140))) <=> (hskp29 | hskp27 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.90/0.91 inference(rewrite,[status(thm)],[])).
% 0.90/0.91 tff(1998,plain,
% 0.90/0.91 (((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp27 | (~ndr1_0) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp27 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140))))),
% 0.90/0.91 inference(monotonicity,[status(thm)],[1997])).
% 0.90/0.91 tff(1999,plain,
% 0.90/0.91 (((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp27 | (~ndr1_0) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))) <=> ((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp29 | hskp27 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.90/0.92 inference(transitivity,[status(thm)],[1998, 1996])).
% 0.90/0.92 tff(2000,plain,
% 0.90/0.92 ((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp29 | hskp27 | (~ndr1_0) | c0_1(a2140) | (~c3_1(a2140)) | (~c2_1(a2140)))),
% 0.90/0.92 inference(quant_inst,[status(thm)],[])).
% 0.90/0.92 tff(2001,plain,
% 0.90/0.92 ((~![U: $i] : (hskp29 | hskp27 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp29 | hskp27 | c0_1(a2140) | (~ndr1_0) | (~c3_1(a2140)) | (~c2_1(a2140))),
% 0.90/0.92 inference(modus_ponens,[status(thm)],[2000, 1999])).
% 0.90/0.92 tff(2002,plain,
% 0.90/0.92 (hskp27),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[2001, 369, 99, 1637, 1636, 1624, 1995])).
% 0.90/0.92 tff(2003,plain,
% 0.90/0.92 (c3_1(a2073)),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[632, 2002])).
% 0.90/0.92 tff(2004,plain,
% 0.90/0.92 (c1_1(a2073)),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[643, 2002])).
% 0.90/0.92 tff(2005,plain,
% 0.90/0.92 (c0_1(a2073)),
% 0.90/0.92 inference(unit_resolution,[status(thm)],[654, 2002])).
% 0.90/0.92 tff(2006,plain,
% 0.90/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(2007,plain,
% 0.90/0.92 (((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087))) <=> (c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.90/0.92 inference(rewrite,[status(thm)],[])).
% 0.90/0.92 tff(2008,plain,
% 0.90/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))))),
% 0.90/0.92 inference(monotonicity,[status(thm)],[2007])).
% 0.90/0.92 tff(2009,plain,
% 0.90/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.90/0.92 inference(transitivity,[status(thm)],[2008, 2006])).
% 0.90/0.92 tff(2010,plain,
% 0.90/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c1_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2073)) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))),
% 0.90/0.92 inference(quant_inst,[status(thm)],[])).
% 0.90/0.92 tff(2011,plain,
% 0.90/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c1_1(a2073)) | (~c0_1(a2073)) | (~c3_1(a2073)) | (~c0_1(a2087)) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2010, 2009])).
% 0.92/0.92 tff(2012,plain,
% 0.92/0.92 (~c0_1(a2087)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2011, 99, 2005, 2004, 2003, 1976, 1975, 1974, 1985, 1984, 344])).
% 0.92/0.92 tff(2013,plain,
% 0.92/0.92 (c2_1(a2087)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[238, 1983])).
% 0.92/0.92 tff(2014,plain,
% 0.92/0.92 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c1_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.92/0.92 inference(rewrite,[status(thm)],[])).
% 0.92/0.92 tff(2015,plain,
% 0.92/0.92 ((hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087))) <=> (hskp29 | c1_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.92/0.92 inference(rewrite,[status(thm)],[])).
% 0.92/0.92 tff(2016,plain,
% 0.92/0.92 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c1_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.92/0.92 inference(monotonicity,[status(thm)],[2015])).
% 0.92/0.92 tff(2017,plain,
% 0.92/0.92 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.92/0.92 inference(transitivity,[status(thm)],[2016, 2014])).
% 0.92/0.92 tff(2018,plain,
% 0.92/0.92 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c2_1(a2074) | (~c1_1(a2074)) | (~c0_1(a2074)) | c1_1(a2087) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.92/0.92 inference(quant_inst,[status(thm)],[])).
% 0.92/0.92 tff(2019,plain,
% 0.92/0.92 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2087) | c2_1(a2074) | (~ndr1_0) | (~c1_1(a2074)) | (~c0_1(a2074)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2018, 2017])).
% 0.92/0.92 tff(2020,plain,
% 0.92/0.92 ($false),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2019, 369, 99, 2013, 1566, 1985, 1562, 1405, 1574, 2012])).
% 0.92/0.92 tff(2021,plain,(c0_1(a2072) | hskp29 | c3_1(a2072) | c1_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.92/0.92 tff(2022,plain,
% 0.92/0.92 ($false),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2021, 1418, 1417, 1416, 369])).
% 0.92/0.92 tff(2023,plain,(hskp29), inference(lemma,lemma(discharge,[]))).
% 0.92/0.92 tff(2024,plain,
% 0.92/0.92 (((~hskp29) | c3_1(a2077)) <=> ((~hskp29) | c3_1(a2077))),
% 0.92/0.92 inference(rewrite,[status(thm)],[])).
% 0.92/0.92 tff(2025,axiom,((~hskp29) | c3_1(a2077)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 0.92/0.92 tff(2026,plain,
% 0.92/0.92 ((~hskp29) | c3_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 0.92/0.92 tff(2027,plain,
% 0.92/0.92 ((~hskp29) | c3_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2026, 2024])).
% 0.92/0.92 tff(2028,plain,
% 0.92/0.92 ((~hskp29) | c3_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2027, 2024])).
% 0.92/0.92 tff(2029,plain,
% 0.92/0.92 ((~hskp29) | c3_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2028, 2024])).
% 0.92/0.92 tff(2030,plain,
% 0.92/0.92 ((~hskp29) | c3_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2029, 2024])).
% 0.92/0.92 tff(2031,plain,
% 0.92/0.92 ((~hskp29) | c3_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2030, 2024])).
% 0.92/0.92 tff(2032,plain,
% 0.92/0.92 ((~hskp29) | c3_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2031, 2024])).
% 0.92/0.92 tff(2033,plain,
% 0.92/0.92 ((~hskp29) | c3_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2032, 2024])).
% 0.92/0.92 tff(2034,plain,
% 0.92/0.92 (c3_1(a2077)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2033, 2023])).
% 0.92/0.92 tff(2035,plain,
% 0.92/0.92 (((~hskp29) | c2_1(a2077)) <=> ((~hskp29) | c2_1(a2077))),
% 0.92/0.92 inference(rewrite,[status(thm)],[])).
% 0.92/0.92 tff(2036,axiom,((~hskp29) | c2_1(a2077)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 0.92/0.92 tff(2037,plain,
% 0.92/0.92 ((~hskp29) | c2_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 0.92/0.92 tff(2038,plain,
% 0.92/0.92 ((~hskp29) | c2_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2037, 2035])).
% 0.92/0.92 tff(2039,plain,
% 0.92/0.92 ((~hskp29) | c2_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2038, 2035])).
% 0.92/0.92 tff(2040,plain,
% 0.92/0.92 ((~hskp29) | c2_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2039, 2035])).
% 0.92/0.92 tff(2041,plain,
% 0.92/0.92 ((~hskp29) | c2_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2040, 2035])).
% 0.92/0.92 tff(2042,plain,
% 0.92/0.92 ((~hskp29) | c2_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2041, 2035])).
% 0.92/0.92 tff(2043,plain,
% 0.92/0.92 ((~hskp29) | c2_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2042, 2035])).
% 0.92/0.92 tff(2044,plain,
% 0.92/0.92 ((~hskp29) | c2_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2043, 2035])).
% 0.92/0.92 tff(2045,plain,
% 0.92/0.92 (c2_1(a2077)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2044, 2023])).
% 0.92/0.92 tff(2046,plain,
% 0.92/0.92 (((~hskp29) | c1_1(a2077)) <=> ((~hskp29) | c1_1(a2077))),
% 0.92/0.92 inference(rewrite,[status(thm)],[])).
% 0.92/0.92 tff(2047,axiom,((~hskp29) | c1_1(a2077)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 0.92/0.92 tff(2048,plain,
% 0.92/0.92 ((~hskp29) | c1_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 0.92/0.92 tff(2049,plain,
% 0.92/0.92 ((~hskp29) | c1_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2048, 2046])).
% 0.92/0.92 tff(2050,plain,
% 0.92/0.92 ((~hskp29) | c1_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2049, 2046])).
% 0.92/0.92 tff(2051,plain,
% 0.92/0.92 ((~hskp29) | c1_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2050, 2046])).
% 0.92/0.92 tff(2052,plain,
% 0.92/0.92 ((~hskp29) | c1_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2051, 2046])).
% 0.92/0.92 tff(2053,plain,
% 0.92/0.92 ((~hskp29) | c1_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2052, 2046])).
% 0.92/0.92 tff(2054,plain,
% 0.92/0.92 ((~hskp29) | c1_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2053, 2046])).
% 0.92/0.92 tff(2055,plain,
% 0.92/0.92 ((~hskp29) | c1_1(a2077)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2054, 2046])).
% 0.92/0.92 tff(2056,plain,
% 0.92/0.92 (c1_1(a2077)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2055, 2023])).
% 0.92/0.92 tff(2057,plain,
% 0.92/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2077)) | (~c3_1(a2077)) | (~c1_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2093)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2077)) | (~c3_1(a2077)) | (~c1_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2093)))),
% 0.92/0.92 inference(rewrite,[status(thm)],[])).
% 0.92/0.92 tff(2058,plain,
% 0.92/0.92 (((~ndr1_0) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2077)) | (~c1_1(a2077)) | (~c3_1(a2077)) | (~c0_1(a2077)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093))) <=> (c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2077)) | (~c3_1(a2077)) | (~c1_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2093)))),
% 0.92/0.92 inference(rewrite,[status(thm)],[])).
% 0.92/0.92 tff(2059,plain,
% 0.92/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2077)) | (~c1_1(a2077)) | (~c3_1(a2077)) | (~c0_1(a2077)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2077)) | (~c3_1(a2077)) | (~c1_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2093))))),
% 0.92/0.92 inference(monotonicity,[status(thm)],[2058])).
% 0.92/0.92 tff(2060,plain,
% 0.92/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2077)) | (~c1_1(a2077)) | (~c3_1(a2077)) | (~c0_1(a2077)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2077)) | (~c3_1(a2077)) | (~c1_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2093)))),
% 0.92/0.92 inference(transitivity,[status(thm)],[2059, 2057])).
% 0.92/0.92 tff(2061,plain,
% 0.92/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2077)) | (~c1_1(a2077)) | (~c3_1(a2077)) | (~c0_1(a2077)) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))),
% 0.92/0.92 inference(quant_inst,[status(thm)],[])).
% 0.92/0.92 tff(2062,plain,
% 0.92/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2077)) | (~c3_1(a2077)) | (~c1_1(a2077)) | (~c2_1(a2077)) | (~c0_1(a2093))),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2061, 2060])).
% 0.92/0.92 tff(2063,plain,
% 0.92/0.92 (~c0_1(a2077)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2062, 99, 2056, 2045, 2034, 368, 357, 351, 344])).
% 0.92/0.92 tff(2064,plain,
% 0.92/0.92 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c1_1(a2077)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c1_1(a2077)))),
% 0.92/0.92 inference(rewrite,[status(thm)],[])).
% 0.92/0.92 tff(2065,plain,
% 0.92/0.92 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c1_1(a2077)))),
% 0.92/0.92 inference(quant_inst,[status(thm)],[])).
% 0.92/0.92 tff(2066,plain,
% 0.92/0.92 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c1_1(a2077))),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2065, 2064])).
% 0.92/0.92 tff(2067,plain,
% 0.92/0.92 (hskp0 | c0_1(a2077)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2066, 99, 2056, 2034, 713])).
% 0.92/0.92 tff(2068,plain,
% 0.92/0.92 (hskp0),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2067, 2063])).
% 0.92/0.92 tff(2069,plain,
% 0.92/0.92 (c3_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[745, 2068])).
% 0.92/0.92 tff(2070,plain,
% 0.92/0.92 (~c2_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[728, 2068])).
% 0.92/0.92 tff(2071,plain,
% 0.92/0.92 (~c1_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[827, 693, 345, 2070, 2069])).
% 0.92/0.92 tff(2072,plain,
% 0.92/0.92 (~c0_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[734, 2068])).
% 0.92/0.92 tff(2073,plain,
% 0.92/0.92 (hskp4 | c1_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[814, 99, 2069, 2072, 2070, 808])).
% 0.92/0.92 tff(2074,plain,
% 0.92/0.92 (hskp4),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2073, 2071])).
% 0.92/0.92 tff(2075,plain,
% 0.92/0.92 (~c2_1(a2074)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[273, 2074])).
% 0.92/0.92 tff(2076,plain,
% 0.92/0.92 (c1_1(a2074)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[295, 2074])).
% 0.92/0.92 tff(2077,plain,
% 0.92/0.92 (c3_1(a2074)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[284, 2074])).
% 0.92/0.92 tff(2078,plain,
% 0.92/0.92 ($false),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1105, 2077, 2076, 693, 345, 2075])).
% 0.92/0.92 tff(2079,plain,(hskp3 | (~hskp11)), inference(lemma,lemma(discharge,[]))).
% 0.92/0.92 tff(2080,plain,
% 0.92/0.92 (hskp3),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2079, 334])).
% 0.92/0.92 tff(2081,plain,
% 0.92/0.92 (~c3_1(a2072)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[386, 2080])).
% 0.92/0.92 tff(2082,plain,
% 0.92/0.92 (~c1_1(a2072)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[392, 2080])).
% 0.92/0.92 tff(2083,plain,
% 0.92/0.92 (~c0_1(a2072)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[398, 2080])).
% 0.92/0.92 tff(2084,plain,
% 0.92/0.92 (~c3_1(a2093)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[350, 334])).
% 0.92/0.92 tff(2085,plain,
% 0.92/0.92 (~c1_1(a2093)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[356, 334])).
% 0.92/0.92 tff(2086,plain,
% 0.92/0.92 (c0_1(a2093)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[367, 334])).
% 0.92/0.92 tff(2087,plain,
% 0.92/0.92 (~c0_1(a2077)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2062, 99, 2056, 2045, 2034, 2086, 2085, 2084, 344])).
% 0.92/0.92 tff(2088,plain,
% 0.92/0.92 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2093)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2093)))),
% 0.92/0.92 inference(rewrite,[status(thm)],[])).
% 0.92/0.92 tff(2089,plain,
% 0.92/0.92 ((hskp8 | hskp1 | (~ndr1_0) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093))) <=> (hskp8 | hskp1 | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2093)))),
% 0.92/0.92 inference(rewrite,[status(thm)],[])).
% 0.92/0.92 tff(2090,plain,
% 0.92/0.92 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2093))))),
% 0.92/0.92 inference(monotonicity,[status(thm)],[2089])).
% 0.92/0.92 tff(2091,plain,
% 0.92/0.92 (((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))) <=> ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2093)))),
% 0.92/0.92 inference(transitivity,[status(thm)],[2090, 2088])).
% 0.92/0.92 tff(2092,plain,
% 0.92/0.92 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp8 | hskp1 | (~ndr1_0) | c1_1(a2093) | c3_1(a2093) | (~c0_1(a2093)))),
% 0.92/0.92 inference(quant_inst,[status(thm)],[])).
% 0.92/0.92 tff(2093,plain,
% 0.92/0.92 ((~![U: $i] : (hskp8 | hskp1 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp8 | hskp1 | c1_1(a2093) | c3_1(a2093) | (~ndr1_0) | (~c0_1(a2093))),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 0.92/0.92 tff(2094,plain,
% 0.92/0.92 (hskp8),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2093, 99, 11, 2086, 2085, 2084, 158])).
% 0.92/0.92 tff(2095,plain,
% 0.92/0.92 (~c0_1(a2082)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[173, 2094])).
% 0.92/0.92 tff(2096,plain,
% 0.92/0.92 (hskp0),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2067, 2087])).
% 0.92/0.92 tff(2097,plain,
% 0.92/0.92 (~c2_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[728, 2096])).
% 0.92/0.92 tff(2098,plain,
% 0.92/0.92 (~c0_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[734, 2096])).
% 0.92/0.92 tff(2099,plain,
% 0.92/0.92 (c3_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[745, 2096])).
% 0.92/0.92 tff(2100,plain,
% 0.92/0.92 (~c1_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[827, 2099, 334, 2097, 693])).
% 0.92/0.92 tff(2101,plain,
% 0.92/0.92 ($false),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1433, 99, 549, 11, 2098, 2097, 998, 2100])).
% 0.92/0.92 tff(2102,plain,(hskp1 | hskp26 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.92/0.92 tff(2103,plain,
% 0.92/0.92 (hskp1),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2102, 693, 549])).
% 0.92/0.92 tff(2104,plain,
% 0.92/0.92 (hskp5),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[570, 2103, 549])).
% 0.92/0.92 tff(2105,plain,
% 0.92/0.92 (~c0_1(a2076)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[680, 2104])).
% 0.92/0.92 tff(2106,plain,
% 0.92/0.92 (c1_1(a2076)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[691, 2104])).
% 0.92/0.92 tff(2107,plain,
% 0.92/0.92 (c3_1(a2076)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[674, 2104])).
% 0.92/0.92 tff(2108,plain,
% 0.92/0.92 ($false),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1357, 2107, 2106, 549, 693, 2105])).
% 0.92/0.92 tff(2109,plain,(hskp3 | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.92/0.92 tff(2110,plain,
% 0.92/0.92 (hskp3),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2109, 549])).
% 0.92/0.92 tff(2111,plain,
% 0.92/0.92 (~c3_1(a2072)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[386, 2110])).
% 0.92/0.92 tff(2112,plain,
% 0.92/0.92 (~c1_1(a2072)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[392, 2110])).
% 0.92/0.92 tff(2113,plain,
% 0.92/0.92 (~c0_1(a2072)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[398, 2110])).
% 0.92/0.92 tff(2114,plain,
% 0.92/0.92 (hskp1 | c2_1(a2072)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1425, 99, 549, 2113, 2112, 998])).
% 0.92/0.92 tff(2115,plain,
% 0.92/0.92 (c2_1(a2072)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2114, 11])).
% 0.92/0.92 tff(2116,assumption,(c2_1(a2072)), introduced(assumption)).
% 0.92/0.92 tff(2117,plain,
% 0.92/0.92 (hskp4 | (~c2_1(a2072))),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[466, 99, 413, 412, 411, 259])).
% 0.92/0.92 tff(2118,plain,
% 0.92/0.92 (hskp4),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2117, 2116])).
% 0.92/0.92 tff(2119,plain,
% 0.92/0.92 (~c2_1(a2074)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[273, 2118])).
% 0.92/0.92 tff(2120,plain,
% 0.92/0.92 (c3_1(a2074)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[284, 2118])).
% 0.92/0.92 tff(2121,plain,
% 0.92/0.92 (c1_1(a2074)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[295, 2118])).
% 0.92/0.92 tff(2122,plain,
% 0.92/0.92 (~c0_1(a2074)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[477, 99, 2121, 2120, 2119, 413, 411, 10, 2116])).
% 0.92/0.92 tff(2123,assumption,(~hskp0), introduced(assumption)).
% 0.92/0.92 tff(2124,plain,
% 0.92/0.92 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2074))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.92/0.92 inference(rewrite,[status(thm)],[])).
% 0.92/0.92 tff(2125,plain,
% 0.92/0.92 ((hskp0 | (~ndr1_0) | c0_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074))) <=> (hskp0 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.92/0.92 inference(rewrite,[status(thm)],[])).
% 0.92/0.92 tff(2126,plain,
% 0.92/0.92 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2074)))),
% 0.92/0.92 inference(monotonicity,[status(thm)],[2125])).
% 0.92/0.92 tff(2127,plain,
% 0.92/0.92 (((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)))) <=> ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2074))),
% 0.92/0.92 inference(transitivity,[status(thm)],[2126, 2124])).
% 0.92/0.92 tff(2128,plain,
% 0.92/0.92 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp0 | (~ndr1_0) | c0_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)))),
% 0.92/0.92 inference(quant_inst,[status(thm)],[])).
% 0.92/0.92 tff(2129,plain,
% 0.92/0.92 ((~![U: $i] : (hskp0 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp0 | (~ndr1_0) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2074)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 0.92/0.92 tff(2130,plain,
% 0.92/0.92 ($false),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2129, 99, 2123, 2121, 2120, 713, 2122])).
% 0.92/0.92 tff(2131,plain,((~c2_1(a2072)) | hskp0 | c0_1(a2072) | c3_1(a2072) | c1_1(a2072)), inference(lemma,lemma(discharge,[]))).
% 0.92/0.92 tff(2132,plain,
% 0.92/0.92 (hskp0),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2131, 2115, 2113, 2111, 2112])).
% 0.92/0.92 tff(2133,plain,
% 0.92/0.92 (~c0_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[734, 2132])).
% 0.92/0.92 tff(2134,plain,
% 0.92/0.92 (~c2_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[728, 2132])).
% 0.92/0.92 tff(2135,plain,
% 0.92/0.92 ($false),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1448, 2134, 2133, 549, 2113, 2112, 2111, 11])).
% 0.92/0.92 tff(2136,plain,(hskp1 | hskp26), inference(lemma,lemma(discharge,[]))).
% 0.92/0.92 tff(2137,plain,
% 0.92/0.92 (hskp1),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2136, 549])).
% 0.92/0.92 tff(2138,plain,
% 0.92/0.92 (~c2_1(a2070)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[561, 2137])).
% 0.92/0.92 tff(2139,plain,
% 0.92/0.92 (hskp5),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[570, 2137, 549])).
% 0.92/0.92 tff(2140,plain,
% 0.92/0.92 (~c0_1(a2076)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[680, 2139])).
% 0.92/0.92 tff(2141,plain,
% 0.92/0.92 (c3_1(a2076)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[674, 2139])).
% 0.92/0.92 tff(2142,plain,
% 0.92/0.92 (c1_1(a2076)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[691, 2139])).
% 0.92/0.92 tff(2143,plain,
% 0.92/0.92 (hskp0),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[722, 99, 2142, 2141, 2140, 713])).
% 0.92/0.92 tff(2144,plain,
% 0.92/0.92 (~c0_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[734, 2143])).
% 0.92/0.92 tff(2145,plain,
% 0.92/0.92 (~c2_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[728, 2143])).
% 0.92/0.92 tff(2146,plain,
% 0.92/0.92 (c3_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[745, 2143])).
% 0.92/0.92 tff(2147,plain,
% 0.92/0.92 (hskp4),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1506, 2146, 2112, 2111, 2145, 2144])).
% 0.92/0.92 tff(2148,plain,
% 0.92/0.92 (~c2_1(a2074)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[273, 2147])).
% 0.92/0.92 tff(2149,plain,
% 0.92/0.92 (c3_1(a2070)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[536, 2137])).
% 0.92/0.92 tff(2150,plain,
% 0.92/0.92 (c0_1(a2070)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[547, 2137])).
% 0.92/0.92 tff(2151,plain,
% 0.92/0.92 (c3_1(a2074)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[284, 2147])).
% 0.92/0.92 tff(2152,plain,
% 0.92/0.92 (c1_1(a2074)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[295, 2147])).
% 0.92/0.92 tff(2153,plain,
% 0.92/0.92 (~c2_1(a2072)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1572, 99, 2152, 2151, 2150, 2149, 2148, 2113, 2111, 2138, 10])).
% 0.92/0.92 tff(2154,plain,
% 0.92/0.92 (~c1_1(a2068)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1493, 99, 2113, 2112, 2111, 2144, 2145, 410, 2153])).
% 0.92/0.92 tff(2155,plain,
% 0.92/0.92 (c2_1(a2076)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1682, 2154, 2140, 2112, 2111, 2144, 2145, 2153, 2142])).
% 0.92/0.92 tff(2156,plain,
% 0.92/0.92 (hskp14 | c2_1(a2072) | (~c2_1(a2076))),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1699, 99, 2142, 2140, 2112, 2111, 1693])).
% 0.92/0.92 tff(2157,plain,
% 0.92/0.92 (hskp14),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[2156, 2155, 2153])).
% 0.92/0.92 tff(2158,plain,
% 0.92/0.92 (~c0_1(a2097)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1706, 2157])).
% 0.92/0.92 tff(2159,plain,
% 0.92/0.92 (c0_1(a2074)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[439, 99, 2152, 2148, 2113, 2112, 2111, 410, 2153])).
% 0.92/0.92 tff(2160,plain,
% 0.92/0.92 (hskp7),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1756, 99, 2152, 2151, 2146, 2144, 1750, 2154, 2159])).
% 0.92/0.92 tff(2161,plain,
% 0.92/0.92 (c1_1(a2079)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1767, 2160])).
% 0.92/0.92 tff(2162,plain,
% 0.92/0.92 (~c3_1(a2079)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[857, 2160])).
% 0.92/0.92 tff(2163,plain,
% 0.92/0.92 (~c1_1(a2097)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1718, 2157])).
% 0.92/0.92 tff(2164,plain,
% 0.92/0.92 (~c2_1(a2097)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1712, 2157])).
% 0.92/0.92 tff(2165,plain,
% 0.92/0.92 (~hskp12),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1968, 2163, 2153, 2164, 2112, 2111, 2158])).
% 0.92/0.92 tff(2166,plain,
% 0.92/0.92 (hskp10),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1865, 2162, 2146, 2159, 2144, 2145, 549, 2165, 2152, 2148, 2161])).
% 0.92/0.92 tff(2167,plain,
% 0.92/0.92 (~c1_1(a2087)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[227, 2166])).
% 0.92/0.92 tff(2168,plain,
% 0.92/0.92 (~c3_1(a2087)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[221, 2166])).
% 0.92/0.92 tff(2169,plain,
% 0.92/0.92 ($false),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1897, 2168, 2167, 2153, 2164, 2163, 2146, 2162, 2144, 2145, 549, 2161, 2152, 2148, 2159, 2151, 2113, 2111, 2158])).
% 0.92/0.92 tff(2170,plain,(hskp26), inference(lemma,lemma(discharge,[]))).
% 0.92/0.92 tff(2171,plain,
% 0.92/0.92 (c3_1(a2069)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[581, 2170])).
% 0.92/0.92 tff(2172,plain,
% 0.92/0.92 (c2_1(a2069)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[592, 2170])).
% 0.92/0.92 tff(2173,plain,
% 0.92/0.92 (c0_1(a2069)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[603, 2170])).
% 0.92/0.92 tff(2174,plain,
% 0.92/0.92 (hskp10),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1066, 99, 2173, 2172, 2171, 2099, 2098, 2097, 703])).
% 0.92/0.92 tff(2175,plain,
% 0.92/0.92 (~c3_1(a2087)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[221, 2174])).
% 0.92/0.92 tff(2176,plain,
% 0.92/0.92 (c2_1(a2082)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[184, 2094])).
% 0.92/0.92 tff(2177,plain,
% 0.92/0.92 (c1_1(a2082)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[195, 2094])).
% 0.92/0.92 tff(2178,plain,
% 0.92/0.92 (c2_1(a2087)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[238, 2174])).
% 0.92/0.92 tff(2179,plain,
% 0.92/0.92 (c0_1(a2087)),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[1037, 99, 11, 2178, 2177, 2176, 2175, 2095, 508])).
% 0.92/0.92 tff(2180,plain,
% 0.92/0.92 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.92/0.92 inference(bind,[status(th)],[])).
% 0.92/0.92 tff(2181,plain,
% 0.92/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/0.92 inference(quant_intro,[status(thm)],[2180])).
% 0.92/0.92 tff(2182,plain,
% 0.92/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/0.92 inference(rewrite,[status(thm)],[])).
% 0.92/0.92 tff(2183,plain,
% 0.92/0.92 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.92/0.93 inference(bind,[status(th)],[])).
% 0.92/0.93 tff(2184,plain,
% 0.92/0.93 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/0.93 inference(quant_intro,[status(thm)],[2183])).
% 0.92/0.93 tff(2185,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 0.92/0.93 tff(2186,plain,
% 0.92/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2185, 2184])).
% 0.92/0.93 tff(2187,plain,
% 0.92/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2186, 2182])).
% 0.92/0.93 tff(2188,plain,(
% 0.92/0.93 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/0.93 inference(skolemize,[status(sab)],[2187])).
% 0.92/0.93 tff(2189,plain,
% 0.92/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2188, 2181])).
% 0.92/0.93 tff(2190,plain,
% 0.92/0.93 (~c1_1(a2087)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[227, 2174])).
% 0.92/0.93 tff(2191,plain,
% 0.92/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2087) | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c2_1(a2072)) | (~c2_1(a2087)) | (~c0_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2087) | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c2_1(a2072)) | (~c2_1(a2087)) | (~c0_1(a2087)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2192,plain,
% 0.92/0.93 (((~ndr1_0) | c1_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072))) <=> (c1_1(a2087) | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c2_1(a2072)) | (~c2_1(a2087)) | (~c0_1(a2087)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2193,plain,
% 0.92/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a2087) | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c2_1(a2072)) | (~c2_1(a2087)) | (~c0_1(a2087))))),
% 0.92/0.93 inference(monotonicity,[status(thm)],[2192])).
% 0.92/0.93 tff(2194,plain,
% 0.92/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2087) | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c2_1(a2072)) | (~c2_1(a2087)) | (~c0_1(a2087)))),
% 0.92/0.93 inference(transitivity,[status(thm)],[2193, 2191])).
% 0.92/0.93 tff(2195,plain,
% 0.92/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | c1_1(a2072) | c0_1(a2072) | (~c2_1(a2072)))),
% 0.92/0.93 inference(quant_inst,[status(thm)],[])).
% 0.92/0.93 tff(2196,plain,
% 0.92/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a2087) | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c0_1(a2077) | (~c3_1(a2077)) | (~c2_1(a2077)) | (~c2_1(a2072)) | (~c2_1(a2087)) | (~c0_1(a2087))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 0.92/0.93 tff(2197,plain,
% 0.92/0.93 (~c2_1(a2072)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2196, 99, 2045, 2034, 2178, 2190, 2083, 2082, 2189, 2179, 2087])).
% 0.92/0.93 tff(2198,plain,
% 0.92/0.93 (hskp5),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[459, 2197, 2083, 2082, 2081])).
% 0.92/0.93 tff(2199,plain,
% 0.92/0.93 (~c0_1(a2076)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[680, 2198])).
% 0.92/0.93 tff(2200,plain,
% 0.92/0.93 (c1_1(a2076)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[691, 2198])).
% 0.92/0.93 tff(2201,plain,
% 0.92/0.93 (c3_1(a2076)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[674, 2198])).
% 0.92/0.93 tff(2202,plain,
% 0.92/0.93 ($false),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[1558, 2201, 2200, 11, 2083, 2081, 2082, 2199])).
% 0.92/0.93 tff(2203,plain,(hskp1), inference(lemma,lemma(discharge,[]))).
% 0.92/0.93 tff(2204,plain,
% 0.92/0.93 (~c2_1(a2070)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[561, 2203])).
% 0.92/0.93 tff(2205,plain,
% 0.92/0.93 (~hskp11),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2079, 693])).
% 0.92/0.93 tff(2206,assumption,(~c1_1(a2070)), introduced(assumption)).
% 0.92/0.93 tff(2207,plain,
% 0.92/0.93 (c3_1(a2070)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[536, 2203])).
% 0.92/0.93 tff(2208,plain,
% 0.92/0.93 (c0_1(a2070)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[547, 2203])).
% 0.92/0.93 tff(2209,plain,
% 0.92/0.93 (hskp11 | hskp10 | c1_1(a2070)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[1350, 99, 2208, 2207, 32])).
% 0.92/0.93 tff(2210,plain,
% 0.92/0.93 (hskp10),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2209, 2206, 22])).
% 0.92/0.93 tff(2211,plain,
% 0.92/0.93 (c2_1(a2087)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[238, 2210])).
% 0.92/0.93 tff(2212,plain,
% 0.92/0.93 (c1_1(a2070) | c0_1(a2087) | (~c2_1(a2087))),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[1394, 99, 22, 2208, 240, 2204, 1383])).
% 0.92/0.93 tff(2213,plain,
% 0.92/0.93 (c0_1(a2087)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2212, 2211, 2206])).
% 0.92/0.93 tff(2214,plain,
% 0.92/0.93 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2087)) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp4 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2087)) | (~c0_1(a2087)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2215,plain,
% 0.92/0.93 ((hskp4 | (~ndr1_0) | c3_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070))) <=> (hskp4 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2087)) | (~c0_1(a2087)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2216,plain,
% 0.92/0.93 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2087)) | (~c0_1(a2087))))),
% 0.92/0.93 inference(monotonicity,[status(thm)],[2215])).
% 0.92/0.93 tff(2217,plain,
% 0.92/0.93 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp4 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2087)) | (~c0_1(a2087)))),
% 0.92/0.93 inference(transitivity,[status(thm)],[2216, 2214])).
% 0.92/0.93 tff(2218,plain,
% 0.92/0.93 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | c3_1(a2087) | (~c2_1(a2087)) | (~c0_1(a2087)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)))),
% 0.92/0.93 inference(quant_inst,[status(thm)],[])).
% 0.92/0.93 tff(2219,plain,
% 0.92/0.93 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp4 | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2087)) | (~c0_1(a2087))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2218, 2217])).
% 0.92/0.93 tff(2220,plain,
% 0.92/0.93 (hskp4 | (~c2_1(a2087)) | (~c0_1(a2087))),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2219, 99, 2208, 2207, 240, 2204, 888])).
% 0.92/0.93 tff(2221,plain,
% 0.92/0.93 (hskp4),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2220, 2213, 2211])).
% 0.92/0.93 tff(2222,plain,
% 0.92/0.93 (~c2_1(a2074)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[273, 2221])).
% 0.92/0.93 tff(2223,plain,
% 0.92/0.93 (~c1_1(a2087)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[227, 2210])).
% 0.92/0.93 tff(2224,plain,
% 0.92/0.93 (^[U: $i] : refl((hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.92/0.93 inference(bind,[status(th)],[])).
% 0.92/0.93 tff(2225,plain,
% 0.92/0.93 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/0.93 inference(quant_intro,[status(thm)],[2224])).
% 0.92/0.93 tff(2226,plain,
% 0.92/0.93 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2227,plain,
% 0.92/0.93 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp19) <=> ((hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp19) <=> (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.92/0.93 inference(bind,[status(th)],[])).
% 0.92/0.93 tff(2228,plain,
% 0.92/0.93 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp19) <=> ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/0.93 inference(quant_intro,[status(thm)],[2227])).
% 0.92/0.93 tff(2229,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp11) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 0.92/0.93 tff(2230,plain,
% 0.92/0.93 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2229, 2228])).
% 0.92/0.93 tff(2231,plain,
% 0.92/0.93 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2230, 2226])).
% 0.92/0.93 tff(2232,plain,(
% 0.92/0.93 ![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/0.93 inference(skolemize,[status(sab)],[2231])).
% 0.92/0.93 tff(2233,plain,
% 0.92/0.93 (![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2232, 2225])).
% 0.92/0.93 tff(2234,plain,
% 0.92/0.93 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp11 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2235,plain,
% 0.92/0.93 ((hskp19 | hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087))) <=> (hskp19 | hskp11 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2236,plain,
% 0.92/0.93 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087))))),
% 0.92/0.93 inference(monotonicity,[status(thm)],[2235])).
% 0.92/0.93 tff(2237,plain,
% 0.92/0.93 (((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))) <=> ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp11 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087)))),
% 0.92/0.93 inference(transitivity,[status(thm)],[2236, 2234])).
% 0.92/0.93 tff(2238,plain,
% 0.92/0.93 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp19 | hskp11 | (~ndr1_0) | c1_1(a2087) | c3_1(a2087) | (~c0_1(a2087)))),
% 0.92/0.93 inference(quant_inst,[status(thm)],[])).
% 0.92/0.93 tff(2239,plain,
% 0.92/0.93 ((~![U: $i] : (hskp19 | hskp11 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c0_1(U)))) | hskp19 | hskp11 | c1_1(a2087) | c3_1(a2087) | (~ndr1_0) | (~c0_1(a2087))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2238, 2237])).
% 0.92/0.93 tff(2240,plain,
% 0.92/0.93 (hskp19 | c1_1(a2087) | (~c0_1(a2087))),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2239, 99, 22, 240, 2233])).
% 0.92/0.93 tff(2241,plain,
% 0.92/0.93 (hskp19),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2240, 2223, 2213])).
% 0.92/0.93 tff(2242,plain,
% 0.92/0.93 (((~hskp19) | (~c3_1(a2122))) <=> ((~hskp19) | (~c3_1(a2122)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2243,plain,
% 0.92/0.93 (((~c3_1(a2122)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a2122)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2244,axiom,((~c3_1(a2122)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 0.92/0.93 tff(2245,plain,
% 0.92/0.93 ((~hskp19) | (~c3_1(a2122))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2244, 2243])).
% 0.92/0.93 tff(2246,plain,
% 0.92/0.93 ((~hskp19) | (~c3_1(a2122))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2245, 2242])).
% 0.92/0.93 tff(2247,plain,
% 0.92/0.93 (~c3_1(a2122)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2246, 2241])).
% 0.92/0.93 tff(2248,plain,
% 0.92/0.93 (((~hskp19) | (~c0_1(a2122))) <=> ((~hskp19) | (~c0_1(a2122)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2249,plain,
% 0.92/0.93 (((~c0_1(a2122)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a2122)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2250,axiom,((~c0_1(a2122)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 0.92/0.93 tff(2251,plain,
% 0.92/0.93 ((~hskp19) | (~c0_1(a2122))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2250, 2249])).
% 0.92/0.93 tff(2252,plain,
% 0.92/0.93 ((~hskp19) | (~c0_1(a2122))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2251, 2248])).
% 0.92/0.93 tff(2253,plain,
% 0.92/0.93 (~c0_1(a2122)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2252, 2241])).
% 0.92/0.93 tff(2254,plain,
% 0.92/0.93 (c3_1(a2074)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[284, 2221])).
% 0.92/0.93 tff(2255,plain,
% 0.92/0.93 (c1_1(a2074)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[295, 2221])).
% 0.92/0.93 tff(2256,plain,
% 0.92/0.93 (((~hskp19) | c2_1(a2122)) <=> ((~hskp19) | c2_1(a2122))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2257,axiom,((~hskp19) | c2_1(a2122)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 0.92/0.93 tff(2258,plain,
% 0.92/0.93 ((~hskp19) | c2_1(a2122)),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 0.92/0.93 tff(2259,plain,
% 0.92/0.93 ((~hskp19) | c2_1(a2122)),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2258, 2256])).
% 0.92/0.93 tff(2260,plain,
% 0.92/0.93 ((~hskp19) | c2_1(a2122)),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2259, 2256])).
% 0.92/0.93 tff(2261,plain,
% 0.92/0.93 ((~hskp19) | c2_1(a2122)),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2260, 2256])).
% 0.92/0.93 tff(2262,plain,
% 0.92/0.93 ((~hskp19) | c2_1(a2122)),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2261, 2256])).
% 0.92/0.93 tff(2263,plain,
% 0.92/0.93 ((~hskp19) | c2_1(a2122)),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2262, 2256])).
% 0.92/0.93 tff(2264,plain,
% 0.92/0.93 ((~hskp19) | c2_1(a2122)),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2263, 2256])).
% 0.92/0.93 tff(2265,plain,
% 0.92/0.93 ((~hskp19) | c2_1(a2122)),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2264, 2256])).
% 0.92/0.93 tff(2266,plain,
% 0.92/0.93 (c2_1(a2122)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2265, 2241])).
% 0.92/0.93 tff(2267,plain,
% 0.92/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2122) | c3_1(a2122) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2122) | c3_1(a2122) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2122)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2268,plain,
% 0.92/0.93 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2122) | c3_1(a2122) | (~c2_1(a2122))) <=> (c0_1(a2122) | c3_1(a2122) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2122)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2269,plain,
% 0.92/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2122) | c3_1(a2122) | (~c2_1(a2122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2122) | c3_1(a2122) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2122))))),
% 0.92/0.93 inference(monotonicity,[status(thm)],[2268])).
% 0.92/0.93 tff(2270,plain,
% 0.92/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2122) | c3_1(a2122) | (~c2_1(a2122)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2122) | c3_1(a2122) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2122)))),
% 0.92/0.93 inference(transitivity,[status(thm)],[2269, 2267])).
% 0.92/0.93 tff(2271,plain,
% 0.92/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2122) | c3_1(a2122) | (~c2_1(a2122)))),
% 0.92/0.93 inference(quant_inst,[status(thm)],[])).
% 0.92/0.93 tff(2272,plain,
% 0.92/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2122) | c3_1(a2122) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | (~c2_1(a2122))),
% 0.92/0.93 inference(modus_ponens,[status(thm)],[2271, 2270])).
% 0.92/0.93 tff(2273,plain,
% 0.92/0.93 ($false),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2272, 99, 2266, 2255, 2254, 2208, 2207, 2253, 2247, 2222, 2204, 10])).
% 0.92/0.93 tff(2274,plain,(c1_1(a2070) | c3_1(a2087) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.92/0.93 tff(2275,plain,
% 0.92/0.93 (c3_1(a2087)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2274, 2206, 22])).
% 0.92/0.93 tff(2276,plain,
% 0.92/0.93 ($false),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[221, 2275, 2210])).
% 0.92/0.93 tff(2277,plain,(c1_1(a2070) | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.92/0.93 tff(2278,plain,
% 0.92/0.93 (c1_1(a2070)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2277, 2205])).
% 0.92/0.93 tff(2279,plain,
% 0.92/0.93 (hskp5 | (~c1_1(a2070))),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[568, 99, 2208, 2207, 2204, 450])).
% 0.92/0.93 tff(2280,plain,
% 0.92/0.93 (hskp5),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2279, 2278])).
% 0.92/0.93 tff(2281,plain,
% 0.92/0.93 (~c0_1(a2076)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[680, 2280])).
% 0.92/0.93 tff(2282,plain,
% 0.92/0.93 (c3_1(a2076)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[674, 2280])).
% 0.92/0.93 tff(2283,plain,
% 0.92/0.93 (c1_1(a2076)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[691, 2280])).
% 0.92/0.93 tff(2284,plain,
% 0.92/0.93 (c1_1(a2070)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2274, 240, 2205])).
% 0.92/0.93 tff(2285,plain,
% 0.92/0.93 (hskp5),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2279, 2284])).
% 0.92/0.93 tff(2286,plain,
% 0.92/0.93 (c3_1(a2076)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[674, 2285])).
% 0.92/0.93 tff(2287,plain,
% 0.92/0.93 (c1_1(a2076)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[691, 2285])).
% 0.92/0.93 tff(2288,plain,
% 0.92/0.93 (hskp0 | (~c3_1(a2076)) | (~c1_1(a2076))),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[722, 99, 714, 713])).
% 0.92/0.93 tff(2289,plain,
% 0.92/0.93 (hskp0),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[2288, 2287, 2286])).
% 0.92/0.93 tff(2290,plain,
% 0.92/0.93 (~c0_1(a2068)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[734, 2289])).
% 0.92/0.93 tff(2291,plain,
% 0.92/0.93 (c3_1(a2068)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[745, 2289])).
% 0.92/0.93 tff(2292,plain,
% 0.92/0.93 (hskp10),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[1066, 99, 2173, 2172, 2171, 2291, 2290, 818, 703])).
% 0.92/0.93 tff(2293,plain,
% 0.92/0.93 (~c1_1(a2087)),
% 0.92/0.93 inference(unit_resolution,[status(thm)],[227, 2292])).
% 0.92/0.93 tff(2294,plain,
% 0.92/0.93 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2087)))),
% 0.92/0.93 inference(rewrite,[status(thm)],[])).
% 0.92/0.93 tff(2295,plain,
% 0.92/0.93 ((hskp3 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087))) <=> (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2087)))),
% 0.92/0.94 inference(rewrite,[status(thm)],[])).
% 0.92/0.94 tff(2296,plain,
% 0.92/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2087))))),
% 0.92/0.94 inference(monotonicity,[status(thm)],[2295])).
% 0.92/0.94 tff(2297,plain,
% 0.92/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2087)))),
% 0.92/0.94 inference(transitivity,[status(thm)],[2296, 2294])).
% 0.92/0.94 tff(2298,plain,
% 0.92/0.94 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp3 | (~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c3_1(a2087) | c1_1(a2087) | (~c0_1(a2087)))),
% 0.92/0.94 inference(quant_inst,[status(thm)],[])).
% 0.92/0.94 tff(2299,plain,
% 0.92/0.94 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp3 | c1_1(a2087) | c3_1(a2087) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2087))),
% 0.92/0.94 inference(modus_ponens,[status(thm)],[2298, 2297])).
% 0.92/0.94 tff(2300,plain,
% 0.92/0.94 (c1_1(a2087) | (~c1_1(a2070)) | (~c0_1(a2087))),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2299, 99, 693, 2207, 240, 2204, 379])).
% 0.92/0.94 tff(2301,plain,
% 0.92/0.94 (~c0_1(a2087)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2300, 2293, 2284])).
% 0.92/0.94 tff(2302,plain,
% 0.92/0.94 (hskp4),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[1073, 2287, 693, 714, 2286])).
% 0.92/0.94 tff(2303,plain,
% 0.92/0.94 (~c2_1(a2074)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[273, 2302])).
% 0.92/0.94 tff(2304,plain,
% 0.92/0.94 (c3_1(a2074)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[284, 2302])).
% 0.92/0.94 tff(2305,plain,
% 0.92/0.94 (c1_1(a2074)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[295, 2302])).
% 0.92/0.94 tff(2306,plain,
% 0.92/0.94 (c2_1(a2087)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[238, 2292])).
% 0.92/0.94 tff(2307,plain,
% 0.92/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a2087) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a2087) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.92/0.94 inference(rewrite,[status(thm)],[])).
% 0.92/0.94 tff(2308,plain,
% 0.92/0.94 (((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087))) <=> (c3_1(a2087) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.92/0.94 inference(rewrite,[status(thm)],[])).
% 0.92/0.94 tff(2309,plain,
% 0.92/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a2087) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2087) | (~c2_1(a2087))))),
% 0.92/0.94 inference(monotonicity,[status(thm)],[2308])).
% 0.92/0.94 tff(2310,plain,
% 0.92/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a2087) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2087) | (~c2_1(a2087)))),
% 0.92/0.94 inference(transitivity,[status(thm)],[2309, 2307])).
% 0.92/0.94 tff(2311,plain,
% 0.92/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2074) | (~c3_1(a2074)) | (~c1_1(a2074)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2087) | c3_1(a2087) | (~c2_1(a2087)))),
% 0.92/0.94 inference(quant_inst,[status(thm)],[])).
% 0.92/0.94 tff(2312,plain,
% 0.92/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a2087) | c2_1(a2074) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c0_1(a2070)) | (~c3_1(a2074)) | (~c1_1(a2074)) | c0_1(a2087) | (~c2_1(a2087))),
% 0.92/0.94 inference(modus_ponens,[status(thm)],[2311, 2310])).
% 0.92/0.94 tff(2313,plain,
% 0.92/0.94 ($false),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2312, 99, 2306, 2305, 2304, 2208, 2207, 240, 2303, 2204, 10, 2301])).
% 0.92/0.94 tff(2314,plain,(c3_1(a2087) | hskp3 | c2_1(a2068) | c0_1(a2076)), inference(lemma,lemma(discharge,[]))).
% 0.92/0.94 tff(2315,plain,
% 0.92/0.94 (c3_1(a2087)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2314, 714, 818, 693])).
% 0.92/0.94 tff(2316,plain,
% 0.92/0.94 (~hskp10),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[221, 2315])).
% 0.92/0.94 tff(2317,plain,
% 0.92/0.94 (c1_1(a2070)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2209, 2316, 2205])).
% 0.92/0.94 tff(2318,plain,
% 0.92/0.94 (hskp5),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2279, 2317])).
% 0.92/0.94 tff(2319,plain,
% 0.92/0.94 (c3_1(a2076)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[674, 2318])).
% 0.92/0.94 tff(2320,plain,
% 0.92/0.94 (c1_1(a2076)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[691, 2318])).
% 0.92/0.94 tff(2321,plain,
% 0.92/0.94 (hskp0),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2288, 2320, 2319])).
% 0.92/0.94 tff(2322,plain,
% 0.92/0.94 (~c0_1(a2068)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[734, 2321])).
% 0.92/0.94 tff(2323,plain,
% 0.92/0.94 (c3_1(a2068)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[745, 2321])).
% 0.92/0.94 tff(2324,plain,
% 0.92/0.94 ($false),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[1066, 99, 2316, 2173, 2172, 2171, 2323, 2322, 818, 703])).
% 0.92/0.94 tff(2325,plain,(c0_1(a2076) | c2_1(a2068) | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.92/0.94 tff(2326,plain,
% 0.92/0.94 (c2_1(a2068)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2325, 2281, 693])).
% 0.92/0.94 tff(2327,plain,
% 0.92/0.94 (~hskp0),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[728, 2326])).
% 0.92/0.94 tff(2328,plain,
% 0.92/0.94 ($false),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[722, 99, 2327, 2283, 2282, 2281, 713])).
% 0.92/0.94 tff(2329,plain,(hskp3), inference(lemma,lemma(discharge,[]))).
% 0.92/0.94 tff(2330,plain,
% 0.92/0.94 (~c3_1(a2072)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[386, 2329])).
% 0.92/0.94 tff(2331,plain,
% 0.92/0.94 (~c0_1(a2072)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[398, 2329])).
% 0.92/0.94 tff(2332,plain,
% 0.92/0.94 (c1_1(a2070)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2277, 22])).
% 0.92/0.94 tff(2333,plain,
% 0.92/0.94 (hskp5),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2279, 2332])).
% 0.92/0.94 tff(2334,plain,
% 0.92/0.94 (c1_1(a2076)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[691, 2333])).
% 0.92/0.94 tff(2335,plain,
% 0.92/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)))),
% 0.92/0.94 inference(rewrite,[status(thm)],[])).
% 0.92/0.94 tff(2336,plain,
% 0.92/0.94 (((~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072))) <=> (c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)))),
% 0.92/0.94 inference(rewrite,[status(thm)],[])).
% 0.92/0.94 tff(2337,plain,
% 0.92/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | (c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072))))),
% 0.92/0.94 inference(monotonicity,[status(thm)],[2336])).
% 0.92/0.94 tff(2338,plain,
% 0.92/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072)))),
% 0.92/0.94 inference(transitivity,[status(thm)],[2337, 2335])).
% 0.92/0.94 tff(2339,plain,
% 0.92/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a2070) | (~c3_1(a2070)) | (~c1_1(a2070)) | c2_1(a2070) | (~c3_1(a2070)) | (~c0_1(a2070)) | c0_1(a2072) | c3_1(a2072) | (~c2_1(a2072)))),
% 0.92/0.94 inference(quant_inst,[status(thm)],[])).
% 0.92/0.94 tff(2340,plain,
% 0.92/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c2_1(W)))) | c0_1(a2072) | c3_1(a2072) | c2_1(a2070) | (~ndr1_0) | (~c3_1(a2070)) | (~c1_1(a2070)) | (~c0_1(a2070)) | (~c2_1(a2072))),
% 0.92/0.94 inference(modus_ponens,[status(thm)],[2339, 2338])).
% 0.92/0.94 tff(2341,plain,
% 0.92/0.94 ((~c1_1(a2070)) | (~c2_1(a2072))),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2340, 99, 2208, 2207, 2331, 2330, 2204, 10])).
% 0.92/0.94 tff(2342,plain,
% 0.92/0.94 (~c2_1(a2072)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2341, 2332])).
% 0.92/0.94 tff(2343,plain,
% 0.92/0.94 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 0.92/0.94 inference(bind,[status(th)],[])).
% 0.92/0.94 tff(2344,plain,
% 0.92/0.94 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.92/0.94 inference(quant_intro,[status(thm)],[2343])).
% 0.92/0.94 tff(2345,plain,
% 0.92/0.94 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.92/0.94 inference(rewrite,[status(thm)],[])).
% 0.92/0.94 tff(2346,plain,
% 0.92/0.94 (^[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)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 0.92/0.94 inference(bind,[status(th)],[])).
% 0.92/0.94 tff(2347,plain,
% 0.92/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.92/0.94 inference(quant_intro,[status(thm)],[2346])).
% 0.92/0.94 tff(2348,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 0.92/0.94 tff(2349,plain,
% 0.92/0.94 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.92/0.94 inference(modus_ponens,[status(thm)],[2348, 2347])).
% 0.92/0.94 tff(2350,plain,
% 0.92/0.94 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.92/0.94 inference(modus_ponens,[status(thm)],[2349, 2345])).
% 0.92/0.94 tff(2351,plain,(
% 0.92/0.94 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.92/0.94 inference(skolemize,[status(sab)],[2350])).
% 0.92/0.94 tff(2352,plain,
% 0.92/0.94 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.92/0.94 inference(modus_ponens,[status(thm)],[2351, 2344])).
% 0.92/0.94 tff(2353,plain,
% 0.92/0.94 (~c1_1(a2072)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[392, 2329])).
% 0.92/0.94 tff(2354,plain,
% 0.92/0.94 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.92/0.94 inference(rewrite,[status(thm)],[])).
% 0.92/0.94 tff(2355,plain,
% 0.92/0.94 ((hskp0 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c1_1(a2072) | c0_1(a2072) | c2_1(a2072)) <=> (hskp0 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.92/0.94 inference(rewrite,[status(thm)],[])).
% 0.92/0.94 tff(2356,plain,
% 0.92/0.94 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c1_1(a2072) | c0_1(a2072) | c2_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))))),
% 0.92/0.94 inference(monotonicity,[status(thm)],[2355])).
% 0.92/0.94 tff(2357,plain,
% 0.92/0.94 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c1_1(a2072) | c0_1(a2072) | c2_1(a2072))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069)))),
% 0.92/0.94 inference(transitivity,[status(thm)],[2356, 2354])).
% 0.92/0.94 tff(2358,plain,
% 0.92/0.94 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | (~c3_1(a2069)) | (~c2_1(a2069)) | (~c0_1(a2069)) | c1_1(a2072) | c0_1(a2072) | c2_1(a2072))),
% 0.92/0.94 inference(quant_inst,[status(thm)],[])).
% 0.92/0.94 tff(2359,plain,
% 0.92/0.94 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a2072) | c1_1(a2072) | (~ndr1_0) | c2_1(a2072) | (~c2_1(a2069)) | (~c0_1(a2069)) | (~c3_1(a2069))),
% 0.92/0.94 inference(modus_ponens,[status(thm)],[2358, 2357])).
% 0.92/0.94 tff(2360,plain,
% 0.92/0.94 (hskp0 | c2_1(a2072)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2359, 99, 2173, 2172, 2171, 2331, 2353, 2352])).
% 0.92/0.94 tff(2361,plain,
% 0.92/0.94 (hskp0),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[2360, 2342])).
% 0.92/0.94 tff(2362,plain,
% 0.92/0.94 (~c2_1(a2068)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[728, 2361])).
% 0.92/0.94 tff(2363,plain,
% 0.92/0.94 (~c0_1(a2068)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[734, 2361])).
% 0.92/0.94 tff(2364,plain,
% 0.92/0.94 (c3_1(a2068)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[745, 2361])).
% 0.92/0.94 tff(2365,plain,
% 0.92/0.94 (hskp10),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[1066, 99, 2173, 2172, 2171, 2364, 2363, 2362, 703])).
% 0.92/0.94 tff(2366,plain,
% 0.92/0.94 (~c3_1(a2087)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[221, 2365])).
% 0.92/0.94 tff(2367,plain,
% 0.92/0.94 (~c1_1(a2087)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[227, 2365])).
% 0.92/0.94 tff(2368,plain,
% 0.92/0.94 (~c1_1(a2068)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[1493, 99, 2331, 2353, 2330, 2363, 2362, 410, 2342])).
% 0.92/0.94 tff(2369,plain,
% 0.92/0.94 (~c0_1(a2076)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[680, 2333])).
% 0.92/0.94 tff(2370,plain,
% 0.92/0.94 (c3_1(a2076)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[674, 2333])).
% 0.92/0.94 tff(2371,plain,
% 0.92/0.94 (c2_1(a2087)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[238, 2365])).
% 0.92/0.94 tff(2372,plain,
% 0.92/0.94 (hskp8),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[1477, 2371, 2370, 2369, 2368, 2367, 2366, 2334])).
% 0.92/0.94 tff(2373,plain,
% 0.92/0.94 (~c0_1(a2082)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[173, 2372])).
% 0.92/0.94 tff(2374,plain,
% 0.92/0.94 (c2_1(a2082)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[184, 2372])).
% 0.92/0.94 tff(2375,plain,
% 0.92/0.94 (c1_1(a2082)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[195, 2372])).
% 0.92/0.94 tff(2376,plain,
% 0.92/0.94 ($false),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[331, 99, 22, 2371, 2375, 2374, 2367, 2366, 2373, 21])).
% 0.92/0.94 tff(2377,plain,(hskp11), inference(lemma,lemma(discharge,[]))).
% 0.92/0.94 tff(2378,plain,
% 0.92/0.94 (~c3_1(a2093)),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[350, 2377])).
% 0.92/0.94 tff(2379,plain,
% 0.92/0.94 (~c1_1(a2093)),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[356, 2377])).
% 0.92/0.95 tff(2380,plain,
% 0.92/0.95 (c0_1(a2093)),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[367, 2377])).
% 0.92/0.95 tff(2381,plain,
% 0.92/0.95 (~c0_1(a2077)),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[2062, 99, 2056, 2045, 2034, 2380, 2379, 2378, 344])).
% 0.92/0.95 tff(2382,plain,
% 0.92/0.95 (hskp0),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[2067, 2381])).
% 0.92/0.95 tff(2383,plain,
% 0.92/0.95 (~c0_1(a2068)),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[734, 2382])).
% 0.92/0.95 tff(2384,plain,
% 0.92/0.95 (~c2_1(a2068)),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[728, 2382])).
% 0.92/0.95 tff(2385,plain,
% 0.92/0.95 (c3_1(a2068)),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[745, 2382])).
% 0.92/0.95 tff(2386,plain,
% 0.92/0.95 (hskp4),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[1506, 2385, 2353, 2330, 2384, 2383])).
% 0.92/0.95 tff(2387,plain,
% 0.92/0.95 (~c2_1(a2074)),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[273, 2386])).
% 0.92/0.95 tff(2388,plain,
% 0.92/0.95 (c3_1(a2074)),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[284, 2386])).
% 0.92/0.95 tff(2389,plain,
% 0.92/0.95 (c1_1(a2074)),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[295, 2386])).
% 0.92/0.95 tff(2390,plain,
% 0.92/0.95 (~c2_1(a2072)),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[1572, 99, 2389, 2388, 2208, 2207, 2387, 2331, 2330, 2204, 10])).
% 0.92/0.95 tff(2391,plain,
% 0.92/0.95 (hskp10),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[1066, 99, 2173, 2172, 2171, 2385, 2383, 2384, 703])).
% 0.92/0.95 tff(2392,plain,
% 0.92/0.95 (~c3_1(a2087)),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[221, 2391])).
% 0.92/0.95 tff(2393,plain,
% 0.92/0.95 (~c1_1(a2087)),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[227, 2391])).
% 0.92/0.95 tff(2394,plain,
% 0.92/0.95 (c2_1(a2087)),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[238, 2391])).
% 0.92/0.95 tff(2395,plain,
% 0.92/0.95 ($false),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[1556, 99, 2394, 2389, 2388, 2393, 2392, 2387, 2331, 2330, 1550, 2390])).
% 0.92/0.95 % SZS output end Proof
%------------------------------------------------------------------------------