TSTP Solution File: SYN468-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN468-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 23:55:40 EDT 2022
% Result : Unsatisfiable 1.11s 0.94s
% Output : Proof 1.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN468-1 : TPTP v8.1.0. Released v2.1.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 04:03:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 1.11/0.94 % SZS status Unsatisfiable
% 1.11/0.94 % SZS output start Proof
% 1.11/0.94 tff(hskp7_type, type, (
% 1.11/0.94 hskp7: $o)).
% 1.11/0.94 tff(c3_1_type, type, (
% 1.11/0.94 c3_1: $i > $o)).
% 1.11/0.94 tff(a297_type, type, (
% 1.11/0.94 a297: $i)).
% 1.11/0.94 tff(c1_1_type, type, (
% 1.11/0.94 c1_1: $i > $o)).
% 1.11/0.94 tff(a301_type, type, (
% 1.11/0.94 a301: $i)).
% 1.11/0.94 tff(c2_1_type, type, (
% 1.11/0.94 c2_1: $i > $o)).
% 1.11/0.94 tff(a300_type, type, (
% 1.11/0.94 a300: $i)).
% 1.11/0.94 tff(c0_1_type, type, (
% 1.11/0.94 c0_1: $i > $o)).
% 1.11/0.94 tff(ndr1_0_type, type, (
% 1.11/0.94 ndr1_0: $o)).
% 1.11/0.94 tff(hskp5_type, type, (
% 1.11/0.94 hskp5: $o)).
% 1.11/0.94 tff(a315_type, type, (
% 1.11/0.94 a315: $i)).
% 1.11/0.94 tff(hskp16_type, type, (
% 1.11/0.94 hskp16: $o)).
% 1.11/0.94 tff(hskp24_type, type, (
% 1.11/0.94 hskp24: $o)).
% 1.11/0.94 tff(a294_type, type, (
% 1.11/0.94 a294: $i)).
% 1.11/0.94 tff(hskp3_type, type, (
% 1.11/0.94 hskp3: $o)).
% 1.11/0.94 tff(hskp29_type, type, (
% 1.11/0.94 hskp29: $o)).
% 1.11/0.94 tff(hskp4_type, type, (
% 1.11/0.94 hskp4: $o)).
% 1.11/0.94 tff(a306_type, type, (
% 1.11/0.94 a306: $i)).
% 1.11/0.94 tff(hskp11_type, type, (
% 1.11/0.94 hskp11: $o)).
% 1.11/0.94 tff(a299_type, type, (
% 1.11/0.94 a299: $i)).
% 1.11/0.94 tff(hskp22_type, type, (
% 1.11/0.94 hskp22: $o)).
% 1.11/0.94 tff(a331_type, type, (
% 1.11/0.94 a331: $i)).
% 1.11/0.94 tff(hskp31_type, type, (
% 1.11/0.94 hskp31: $o)).
% 1.11/0.94 tff(hskp27_type, type, (
% 1.11/0.94 hskp27: $o)).
% 1.11/0.94 tff(a368_type, type, (
% 1.11/0.94 a368: $i)).
% 1.11/0.94 tff(hskp26_type, type, (
% 1.11/0.94 hskp26: $o)).
% 1.11/0.94 tff(a367_type, type, (
% 1.11/0.94 a367: $i)).
% 1.11/0.94 tff(a359_type, type, (
% 1.11/0.94 a359: $i)).
% 1.11/0.94 tff(a308_type, type, (
% 1.11/0.94 a308: $i)).
% 1.11/0.94 tff(a341_type, type, (
% 1.11/0.94 a341: $i)).
% 1.11/0.94 tff(hskp8_type, type, (
% 1.11/0.94 hskp8: $o)).
% 1.11/0.94 tff(hskp13_type, type, (
% 1.11/0.94 hskp13: $o)).
% 1.11/0.94 tff(a311_type, type, (
% 1.11/0.94 a311: $i)).
% 1.11/0.94 tff(hskp15_type, type, (
% 1.11/0.94 hskp15: $o)).
% 1.11/0.94 tff(a337_type, type, (
% 1.11/0.94 a337: $i)).
% 1.11/0.94 tff(hskp23_type, type, (
% 1.11/0.94 hskp23: $o)).
% 1.11/0.94 tff(hskp12_type, type, (
% 1.11/0.94 hskp12: $o)).
% 1.11/0.94 tff(a291_type, type, (
% 1.11/0.94 a291: $i)).
% 1.11/0.94 tff(hskp0_type, type, (
% 1.11/0.94 hskp0: $o)).
% 1.11/0.94 tff(a307_type, type, (
% 1.11/0.94 a307: $i)).
% 1.11/0.94 tff(a295_type, type, (
% 1.11/0.94 a295: $i)).
% 1.11/0.94 tff(a304_type, type, (
% 1.11/0.94 a304: $i)).
% 1.11/0.94 tff(hskp9_type, type, (
% 1.11/0.94 hskp9: $o)).
% 1.11/0.94 tff(a296_type, type, (
% 1.11/0.94 a296: $i)).
% 1.11/0.94 tff(hskp2_type, type, (
% 1.11/0.94 hskp2: $o)).
% 1.11/0.94 tff(hskp28_type, type, (
% 1.11/0.94 hskp28: $o)).
% 1.11/0.94 tff(a293_type, type, (
% 1.11/0.94 a293: $i)).
% 1.11/0.94 tff(a330_type, type, (
% 1.11/0.94 a330: $i)).
% 1.11/0.94 tff(hskp21_type, type, (
% 1.11/0.94 hskp21: $o)).
% 1.11/0.94 tff(a329_type, type, (
% 1.11/0.94 a329: $i)).
% 1.11/0.94 tff(hskp20_type, type, (
% 1.11/0.94 hskp20: $o)).
% 1.11/0.94 tff(a325_type, type, (
% 1.11/0.94 a325: $i)).
% 1.11/0.94 tff(hskp18_type, type, (
% 1.11/0.94 hskp18: $o)).
% 1.11/0.94 tff(1,assumption,(~c3_1(a297)), introduced(assumption)).
% 1.11/0.94 tff(2,plain,
% 1.11/0.94 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.11/0.94 inference(bind,[status(th)],[])).
% 1.11/0.94 tff(3,plain,
% 1.11/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.94 inference(quant_intro,[status(thm)],[2])).
% 1.11/0.94 tff(4,plain,
% 1.11/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(5,plain,
% 1.11/0.94 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.11/0.94 inference(bind,[status(th)],[])).
% 1.11/0.94 tff(6,plain,
% 1.11/0.94 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.94 inference(quant_intro,[status(thm)],[5])).
% 1.11/0.94 tff(7,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 1.11/0.94 tff(8,plain,
% 1.11/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[7, 6])).
% 1.11/0.94 tff(9,plain,
% 1.11/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.11/0.94 tff(10,plain,(
% 1.11/0.94 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.94 inference(skolemize,[status(sab)],[9])).
% 1.11/0.94 tff(11,plain,
% 1.11/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.94 inference(modus_ponens,[status(thm)],[10, 3])).
% 1.11/0.94 tff(12,plain,
% 1.11/0.94 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.11/0.94 inference(bind,[status(th)],[])).
% 1.11/0.94 tff(13,plain,
% 1.11/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/0.94 inference(quant_intro,[status(thm)],[12])).
% 1.11/0.94 tff(14,plain,
% 1.11/0.94 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/0.94 inference(rewrite,[status(thm)],[])).
% 1.11/0.94 tff(15,plain,
% 1.11/0.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(16,plain,
% 1.11/0.95 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[15])).
% 1.11/0.95 tff(17,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.11/0.95 tff(18,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.11/0.95 tff(19,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.11/0.95 tff(20,plain,(
% 1.11/0.95 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/0.95 inference(skolemize,[status(sab)],[19])).
% 1.11/0.95 tff(21,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.11/0.95 tff(22,plain,
% 1.11/0.95 (^[U: $i] : refl((hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(23,plain,
% 1.11/0.95 (![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[22])).
% 1.11/0.95 tff(24,plain,
% 1.11/0.95 (![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(25,plain,
% 1.11/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp24))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) <=> (hskp24 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp16) <=> ((hskp24 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16))), rewrite(((hskp24 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp16) <=> (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(26,plain,
% 1.11/0.95 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp16) <=> ![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[25])).
% 1.11/0.95 tff(27,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp24) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.11/0.95 tff(28,plain,
% 1.11/0.95 (![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.11/0.95 tff(29,plain,
% 1.11/0.95 (![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.11/0.95 tff(30,plain,(
% 1.11/0.95 ![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.11/0.95 inference(skolemize,[status(sab)],[29])).
% 1.11/0.95 tff(31,plain,
% 1.11/0.95 (![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.11/0.95 tff(32,assumption,(~hskp16), introduced(assumption)).
% 1.11/0.95 tff(33,plain,
% 1.11/0.95 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(34,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[33])).
% 1.11/0.95 tff(35,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(36,plain,
% 1.11/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V))), ((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)))), (((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(37,plain,
% 1.11/0.95 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[36])).
% 1.11/0.95 tff(38,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c1_1(U))) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.11/0.95 tff(39,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.11/0.95 tff(40,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[39, 35])).
% 1.11/0.95 tff(41,plain,(
% 1.11/0.95 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.95 inference(skolemize,[status(sab)],[40])).
% 1.11/0.95 tff(42,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[41, 34])).
% 1.11/0.95 tff(43,plain,
% 1.11/0.95 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(44,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[43])).
% 1.11/0.95 tff(45,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(46,plain,
% 1.11/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(47,plain,
% 1.11/0.95 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[46])).
% 1.11/0.95 tff(48,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 1.11/0.95 tff(49,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.11/0.95 tff(50,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[49, 45])).
% 1.11/0.95 tff(51,plain,(
% 1.11/0.95 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.95 inference(skolemize,[status(sab)],[50])).
% 1.11/0.95 tff(52,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[51, 44])).
% 1.11/0.95 tff(53,assumption,(~hskp29), introduced(assumption)).
% 1.11/0.95 tff(54,plain,
% 1.11/0.95 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(55,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[54])).
% 1.11/0.95 tff(56,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(57,plain,
% 1.11/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp29))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(58,plain,
% 1.11/0.95 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[57])).
% 1.11/0.95 tff(59,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 1.11/0.95 tff(60,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.11/0.95 tff(61,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[60, 56])).
% 1.11/0.95 tff(62,plain,(
% 1.11/0.95 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.11/0.95 inference(skolemize,[status(sab)],[61])).
% 1.11/0.95 tff(63,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[62, 55])).
% 1.11/0.95 tff(64,assumption,(~hskp3), introduced(assumption)).
% 1.11/0.95 tff(65,assumption,(hskp22), introduced(assumption)).
% 1.11/0.95 tff(66,plain,
% 1.11/0.95 (((~hskp22) | (~c2_1(a331))) <=> ((~hskp22) | (~c2_1(a331)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(67,plain,
% 1.11/0.95 (((~c2_1(a331)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a331)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(68,axiom,((~c2_1(a331)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.11/0.95 tff(69,plain,
% 1.11/0.95 ((~hskp22) | (~c2_1(a331))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[68, 67])).
% 1.11/0.95 tff(70,plain,
% 1.11/0.95 ((~hskp22) | (~c2_1(a331))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[69, 66])).
% 1.11/0.95 tff(71,plain,
% 1.11/0.95 (~c2_1(a331)),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[70, 65])).
% 1.11/0.95 tff(72,plain,
% 1.11/0.95 (((~hskp22) | (~c1_1(a331))) <=> ((~hskp22) | (~c1_1(a331)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(73,plain,
% 1.11/0.95 (((~c1_1(a331)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a331)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(74,axiom,((~c1_1(a331)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.11/0.95 tff(75,plain,
% 1.11/0.95 ((~hskp22) | (~c1_1(a331))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.11/0.95 tff(76,plain,
% 1.11/0.95 ((~hskp22) | (~c1_1(a331))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[75, 72])).
% 1.11/0.95 tff(77,plain,
% 1.11/0.95 (~c1_1(a331)),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[76, 65])).
% 1.11/0.95 tff(78,plain,
% 1.11/0.95 (((~hskp22) | (~c3_1(a331))) <=> ((~hskp22) | (~c3_1(a331)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(79,plain,
% 1.11/0.95 (((~c3_1(a331)) | (~hskp22)) <=> ((~hskp22) | (~c3_1(a331)))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(80,axiom,((~c3_1(a331)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.11/0.95 tff(81,plain,
% 1.11/0.95 ((~hskp22) | (~c3_1(a331))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.11/0.95 tff(82,plain,
% 1.11/0.95 ((~hskp22) | (~c3_1(a331))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[81, 78])).
% 1.11/0.95 tff(83,plain,
% 1.11/0.95 (~c3_1(a331)),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[82, 65])).
% 1.11/0.95 tff(84,plain,
% 1.11/0.95 (^[U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(85,plain,
% 1.11/0.95 (![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[84])).
% 1.11/0.95 tff(86,plain,
% 1.11/0.95 (![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(87,plain,
% 1.11/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(88,plain,
% 1.11/0.95 (![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> ![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[87])).
% 1.11/0.95 tff(89,axiom,(![U: $i] : (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.11/0.95 tff(90,plain,
% 1.11/0.95 (![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.11/0.95 tff(91,plain,
% 1.11/0.95 (![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[90, 86])).
% 1.11/0.95 tff(92,plain,(
% 1.11/0.95 ![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.11/0.95 inference(skolemize,[status(sab)],[91])).
% 1.11/0.95 tff(93,plain,
% 1.11/0.95 (![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[92, 85])).
% 1.11/0.95 tff(94,assumption,(~c3_1(a331)), introduced(assumption)).
% 1.11/0.95 tff(95,assumption,(~c1_1(a331)), introduced(assumption)).
% 1.11/0.95 tff(96,assumption,(~ndr1_0), introduced(assumption)).
% 1.11/0.95 tff(97,plain,
% 1.11/0.95 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(98,plain,
% 1.11/0.95 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(99,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause8')).
% 1.11/0.95 tff(100,plain,
% 1.11/0.95 (ndr1_0 | (~hskp24)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.11/0.95 tff(101,plain,
% 1.11/0.95 (ndr1_0 | (~hskp24)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[100, 97])).
% 1.11/0.95 tff(102,plain,
% 1.11/0.95 (~hskp24),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[101, 96])).
% 1.11/0.95 tff(103,plain,
% 1.11/0.95 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(104,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 1.11/0.95 tff(105,plain,
% 1.11/0.95 ((~hskp31) | ndr1_0),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[104, 103])).
% 1.11/0.95 tff(106,plain,
% 1.11/0.95 ((~hskp31) | ndr1_0),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[105, 103])).
% 1.11/0.95 tff(107,plain,
% 1.11/0.95 ((~hskp31) | ndr1_0),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[106, 103])).
% 1.11/0.95 tff(108,plain,
% 1.11/0.95 ((~hskp31) | ndr1_0),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[107, 103])).
% 1.11/0.95 tff(109,plain,
% 1.11/0.95 ((~hskp31) | ndr1_0),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[108, 103])).
% 1.11/0.95 tff(110,plain,
% 1.11/0.95 ((~hskp31) | ndr1_0),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[109, 103])).
% 1.11/0.95 tff(111,plain,
% 1.11/0.95 ((~hskp31) | ndr1_0),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[110, 103])).
% 1.11/0.95 tff(112,plain,
% 1.11/0.95 ((~hskp31) | ndr1_0),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[111, 103])).
% 1.11/0.95 tff(113,plain,
% 1.11/0.95 (~hskp31),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[112, 96])).
% 1.11/0.95 tff(114,plain,
% 1.11/0.95 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(115,plain,
% 1.11/0.95 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(116,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause5')).
% 1.11/0.95 tff(117,plain,
% 1.11/0.95 (ndr1_0 | (~hskp27)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[116, 115])).
% 1.11/0.95 tff(118,plain,
% 1.11/0.95 (ndr1_0 | (~hskp27)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[117, 114])).
% 1.11/0.95 tff(119,plain,
% 1.11/0.95 (~hskp27),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[118, 96])).
% 1.11/0.95 tff(120,plain,
% 1.11/0.95 ((hskp31 | hskp27 | hskp24) <=> (hskp31 | hskp27 | hskp24)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(121,plain,
% 1.11/0.95 (((hskp31 | hskp27) | hskp24) <=> (hskp31 | hskp27 | hskp24)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(122,plain,
% 1.11/0.95 ((hskp31 | hskp27) <=> (hskp31 | hskp27)),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(123,plain,
% 1.11/0.95 (((hskp31 | hskp27) | hskp24) <=> ((hskp31 | hskp27) | hskp24)),
% 1.11/0.95 inference(monotonicity,[status(thm)],[122])).
% 1.11/0.95 tff(124,plain,
% 1.11/0.95 (((hskp31 | hskp27) | hskp24) <=> (hskp31 | hskp27 | hskp24)),
% 1.11/0.95 inference(transitivity,[status(thm)],[123, 121])).
% 1.11/0.95 tff(125,axiom,((hskp31 | hskp27) | hskp24), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause33')).
% 1.11/0.95 tff(126,plain,
% 1.11/0.95 (hskp31 | hskp27 | hskp24),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[125, 124])).
% 1.11/0.95 tff(127,plain,
% 1.11/0.95 (hskp31 | hskp27 | hskp24),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[126, 120])).
% 1.11/0.95 tff(128,plain,
% 1.11/0.95 (hskp31 | hskp27 | hskp24),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[127, 120])).
% 1.11/0.95 tff(129,plain,
% 1.11/0.95 (hskp31 | hskp27 | hskp24),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[128, 120])).
% 1.11/0.95 tff(130,plain,
% 1.11/0.95 (hskp31 | hskp27 | hskp24),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[129, 120])).
% 1.11/0.95 tff(131,plain,
% 1.11/0.95 (hskp31 | hskp27 | hskp24),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[130, 120])).
% 1.11/0.95 tff(132,plain,
% 1.11/0.95 (hskp31 | hskp27 | hskp24),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[131, 120])).
% 1.11/0.95 tff(133,plain,
% 1.11/0.95 (hskp31 | hskp27 | hskp24),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[132, 120])).
% 1.11/0.95 tff(134,plain,
% 1.11/0.95 ($false),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[133, 119, 113, 102])).
% 1.11/0.95 tff(135,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.11/0.95 tff(136,plain,
% 1.11/0.95 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c1_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c1_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(137,plain,
% 1.11/0.95 ((hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | c0_1(a331)) <=> (hskp3 | c1_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(138,plain,
% 1.11/0.95 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | c0_1(a331))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c1_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331)))),
% 1.11/0.95 inference(monotonicity,[status(thm)],[137])).
% 1.11/0.95 tff(139,plain,
% 1.11/0.95 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | c0_1(a331))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c1_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331))),
% 1.11/0.95 inference(transitivity,[status(thm)],[138, 136])).
% 1.11/0.95 tff(140,plain,
% 1.11/0.95 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | c0_1(a331))),
% 1.11/0.95 inference(quant_inst,[status(thm)],[])).
% 1.11/0.95 tff(141,plain,
% 1.11/0.95 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c1_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331)),
% 1.11/0.95 inference(modus_ponens,[status(thm)],[140, 139])).
% 1.11/0.95 tff(142,plain,
% 1.11/0.95 (hskp3 | c0_1(a331)),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[141, 135, 95, 94, 93])).
% 1.11/0.95 tff(143,plain,
% 1.11/0.95 (c0_1(a331)),
% 1.11/0.95 inference(unit_resolution,[status(thm)],[142, 64])).
% 1.11/0.95 tff(144,plain,
% 1.11/0.95 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(145,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.95 inference(quant_intro,[status(thm)],[144])).
% 1.11/0.95 tff(146,plain,
% 1.11/0.95 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.95 inference(rewrite,[status(thm)],[])).
% 1.11/0.95 tff(147,plain,
% 1.11/0.95 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(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) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.11/0.95 inference(bind,[status(th)],[])).
% 1.11/0.95 tff(148,plain,
% 1.11/0.95 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[147])).
% 1.11/0.96 tff(149,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause170')).
% 1.11/0.96 tff(150,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.11/0.96 tff(151,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[150, 146])).
% 1.11/0.96 tff(152,plain,(
% 1.11/0.96 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.96 inference(skolemize,[status(sab)],[151])).
% 1.11/0.96 tff(153,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[152, 145])).
% 1.11/0.96 tff(154,assumption,(~c2_1(a331)), introduced(assumption)).
% 1.11/0.96 tff(155,plain,
% 1.11/0.96 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | (~c0_1(a331)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | (~c0_1(a331)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(156,plain,
% 1.11/0.96 ((hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | (~c0_1(a331)) | c2_1(a331) | c1_1(a331) | c3_1(a331)) <=> (hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | (~c0_1(a331)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(157,plain,
% 1.11/0.96 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | (~c0_1(a331)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | (~c0_1(a331))))),
% 1.11/0.96 inference(monotonicity,[status(thm)],[156])).
% 1.11/0.96 tff(158,plain,
% 1.11/0.96 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | (~c0_1(a331)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | (~c0_1(a331)))),
% 1.11/0.96 inference(transitivity,[status(thm)],[157, 155])).
% 1.11/0.96 tff(159,plain,
% 1.11/0.96 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a331) | c1_1(a331) | (~c0_1(a331)) | c2_1(a331) | c1_1(a331) | c3_1(a331))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(160,plain,
% 1.11/0.96 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | (~c0_1(a331))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[159, 158])).
% 1.11/0.96 tff(161,plain,
% 1.11/0.96 (hskp3 | (~c0_1(a331))),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[160, 135, 95, 154, 94, 153])).
% 1.11/0.96 tff(162,plain,
% 1.11/0.96 ($false),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[161, 143, 64])).
% 1.11/0.96 tff(163,plain,(hskp3 | c1_1(a331) | c2_1(a331) | c3_1(a331)), inference(lemma,lemma(discharge,[]))).
% 1.11/0.96 tff(164,plain,
% 1.11/0.96 ($false),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[163, 83, 77, 64, 71])).
% 1.11/0.96 tff(165,plain,((~hskp22) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.11/0.96 tff(166,plain,
% 1.11/0.96 (~hskp22),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[165, 64])).
% 1.11/0.96 tff(167,plain,
% 1.11/0.96 (^[U: $i] : refl((hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(168,plain,
% 1.11/0.96 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[167])).
% 1.11/0.96 tff(169,plain,
% 1.11/0.96 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(170,plain,
% 1.11/0.96 (^[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)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp26) <=> ((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp26))), rewrite(((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp26) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp26) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(171,plain,
% 1.11/0.96 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp26) <=> ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[170])).
% 1.11/0.96 tff(172,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 1.11/0.96 tff(173,plain,
% 1.11/0.96 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.11/0.96 tff(174,plain,
% 1.11/0.96 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[173, 169])).
% 1.11/0.96 tff(175,plain,(
% 1.11/0.96 ![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.96 inference(skolemize,[status(sab)],[174])).
% 1.11/0.96 tff(176,plain,
% 1.11/0.96 (![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[175, 168])).
% 1.11/0.96 tff(177,assumption,(hskp31), introduced(assumption)).
% 1.11/0.96 tff(178,plain,
% 1.11/0.96 (((~hskp31) | c2_1(a367)) <=> ((~hskp31) | c2_1(a367))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(179,axiom,((~hskp31) | c2_1(a367)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.11/0.96 tff(180,plain,
% 1.11/0.96 ((~hskp31) | c2_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[179, 178])).
% 1.11/0.96 tff(181,plain,
% 1.11/0.96 ((~hskp31) | c2_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[180, 178])).
% 1.11/0.96 tff(182,plain,
% 1.11/0.96 ((~hskp31) | c2_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[181, 178])).
% 1.11/0.96 tff(183,plain,
% 1.11/0.96 ((~hskp31) | c2_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[182, 178])).
% 1.11/0.96 tff(184,plain,
% 1.11/0.96 ((~hskp31) | c2_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[183, 178])).
% 1.11/0.96 tff(185,plain,
% 1.11/0.96 ((~hskp31) | c2_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[184, 178])).
% 1.11/0.96 tff(186,plain,
% 1.11/0.96 ((~hskp31) | c2_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[185, 178])).
% 1.11/0.96 tff(187,plain,
% 1.11/0.96 ((~hskp31) | c2_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[186, 178])).
% 1.11/0.96 tff(188,plain,
% 1.11/0.96 (c2_1(a367)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[187, 177])).
% 1.11/0.96 tff(189,plain,
% 1.11/0.96 (((~hskp31) | c1_1(a367)) <=> ((~hskp31) | c1_1(a367))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(190,axiom,((~hskp31) | c1_1(a367)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.11/0.96 tff(191,plain,
% 1.11/0.96 ((~hskp31) | c1_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[190, 189])).
% 1.11/0.96 tff(192,plain,
% 1.11/0.96 ((~hskp31) | c1_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[191, 189])).
% 1.11/0.96 tff(193,plain,
% 1.11/0.96 ((~hskp31) | c1_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[192, 189])).
% 1.11/0.96 tff(194,plain,
% 1.11/0.96 ((~hskp31) | c1_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[193, 189])).
% 1.11/0.96 tff(195,plain,
% 1.11/0.96 ((~hskp31) | c1_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[194, 189])).
% 1.11/0.96 tff(196,plain,
% 1.11/0.96 ((~hskp31) | c1_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[195, 189])).
% 1.11/0.96 tff(197,plain,
% 1.11/0.96 ((~hskp31) | c1_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[196, 189])).
% 1.11/0.96 tff(198,plain,
% 1.11/0.96 ((~hskp31) | c1_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[197, 189])).
% 1.11/0.96 tff(199,plain,
% 1.11/0.96 (c1_1(a367)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[198, 177])).
% 1.11/0.96 tff(200,plain,
% 1.11/0.96 (((~hskp31) | c0_1(a367)) <=> ((~hskp31) | c0_1(a367))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(201,axiom,((~hskp31) | c0_1(a367)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.11/0.96 tff(202,plain,
% 1.11/0.96 ((~hskp31) | c0_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[201, 200])).
% 1.11/0.96 tff(203,plain,
% 1.11/0.96 ((~hskp31) | c0_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[202, 200])).
% 1.11/0.96 tff(204,plain,
% 1.11/0.96 ((~hskp31) | c0_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[203, 200])).
% 1.11/0.96 tff(205,plain,
% 1.11/0.96 ((~hskp31) | c0_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[204, 200])).
% 1.11/0.96 tff(206,plain,
% 1.11/0.96 ((~hskp31) | c0_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[205, 200])).
% 1.11/0.96 tff(207,plain,
% 1.11/0.96 ((~hskp31) | c0_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[206, 200])).
% 1.11/0.96 tff(208,plain,
% 1.11/0.96 ((~hskp31) | c0_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[207, 200])).
% 1.11/0.96 tff(209,plain,
% 1.11/0.96 ((~hskp31) | c0_1(a367)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[208, 200])).
% 1.11/0.96 tff(210,plain,
% 1.11/0.96 (c0_1(a367)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[209, 177])).
% 1.11/0.96 tff(211,assumption,(hskp26), introduced(assumption)).
% 1.11/0.96 tff(212,plain,
% 1.11/0.96 (((~hskp26) | (~c3_1(a359))) <=> ((~hskp26) | (~c3_1(a359)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(213,plain,
% 1.11/0.96 (((~c3_1(a359)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a359)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(214,axiom,((~c3_1(a359)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.11/0.96 tff(215,plain,
% 1.11/0.96 ((~hskp26) | (~c3_1(a359))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.11/0.96 tff(216,plain,
% 1.11/0.96 ((~hskp26) | (~c3_1(a359))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[215, 212])).
% 1.11/0.96 tff(217,plain,
% 1.11/0.96 (~c3_1(a359)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[216, 211])).
% 1.11/0.96 tff(218,plain,
% 1.11/0.96 (((~hskp26) | (~c1_1(a359))) <=> ((~hskp26) | (~c1_1(a359)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(219,plain,
% 1.11/0.96 (((~c1_1(a359)) | (~hskp26)) <=> ((~hskp26) | (~c1_1(a359)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(220,axiom,((~c1_1(a359)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.11/0.96 tff(221,plain,
% 1.11/0.96 ((~hskp26) | (~c1_1(a359))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[220, 219])).
% 1.11/0.96 tff(222,plain,
% 1.11/0.96 ((~hskp26) | (~c1_1(a359))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[221, 218])).
% 1.11/0.96 tff(223,plain,
% 1.11/0.96 (~c1_1(a359)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[222, 211])).
% 1.11/0.96 tff(224,plain,
% 1.11/0.96 (((~hskp26) | (~c0_1(a359))) <=> ((~hskp26) | (~c0_1(a359)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(225,plain,
% 1.11/0.96 (((~c0_1(a359)) | (~hskp26)) <=> ((~hskp26) | (~c0_1(a359)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(226,axiom,((~c0_1(a359)) | (~hskp26)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 1.11/0.96 tff(227,plain,
% 1.11/0.96 ((~hskp26) | (~c0_1(a359))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[226, 225])).
% 1.11/0.96 tff(228,plain,
% 1.11/0.96 ((~hskp26) | (~c0_1(a359))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[227, 224])).
% 1.11/0.96 tff(229,plain,
% 1.11/0.96 (~c0_1(a359)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[228, 211])).
% 1.11/0.96 tff(230,plain,
% 1.11/0.96 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(231,plain,
% 1.11/0.96 ((hskp3 | (~ndr1_0) | c3_1(a359) | c1_1(a359) | c0_1(a359)) <=> (hskp3 | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(232,plain,
% 1.11/0.96 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a359) | c1_1(a359) | c0_1(a359))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0)))),
% 1.11/0.96 inference(monotonicity,[status(thm)],[231])).
% 1.11/0.96 tff(233,plain,
% 1.11/0.96 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a359) | c1_1(a359) | c0_1(a359))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0))),
% 1.11/0.96 inference(transitivity,[status(thm)],[232, 230])).
% 1.11/0.96 tff(234,plain,
% 1.11/0.96 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a359) | c1_1(a359) | c0_1(a359))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(235,plain,
% 1.11/0.96 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a359) | c1_1(a359) | c3_1(a359) | (~ndr1_0)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[234, 233])).
% 1.11/0.96 tff(236,plain,
% 1.11/0.96 ($false),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[235, 135, 64, 229, 223, 217, 93])).
% 1.11/0.96 tff(237,plain,((~hskp26) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.11/0.96 tff(238,plain,
% 1.11/0.96 (~hskp26),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[237, 64])).
% 1.11/0.96 tff(239,plain,
% 1.11/0.96 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a367)) | (~c1_1(a367)) | (~c2_1(a367)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a367)) | (~c1_1(a367)) | (~c2_1(a367)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(240,plain,
% 1.11/0.96 ((hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a367)) | (~c1_1(a367)) | (~c0_1(a367))) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a367)) | (~c1_1(a367)) | (~c2_1(a367)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(241,plain,
% 1.11/0.96 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a367)) | (~c1_1(a367)) | (~c0_1(a367)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a367)) | (~c1_1(a367)) | (~c2_1(a367))))),
% 1.11/0.96 inference(monotonicity,[status(thm)],[240])).
% 1.11/0.96 tff(242,plain,
% 1.11/0.96 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a367)) | (~c1_1(a367)) | (~c0_1(a367)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a367)) | (~c1_1(a367)) | (~c2_1(a367)))),
% 1.11/0.96 inference(transitivity,[status(thm)],[241, 239])).
% 1.11/0.96 tff(243,plain,
% 1.11/0.96 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a367)) | (~c1_1(a367)) | (~c0_1(a367)))),
% 1.11/0.96 inference(quant_inst,[status(thm)],[])).
% 1.11/0.96 tff(244,plain,
% 1.11/0.96 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c0_1(a367)) | (~c1_1(a367)) | (~c2_1(a367))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[243, 242])).
% 1.11/0.96 tff(245,plain,
% 1.11/0.96 ($false),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[244, 135, 238, 64, 210, 199, 188, 176])).
% 1.11/0.96 tff(246,plain,((~hskp31) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.11/0.96 tff(247,plain,
% 1.11/0.96 (~hskp31),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[246, 64])).
% 1.11/0.96 tff(248,assumption,(hskp24), introduced(assumption)).
% 1.11/0.96 tff(249,plain,
% 1.11/0.96 (((~hskp24) | (~c3_1(a341))) <=> ((~hskp24) | (~c3_1(a341)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(250,plain,
% 1.11/0.96 (((~c3_1(a341)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a341)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(251,axiom,((~c3_1(a341)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.11/0.96 tff(252,plain,
% 1.11/0.96 ((~hskp24) | (~c3_1(a341))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[251, 250])).
% 1.11/0.96 tff(253,plain,
% 1.11/0.96 ((~hskp24) | (~c3_1(a341))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[252, 249])).
% 1.11/0.96 tff(254,plain,
% 1.11/0.96 (~c3_1(a341)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[253, 248])).
% 1.11/0.96 tff(255,plain,
% 1.11/0.96 (((~hskp24) | (~c0_1(a341))) <=> ((~hskp24) | (~c0_1(a341)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(256,plain,
% 1.11/0.96 (((~c0_1(a341)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a341)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(257,axiom,((~c0_1(a341)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.11/0.96 tff(258,plain,
% 1.11/0.96 ((~hskp24) | (~c0_1(a341))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[257, 256])).
% 1.11/0.96 tff(259,plain,
% 1.11/0.96 ((~hskp24) | (~c0_1(a341))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[258, 255])).
% 1.11/0.96 tff(260,plain,
% 1.11/0.96 (~c0_1(a341)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[259, 248])).
% 1.11/0.96 tff(261,plain,
% 1.11/0.96 (((~hskp24) | c1_1(a341)) <=> ((~hskp24) | c1_1(a341))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(262,axiom,((~hskp24) | c1_1(a341)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.11/0.96 tff(263,plain,
% 1.11/0.96 ((~hskp24) | c1_1(a341)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[262, 261])).
% 1.11/0.96 tff(264,plain,
% 1.11/0.96 ((~hskp24) | c1_1(a341)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[263, 261])).
% 1.11/0.96 tff(265,plain,
% 1.11/0.96 ((~hskp24) | c1_1(a341)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[264, 261])).
% 1.11/0.96 tff(266,plain,
% 1.11/0.96 ((~hskp24) | c1_1(a341)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[265, 261])).
% 1.11/0.96 tff(267,plain,
% 1.11/0.96 ((~hskp24) | c1_1(a341)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[266, 261])).
% 1.11/0.96 tff(268,plain,
% 1.11/0.96 ((~hskp24) | c1_1(a341)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[267, 261])).
% 1.11/0.96 tff(269,plain,
% 1.11/0.96 ((~hskp24) | c1_1(a341)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[268, 261])).
% 1.11/0.96 tff(270,plain,
% 1.11/0.96 ((~hskp24) | c1_1(a341)),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[269, 261])).
% 1.11/0.96 tff(271,plain,
% 1.11/0.96 (c1_1(a341)),
% 1.11/0.96 inference(unit_resolution,[status(thm)],[270, 248])).
% 1.11/0.96 tff(272,plain,
% 1.11/0.96 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(273,plain,
% 1.11/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[272])).
% 1.11/0.96 tff(274,plain,
% 1.11/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(275,plain,
% 1.11/0.96 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(276,plain,
% 1.11/0.96 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[275])).
% 1.11/0.96 tff(277,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c1_1(W))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 1.11/0.96 tff(278,plain,
% 1.11/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[277, 276])).
% 1.11/0.96 tff(279,plain,
% 1.11/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[278, 274])).
% 1.11/0.96 tff(280,plain,(
% 1.11/0.96 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.96 inference(skolemize,[status(sab)],[279])).
% 1.11/0.96 tff(281,plain,
% 1.11/0.96 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[280, 273])).
% 1.11/0.96 tff(282,plain,
% 1.11/0.96 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(283,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[282])).
% 1.11/0.96 tff(284,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(285,plain,
% 1.11/0.96 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(286,plain,
% 1.11/0.96 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[285])).
% 1.11/0.96 tff(287,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 1.11/0.96 tff(288,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[287, 286])).
% 1.11/0.96 tff(289,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[288, 284])).
% 1.11/0.96 tff(290,plain,(
% 1.11/0.96 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(skolemize,[status(sab)],[289])).
% 1.11/0.96 tff(291,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[290, 283])).
% 1.11/0.96 tff(292,assumption,(~c3_1(a341)), introduced(assumption)).
% 1.11/0.96 tff(293,assumption,(~c0_1(a341)), introduced(assumption)).
% 1.11/0.96 tff(294,assumption,(c1_1(a341)), introduced(assumption)).
% 1.11/0.96 tff(295,plain,
% 1.11/0.96 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(296,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[295])).
% 1.11/0.96 tff(297,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(298,plain,
% 1.11/0.96 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp13))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(299,plain,
% 1.11/0.96 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[298])).
% 1.11/0.96 tff(300,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 1.11/0.96 tff(301,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[300, 299])).
% 1.11/0.96 tff(302,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[301, 297])).
% 1.11/0.96 tff(303,plain,(
% 1.11/0.96 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(skolemize,[status(sab)],[302])).
% 1.11/0.96 tff(304,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.11/0.96 inference(modus_ponens,[status(thm)],[303, 296])).
% 1.11/0.96 tff(305,assumption,(~c2_1(a341)), introduced(assumption)).
% 1.11/0.96 tff(306,plain,
% 1.11/0.96 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 1.11/0.96 inference(bind,[status(th)],[])).
% 1.11/0.96 tff(307,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.11/0.96 inference(quant_intro,[status(thm)],[306])).
% 1.11/0.96 tff(308,plain,
% 1.11/0.96 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.11/0.96 inference(rewrite,[status(thm)],[])).
% 1.11/0.96 tff(309,plain,
% 1.11/0.96 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 1.11/0.97 inference(bind,[status(th)],[])).
% 1.11/0.97 tff(310,plain,
% 1.11/0.97 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.11/0.97 inference(quant_intro,[status(thm)],[309])).
% 1.11/0.97 tff(311,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.11/0.97 tff(312,plain,
% 1.11/0.97 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[311, 310])).
% 1.11/0.97 tff(313,plain,
% 1.11/0.97 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[312, 308])).
% 1.11/0.97 tff(314,plain,(
% 1.11/0.97 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.11/0.97 inference(skolemize,[status(sab)],[313])).
% 1.11/0.97 tff(315,plain,
% 1.11/0.97 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[314, 307])).
% 1.11/0.97 tff(316,plain,
% 1.11/0.97 (^[U: $i] : refl((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.11/0.97 inference(bind,[status(th)],[])).
% 1.11/0.97 tff(317,plain,
% 1.11/0.97 (![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(quant_intro,[status(thm)],[316])).
% 1.11/0.97 tff(318,plain,
% 1.11/0.97 (![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(319,plain,
% 1.11/0.97 (^[U: $i] : 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)) | hskp23) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.11/0.97 inference(bind,[status(th)],[])).
% 1.11/0.97 tff(320,plain,
% 1.11/0.97 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) <=> ![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(quant_intro,[status(thm)],[319])).
% 1.11/0.97 tff(321,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 1.11/0.97 tff(322,plain,
% 1.11/0.97 (![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[321, 320])).
% 1.11/0.97 tff(323,plain,
% 1.11/0.97 (![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[322, 318])).
% 1.11/0.97 tff(324,plain,(
% 1.11/0.97 ![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(skolemize,[status(sab)],[323])).
% 1.11/0.97 tff(325,plain,
% 1.11/0.97 (![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[324, 317])).
% 1.11/0.97 tff(326,plain,
% 1.11/0.97 (^[U: $i] : refl((hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 1.11/0.97 inference(bind,[status(th)],[])).
% 1.11/0.97 tff(327,plain,
% 1.11/0.97 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(quant_intro,[status(thm)],[326])).
% 1.11/0.97 tff(328,plain,
% 1.11/0.97 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(329,plain,
% 1.11/0.97 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp29) <=> ((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp29))), rewrite(((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp29) <=> (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.11/0.97 inference(bind,[status(th)],[])).
% 1.11/0.97 tff(330,plain,
% 1.11/0.97 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp29) <=> ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(quant_intro,[status(thm)],[329])).
% 1.11/0.97 tff(331,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.11/0.97 tff(332,plain,
% 1.11/0.97 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[331, 330])).
% 1.11/0.97 tff(333,plain,
% 1.11/0.97 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[332, 328])).
% 1.11/0.97 tff(334,plain,(
% 1.11/0.97 ![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(skolemize,[status(sab)],[333])).
% 1.11/0.97 tff(335,plain,
% 1.11/0.97 (![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[334, 327])).
% 1.11/0.97 tff(336,assumption,(~hskp23), introduced(assumption)).
% 1.11/0.97 tff(337,assumption,(hskp29), introduced(assumption)).
% 1.11/0.97 tff(338,plain,
% 1.11/0.97 (((~hskp29) | c2_1(a301)) <=> ((~hskp29) | c2_1(a301))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(339,axiom,((~hskp29) | c2_1(a301)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.11/0.97 tff(340,plain,
% 1.11/0.97 ((~hskp29) | c2_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[339, 338])).
% 1.11/0.97 tff(341,plain,
% 1.11/0.97 ((~hskp29) | c2_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[340, 338])).
% 1.11/0.97 tff(342,plain,
% 1.11/0.97 ((~hskp29) | c2_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[341, 338])).
% 1.11/0.97 tff(343,plain,
% 1.11/0.97 ((~hskp29) | c2_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[342, 338])).
% 1.11/0.97 tff(344,plain,
% 1.11/0.97 ((~hskp29) | c2_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[343, 338])).
% 1.11/0.97 tff(345,plain,
% 1.11/0.97 ((~hskp29) | c2_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[344, 338])).
% 1.11/0.97 tff(346,plain,
% 1.11/0.97 ((~hskp29) | c2_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[345, 338])).
% 1.11/0.97 tff(347,plain,
% 1.11/0.97 ((~hskp29) | c2_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[346, 338])).
% 1.11/0.97 tff(348,plain,
% 1.11/0.97 (c2_1(a301)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[347, 337])).
% 1.11/0.97 tff(349,plain,
% 1.11/0.97 (((~hskp29) | c0_1(a301)) <=> ((~hskp29) | c0_1(a301))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(350,axiom,((~hskp29) | c0_1(a301)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause50')).
% 1.11/0.97 tff(351,plain,
% 1.11/0.97 ((~hskp29) | c0_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[350, 349])).
% 1.11/0.97 tff(352,plain,
% 1.11/0.97 ((~hskp29) | c0_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[351, 349])).
% 1.11/0.97 tff(353,plain,
% 1.11/0.97 ((~hskp29) | c0_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[352, 349])).
% 1.11/0.97 tff(354,plain,
% 1.11/0.97 ((~hskp29) | c0_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[353, 349])).
% 1.11/0.97 tff(355,plain,
% 1.11/0.97 ((~hskp29) | c0_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[354, 349])).
% 1.11/0.97 tff(356,plain,
% 1.11/0.97 ((~hskp29) | c0_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[355, 349])).
% 1.11/0.97 tff(357,plain,
% 1.11/0.97 ((~hskp29) | c0_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[356, 349])).
% 1.11/0.97 tff(358,plain,
% 1.11/0.97 ((~hskp29) | c0_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[357, 349])).
% 1.11/0.97 tff(359,plain,
% 1.11/0.97 (c0_1(a301)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[358, 337])).
% 1.11/0.97 tff(360,plain,
% 1.11/0.97 (((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(361,plain,
% 1.11/0.97 ((hskp23 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301))) <=> (hskp23 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(362,plain,
% 1.11/0.97 (((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 1.11/0.97 inference(monotonicity,[status(thm)],[361])).
% 1.11/0.97 tff(363,plain,
% 1.11/0.97 (((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.11/0.97 inference(transitivity,[status(thm)],[362, 360])).
% 1.11/0.97 tff(364,plain,
% 1.11/0.97 ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301)))),
% 1.11/0.97 inference(quant_inst,[status(thm)],[])).
% 1.11/0.97 tff(365,plain,
% 1.11/0.97 ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[364, 363])).
% 1.11/0.97 tff(366,plain,
% 1.11/0.97 (~c1_1(a301)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[365, 135, 336, 359, 348, 325])).
% 1.11/0.97 tff(367,plain,
% 1.11/0.97 (((~hskp29) | c3_1(a301)) <=> ((~hskp29) | c3_1(a301))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(368,axiom,((~hskp29) | c3_1(a301)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 1.11/0.97 tff(369,plain,
% 1.11/0.97 ((~hskp29) | c3_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[368, 367])).
% 1.11/0.97 tff(370,plain,
% 1.11/0.97 ((~hskp29) | c3_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[369, 367])).
% 1.11/0.97 tff(371,plain,
% 1.11/0.97 ((~hskp29) | c3_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[370, 367])).
% 1.11/0.97 tff(372,plain,
% 1.11/0.97 ((~hskp29) | c3_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[371, 367])).
% 1.11/0.97 tff(373,plain,
% 1.11/0.97 ((~hskp29) | c3_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[372, 367])).
% 1.11/0.97 tff(374,plain,
% 1.11/0.97 ((~hskp29) | c3_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[373, 367])).
% 1.11/0.97 tff(375,plain,
% 1.11/0.97 ((~hskp29) | c3_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[374, 367])).
% 1.11/0.97 tff(376,plain,
% 1.11/0.97 ((~hskp29) | c3_1(a301)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[375, 367])).
% 1.11/0.97 tff(377,plain,
% 1.11/0.97 (c3_1(a301)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[376, 337])).
% 1.11/0.97 tff(378,plain,
% 1.11/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | (~ndr1_0) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | (~ndr1_0) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(379,plain,
% 1.11/0.97 (((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (c0_1(a341) | c3_1(a341) | (~ndr1_0) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(380,plain,
% 1.11/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | (~ndr1_0) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)) | (~c1_1(a341))))),
% 1.11/0.97 inference(monotonicity,[status(thm)],[379])).
% 1.11/0.97 tff(381,plain,
% 1.11/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | (~ndr1_0) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)))),
% 1.11/0.97 inference(transitivity,[status(thm)],[380, 378])).
% 1.11/0.97 tff(382,plain,
% 1.11/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 1.11/0.97 inference(quant_inst,[status(thm)],[])).
% 1.11/0.97 tff(383,plain,
% 1.11/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | (~ndr1_0) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)) | (~c1_1(a341))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[382, 381])).
% 1.11/0.97 tff(384,plain,
% 1.11/0.97 ($false),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[383, 135, 359, 348, 377, 294, 293, 292, 11, 366])).
% 1.11/0.97 tff(385,plain,((~hskp29) | (~c1_1(a341)) | c0_1(a341) | c3_1(a341) | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.11/0.97 tff(386,plain,
% 1.11/0.97 (~hskp29),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[385, 336, 293, 292, 294])).
% 1.11/0.97 tff(387,assumption,(hskp5), introduced(assumption)).
% 1.11/0.97 tff(388,plain,
% 1.11/0.97 (((~hskp5) | (~c0_1(a297))) <=> ((~hskp5) | (~c0_1(a297)))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(389,plain,
% 1.11/0.97 (((~c0_1(a297)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a297)))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(390,axiom,((~c0_1(a297)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.11/0.97 tff(391,plain,
% 1.11/0.97 ((~hskp5) | (~c0_1(a297))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[390, 389])).
% 1.11/0.97 tff(392,plain,
% 1.11/0.97 ((~hskp5) | (~c0_1(a297))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[391, 388])).
% 1.11/0.97 tff(393,plain,
% 1.11/0.97 (~c0_1(a297)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[392, 387])).
% 1.11/0.97 tff(394,plain,
% 1.11/0.97 (((~hskp5) | c1_1(a297)) <=> ((~hskp5) | c1_1(a297))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(395,axiom,((~hskp5) | c1_1(a297)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 1.11/0.97 tff(396,plain,
% 1.11/0.97 ((~hskp5) | c1_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[395, 394])).
% 1.11/0.97 tff(397,plain,
% 1.11/0.97 ((~hskp5) | c1_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[396, 394])).
% 1.11/0.97 tff(398,plain,
% 1.11/0.97 ((~hskp5) | c1_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[397, 394])).
% 1.11/0.97 tff(399,plain,
% 1.11/0.97 ((~hskp5) | c1_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[398, 394])).
% 1.11/0.97 tff(400,plain,
% 1.11/0.97 ((~hskp5) | c1_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[399, 394])).
% 1.11/0.97 tff(401,plain,
% 1.11/0.97 ((~hskp5) | c1_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[400, 394])).
% 1.11/0.97 tff(402,plain,
% 1.11/0.97 ((~hskp5) | c1_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[401, 394])).
% 1.11/0.97 tff(403,plain,
% 1.11/0.97 ((~hskp5) | c1_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[402, 394])).
% 1.11/0.97 tff(404,plain,
% 1.11/0.97 (c1_1(a297)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[403, 387])).
% 1.11/0.97 tff(405,plain,
% 1.11/0.97 (((~hskp5) | c2_1(a297)) <=> ((~hskp5) | c2_1(a297))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(406,axiom,((~hskp5) | c2_1(a297)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.11/0.97 tff(407,plain,
% 1.11/0.97 ((~hskp5) | c2_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[406, 405])).
% 1.11/0.97 tff(408,plain,
% 1.11/0.97 ((~hskp5) | c2_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[407, 405])).
% 1.11/0.97 tff(409,plain,
% 1.11/0.97 ((~hskp5) | c2_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[408, 405])).
% 1.11/0.97 tff(410,plain,
% 1.11/0.97 ((~hskp5) | c2_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[409, 405])).
% 1.11/0.97 tff(411,plain,
% 1.11/0.97 ((~hskp5) | c2_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[410, 405])).
% 1.11/0.97 tff(412,plain,
% 1.11/0.97 ((~hskp5) | c2_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[411, 405])).
% 1.11/0.97 tff(413,plain,
% 1.11/0.97 ((~hskp5) | c2_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[412, 405])).
% 1.11/0.97 tff(414,plain,
% 1.11/0.97 ((~hskp5) | c2_1(a297)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[413, 405])).
% 1.11/0.97 tff(415,plain,
% 1.11/0.97 (c2_1(a297)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[414, 387])).
% 1.11/0.97 tff(416,assumption,(~c0_1(a297)), introduced(assumption)).
% 1.11/0.97 tff(417,plain,
% 1.11/0.97 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a341)) | c2_1(a341))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a341)) | c2_1(a341))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(418,plain,
% 1.11/0.97 ((hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (hskp29 | c0_1(a341) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a341)) | c2_1(a341))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(419,plain,
% 1.11/0.97 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a341)) | c2_1(a341)))),
% 1.11/0.97 inference(monotonicity,[status(thm)],[418])).
% 1.11/0.97 tff(420,plain,
% 1.11/0.97 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a341)) | c2_1(a341))),
% 1.11/0.97 inference(transitivity,[status(thm)],[419, 417])).
% 1.11/0.97 tff(421,plain,
% 1.11/0.97 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 1.11/0.97 inference(quant_inst,[status(thm)],[])).
% 1.11/0.97 tff(422,plain,
% 1.11/0.97 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a341)) | c2_1(a341)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[421, 420])).
% 1.11/0.97 tff(423,plain,
% 1.11/0.97 ((~c2_1(a297)) | (~c1_1(a297))),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[422, 135, 53, 294, 293, 416, 63, 305])).
% 1.11/0.97 tff(424,plain,
% 1.11/0.97 ($false),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[423, 415, 404])).
% 1.11/0.97 tff(425,plain,((~hskp5) | hskp29 | (~c1_1(a341)) | c0_1(a341) | c0_1(a297) | c2_1(a341)), inference(lemma,lemma(discharge,[]))).
% 1.11/0.97 tff(426,plain,
% 1.11/0.97 ($false),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[425, 393, 387, 294, 293, 53, 305])).
% 1.11/0.97 tff(427,plain,((~hskp5) | (~c1_1(a341)) | c0_1(a341) | hskp29 | c2_1(a341)), inference(lemma,lemma(discharge,[]))).
% 1.11/0.97 tff(428,plain,
% 1.11/0.97 (~hskp5),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[427, 305, 293, 53, 294])).
% 1.11/0.97 tff(429,plain,
% 1.11/0.97 ((hskp22 | hskp16 | hskp5) <=> (hskp22 | hskp16 | hskp5)),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(430,plain,
% 1.11/0.97 (((hskp16 | hskp5) | hskp22) <=> (hskp22 | hskp16 | hskp5)),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(431,plain,
% 1.11/0.97 ((hskp5 | hskp16) <=> (hskp16 | hskp5)),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(432,plain,
% 1.11/0.97 (((hskp5 | hskp16) | hskp22) <=> ((hskp16 | hskp5) | hskp22)),
% 1.11/0.97 inference(monotonicity,[status(thm)],[431])).
% 1.11/0.97 tff(433,plain,
% 1.11/0.97 (((hskp5 | hskp16) | hskp22) <=> (hskp22 | hskp16 | hskp5)),
% 1.11/0.97 inference(transitivity,[status(thm)],[432, 430])).
% 1.11/0.97 tff(434,axiom,((hskp5 | hskp16) | hskp22), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 1.11/0.97 tff(435,plain,
% 1.11/0.97 (hskp22 | hskp16 | hskp5),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[434, 433])).
% 1.11/0.97 tff(436,plain,
% 1.11/0.97 (hskp22 | hskp16 | hskp5),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[435, 429])).
% 1.11/0.97 tff(437,plain,
% 1.11/0.97 (hskp22 | hskp16 | hskp5),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[436, 429])).
% 1.11/0.97 tff(438,plain,
% 1.11/0.97 (hskp22 | hskp16 | hskp5),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[437, 429])).
% 1.11/0.97 tff(439,plain,
% 1.11/0.97 (hskp22 | hskp16 | hskp5),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[438, 429])).
% 1.11/0.97 tff(440,plain,
% 1.11/0.97 (hskp22 | hskp16 | hskp5),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[439, 429])).
% 1.11/0.97 tff(441,plain,
% 1.11/0.97 (hskp22 | hskp16 | hskp5),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[440, 429])).
% 1.11/0.97 tff(442,plain,
% 1.11/0.97 (hskp22 | hskp16 | hskp5),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[441, 429])).
% 1.11/0.97 tff(443,plain,
% 1.11/0.97 (hskp16),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[442, 428, 166])).
% 1.11/0.97 tff(444,plain,
% 1.11/0.97 (((~hskp16) | c2_1(a315)) <=> ((~hskp16) | c2_1(a315))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(445,axiom,((~hskp16) | c2_1(a315)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.11/0.97 tff(446,plain,
% 1.11/0.97 ((~hskp16) | c2_1(a315)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[445, 444])).
% 1.11/0.97 tff(447,plain,
% 1.11/0.97 ((~hskp16) | c2_1(a315)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[446, 444])).
% 1.11/0.97 tff(448,plain,
% 1.11/0.97 ((~hskp16) | c2_1(a315)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[447, 444])).
% 1.11/0.97 tff(449,plain,
% 1.11/0.97 ((~hskp16) | c2_1(a315)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[448, 444])).
% 1.11/0.97 tff(450,plain,
% 1.11/0.97 ((~hskp16) | c2_1(a315)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[449, 444])).
% 1.11/0.97 tff(451,plain,
% 1.11/0.97 ((~hskp16) | c2_1(a315)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[450, 444])).
% 1.11/0.97 tff(452,plain,
% 1.11/0.97 ((~hskp16) | c2_1(a315)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[451, 444])).
% 1.11/0.97 tff(453,plain,
% 1.11/0.97 ((~hskp16) | c2_1(a315)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[452, 444])).
% 1.11/0.97 tff(454,plain,
% 1.11/0.97 (c2_1(a315)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[453, 443])).
% 1.11/0.97 tff(455,plain,
% 1.11/0.97 (((~hskp16) | (~c0_1(a315))) <=> ((~hskp16) | (~c0_1(a315)))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(456,plain,
% 1.11/0.97 (((~c0_1(a315)) | (~hskp16)) <=> ((~hskp16) | (~c0_1(a315)))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(457,axiom,((~c0_1(a315)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause116')).
% 1.11/0.97 tff(458,plain,
% 1.11/0.97 ((~hskp16) | (~c0_1(a315))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[457, 456])).
% 1.11/0.97 tff(459,plain,
% 1.11/0.97 ((~hskp16) | (~c0_1(a315))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[458, 455])).
% 1.11/0.97 tff(460,plain,
% 1.11/0.97 (~c0_1(a315)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[459, 443])).
% 1.11/0.97 tff(461,assumption,(c1_1(a315)), introduced(assumption)).
% 1.11/0.97 tff(462,assumption,(~c0_1(a315)), introduced(assumption)).
% 1.11/0.97 tff(463,assumption,(c2_1(a315)), introduced(assumption)).
% 1.11/0.97 tff(464,plain,
% 1.11/0.97 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a341)) | c2_1(a341))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a341)) | c2_1(a341))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(465,plain,
% 1.11/0.97 ((hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (hskp29 | c0_1(a341) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a341)) | c2_1(a341))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(466,plain,
% 1.11/0.97 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a341)) | c2_1(a341)))),
% 1.11/0.97 inference(monotonicity,[status(thm)],[465])).
% 1.11/0.97 tff(467,plain,
% 1.11/0.97 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a341)) | c2_1(a341))),
% 1.11/0.97 inference(transitivity,[status(thm)],[466, 464])).
% 1.11/0.97 tff(468,plain,
% 1.11/0.97 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 1.11/0.97 inference(quant_inst,[status(thm)],[])).
% 1.11/0.97 tff(469,plain,
% 1.11/0.97 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a341)) | c2_1(a341)),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[468, 467])).
% 1.11/0.97 tff(470,plain,
% 1.11/0.97 ($false),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[469, 135, 53, 294, 463, 293, 462, 63, 305, 461])).
% 1.11/0.97 tff(471,plain,(c2_1(a341) | hskp29 | (~c1_1(a341)) | (~c2_1(a315)) | c0_1(a341) | c0_1(a315) | (~c1_1(a315))), inference(lemma,lemma(discharge,[]))).
% 1.11/0.97 tff(472,plain,
% 1.11/0.97 (~c1_1(a315)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[471, 460, 294, 53, 293, 305, 454])).
% 1.11/0.97 tff(473,plain,
% 1.11/0.97 (((~hskp16) | (~c3_1(a315))) <=> ((~hskp16) | (~c3_1(a315)))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(474,plain,
% 1.11/0.97 (((~c3_1(a315)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a315)))),
% 1.11/0.97 inference(rewrite,[status(thm)],[])).
% 1.11/0.97 tff(475,axiom,((~c3_1(a315)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.11/0.97 tff(476,plain,
% 1.11/0.97 ((~hskp16) | (~c3_1(a315))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[475, 474])).
% 1.11/0.97 tff(477,plain,
% 1.11/0.97 ((~hskp16) | (~c3_1(a315))),
% 1.11/0.97 inference(modus_ponens,[status(thm)],[476, 473])).
% 1.11/0.97 tff(478,plain,
% 1.11/0.97 (~c3_1(a315)),
% 1.11/0.97 inference(unit_resolution,[status(thm)],[477, 443])).
% 1.11/0.98 tff(479,plain,
% 1.11/0.98 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(480,plain,
% 1.11/0.98 ((hskp3 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315)) <=> (hskp3 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(481,plain,
% 1.11/0.98 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315)))),
% 1.11/0.98 inference(monotonicity,[status(thm)],[480])).
% 1.11/0.98 tff(482,plain,
% 1.11/0.98 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))),
% 1.11/0.98 inference(transitivity,[status(thm)],[481, 479])).
% 1.11/0.98 tff(483,plain,
% 1.11/0.98 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315))),
% 1.11/0.98 inference(quant_inst,[status(thm)],[])).
% 1.11/0.98 tff(484,plain,
% 1.11/0.98 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[483, 482])).
% 1.11/0.98 tff(485,plain,
% 1.11/0.98 ($false),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[484, 135, 64, 460, 478, 93, 472])).
% 1.11/0.98 tff(486,plain,(c2_1(a341) | hskp3 | (~c1_1(a341)) | hskp29 | c0_1(a341)), inference(lemma,lemma(discharge,[]))).
% 1.11/0.98 tff(487,plain,
% 1.11/0.98 (c2_1(a341)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[486, 64, 294, 386, 293])).
% 1.11/0.98 tff(488,plain,
% 1.11/0.98 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(489,plain,
% 1.11/0.98 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.11/0.98 inference(quant_intro,[status(thm)],[488])).
% 1.11/0.98 tff(490,plain,
% 1.11/0.98 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(491,plain,
% 1.11/0.98 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp7) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp7))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(492,plain,
% 1.11/0.98 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.11/0.98 inference(quant_intro,[status(thm)],[491])).
% 1.11/0.98 tff(493,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.11/0.98 tff(494,plain,
% 1.11/0.98 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[493, 492])).
% 1.11/0.98 tff(495,plain,
% 1.11/0.98 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[494, 490])).
% 1.11/0.98 tff(496,plain,(
% 1.11/0.98 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.11/0.98 inference(skolemize,[status(sab)],[495])).
% 1.11/0.98 tff(497,plain,
% 1.11/0.98 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[496, 489])).
% 1.11/0.98 tff(498,plain,
% 1.11/0.98 ((hskp23 | hskp3 | hskp0) <=> (hskp23 | hskp3 | hskp0)),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(499,plain,
% 1.11/0.98 (((hskp23 | hskp3) | hskp0) <=> (hskp23 | hskp3 | hskp0)),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(500,plain,
% 1.11/0.98 ((hskp3 | hskp23) <=> (hskp23 | hskp3)),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(501,plain,
% 1.11/0.98 (((hskp3 | hskp23) | hskp0) <=> ((hskp23 | hskp3) | hskp0)),
% 1.11/0.98 inference(monotonicity,[status(thm)],[500])).
% 1.11/0.98 tff(502,plain,
% 1.11/0.98 (((hskp3 | hskp23) | hskp0) <=> (hskp23 | hskp3 | hskp0)),
% 1.11/0.98 inference(transitivity,[status(thm)],[501, 499])).
% 1.11/0.98 tff(503,axiom,((hskp3 | hskp23) | hskp0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause35')).
% 1.11/0.98 tff(504,plain,
% 1.11/0.98 (hskp23 | hskp3 | hskp0),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[503, 502])).
% 1.11/0.98 tff(505,plain,
% 1.11/0.98 (hskp23 | hskp3 | hskp0),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[504, 498])).
% 1.11/0.98 tff(506,plain,
% 1.11/0.98 (hskp23 | hskp3 | hskp0),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[505, 498])).
% 1.11/0.98 tff(507,plain,
% 1.11/0.98 (hskp23 | hskp3 | hskp0),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[506, 498])).
% 1.11/0.98 tff(508,plain,
% 1.11/0.98 (hskp23 | hskp3 | hskp0),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[507, 498])).
% 1.11/0.98 tff(509,plain,
% 1.11/0.98 (hskp23 | hskp3 | hskp0),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[508, 498])).
% 1.11/0.98 tff(510,plain,
% 1.11/0.98 (hskp23 | hskp3 | hskp0),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[509, 498])).
% 1.11/0.98 tff(511,plain,
% 1.11/0.98 (hskp23 | hskp3 | hskp0),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[510, 498])).
% 1.11/0.98 tff(512,plain,
% 1.11/0.98 (hskp0),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[511, 64, 336])).
% 1.11/0.98 tff(513,plain,
% 1.11/0.98 (((~hskp0) | (~c2_1(a291))) <=> ((~hskp0) | (~c2_1(a291)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(514,plain,
% 1.11/0.98 (((~c2_1(a291)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a291)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(515,axiom,((~c2_1(a291)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.11/0.98 tff(516,plain,
% 1.11/0.98 ((~hskp0) | (~c2_1(a291))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[515, 514])).
% 1.11/0.98 tff(517,plain,
% 1.11/0.98 ((~hskp0) | (~c2_1(a291))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[516, 513])).
% 1.11/0.98 tff(518,plain,
% 1.11/0.98 (~c2_1(a291)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[517, 512])).
% 1.11/0.98 tff(519,plain,
% 1.11/0.98 (((~hskp0) | c1_1(a291)) <=> ((~hskp0) | c1_1(a291))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(520,axiom,((~hskp0) | c1_1(a291)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.11/0.98 tff(521,plain,
% 1.11/0.98 ((~hskp0) | c1_1(a291)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[520, 519])).
% 1.11/0.98 tff(522,plain,
% 1.11/0.98 ((~hskp0) | c1_1(a291)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[521, 519])).
% 1.11/0.98 tff(523,plain,
% 1.11/0.98 ((~hskp0) | c1_1(a291)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[522, 519])).
% 1.11/0.98 tff(524,plain,
% 1.11/0.98 ((~hskp0) | c1_1(a291)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[523, 519])).
% 1.11/0.98 tff(525,plain,
% 1.11/0.98 ((~hskp0) | c1_1(a291)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[524, 519])).
% 1.11/0.98 tff(526,plain,
% 1.11/0.98 ((~hskp0) | c1_1(a291)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[525, 519])).
% 1.11/0.98 tff(527,plain,
% 1.11/0.98 ((~hskp0) | c1_1(a291)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[526, 519])).
% 1.11/0.98 tff(528,plain,
% 1.11/0.98 ((~hskp0) | c1_1(a291)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[527, 519])).
% 1.11/0.98 tff(529,plain,
% 1.11/0.98 (c1_1(a291)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[528, 512])).
% 1.11/0.98 tff(530,plain,
% 1.11/0.98 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c2_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c2_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(531,plain,
% 1.11/0.98 ((hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a291) | c0_1(a291) | (~c1_1(a291))) <=> (hskp29 | c0_1(a341) | c2_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(532,plain,
% 1.11/0.98 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a291) | c0_1(a291) | (~c1_1(a291)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c2_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 1.11/0.98 inference(monotonicity,[status(thm)],[531])).
% 1.11/0.98 tff(533,plain,
% 1.11/0.98 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a291) | c0_1(a291) | (~c1_1(a291)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c2_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.11/0.98 inference(transitivity,[status(thm)],[532, 530])).
% 1.11/0.98 tff(534,plain,
% 1.11/0.98 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a291) | c0_1(a291) | (~c1_1(a291)))),
% 1.11/0.98 inference(quant_inst,[status(thm)],[])).
% 1.11/0.98 tff(535,plain,
% 1.11/0.98 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c2_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | (~c1_1(a341)) | (~c2_1(a341))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[534, 533])).
% 1.11/0.98 tff(536,plain,
% 1.11/0.98 (c0_1(a291) | (~c2_1(a341))),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[535, 135, 386, 294, 529, 293, 518, 63])).
% 1.11/0.98 tff(537,plain,
% 1.11/0.98 (c0_1(a291)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[536, 487])).
% 1.11/0.98 tff(538,plain,
% 1.11/0.98 (((~hskp0) | (~c3_1(a291))) <=> ((~hskp0) | (~c3_1(a291)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(539,plain,
% 1.11/0.98 (((~c3_1(a291)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a291)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(540,axiom,((~c3_1(a291)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.11/0.98 tff(541,plain,
% 1.11/0.98 ((~hskp0) | (~c3_1(a291))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[540, 539])).
% 1.11/0.98 tff(542,plain,
% 1.11/0.98 ((~hskp0) | (~c3_1(a291))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[541, 538])).
% 1.11/0.98 tff(543,plain,
% 1.11/0.98 (~c3_1(a291)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[542, 512])).
% 1.11/0.98 tff(544,assumption,(hskp8), introduced(assumption)).
% 1.11/0.98 tff(545,plain,
% 1.11/0.98 (((~hskp8) | (~c1_1(a300))) <=> ((~hskp8) | (~c1_1(a300)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(546,plain,
% 1.11/0.98 (((~c1_1(a300)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a300)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(547,axiom,((~c1_1(a300)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 1.11/0.98 tff(548,plain,
% 1.11/0.98 ((~hskp8) | (~c1_1(a300))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[547, 546])).
% 1.11/0.98 tff(549,plain,
% 1.11/0.98 ((~hskp8) | (~c1_1(a300))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[548, 545])).
% 1.11/0.98 tff(550,plain,
% 1.11/0.98 (~c1_1(a300)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[549, 544])).
% 1.11/0.98 tff(551,plain,
% 1.11/0.98 (((~hskp8) | c3_1(a300)) <=> ((~hskp8) | c3_1(a300))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(552,axiom,((~hskp8) | c3_1(a300)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.11/0.98 tff(553,plain,
% 1.11/0.98 ((~hskp8) | c3_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[552, 551])).
% 1.11/0.98 tff(554,plain,
% 1.11/0.98 ((~hskp8) | c3_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[553, 551])).
% 1.11/0.98 tff(555,plain,
% 1.11/0.98 ((~hskp8) | c3_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[554, 551])).
% 1.11/0.98 tff(556,plain,
% 1.11/0.98 ((~hskp8) | c3_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[555, 551])).
% 1.11/0.98 tff(557,plain,
% 1.11/0.98 ((~hskp8) | c3_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[556, 551])).
% 1.11/0.98 tff(558,plain,
% 1.11/0.98 ((~hskp8) | c3_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[557, 551])).
% 1.11/0.98 tff(559,plain,
% 1.11/0.98 ((~hskp8) | c3_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[558, 551])).
% 1.11/0.98 tff(560,plain,
% 1.11/0.98 ((~hskp8) | c3_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[559, 551])).
% 1.11/0.98 tff(561,plain,
% 1.11/0.98 (c3_1(a300)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[560, 544])).
% 1.11/0.98 tff(562,plain,
% 1.11/0.98 (((~hskp8) | c0_1(a300)) <=> ((~hskp8) | c0_1(a300))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(563,axiom,((~hskp8) | c0_1(a300)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.11/0.98 tff(564,plain,
% 1.11/0.98 ((~hskp8) | c0_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[563, 562])).
% 1.11/0.98 tff(565,plain,
% 1.11/0.98 ((~hskp8) | c0_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[564, 562])).
% 1.11/0.98 tff(566,plain,
% 1.11/0.98 ((~hskp8) | c0_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[565, 562])).
% 1.11/0.98 tff(567,plain,
% 1.11/0.98 ((~hskp8) | c0_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[566, 562])).
% 1.11/0.98 tff(568,plain,
% 1.11/0.98 ((~hskp8) | c0_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[567, 562])).
% 1.11/0.98 tff(569,plain,
% 1.11/0.98 ((~hskp8) | c0_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[568, 562])).
% 1.11/0.98 tff(570,plain,
% 1.11/0.98 ((~hskp8) | c0_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[569, 562])).
% 1.11/0.98 tff(571,plain,
% 1.11/0.98 ((~hskp8) | c0_1(a300)),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[570, 562])).
% 1.11/0.98 tff(572,plain,
% 1.11/0.98 (c0_1(a300)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[571, 544])).
% 1.11/0.98 tff(573,plain,
% 1.11/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)) | (~c1_1(a341)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(574,plain,
% 1.11/0.98 (((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)) | (~c1_1(a341)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(575,plain,
% 1.11/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)) | (~c1_1(a341))))),
% 1.11/0.98 inference(monotonicity,[status(thm)],[574])).
% 1.11/0.98 tff(576,plain,
% 1.11/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)) | (~c1_1(a341)))),
% 1.11/0.98 inference(transitivity,[status(thm)],[575, 573])).
% 1.11/0.98 tff(577,plain,
% 1.11/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 1.11/0.98 inference(quant_inst,[status(thm)],[])).
% 1.11/0.98 tff(578,plain,
% 1.11/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)) | (~c1_1(a341))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[577, 576])).
% 1.11/0.98 tff(579,plain,
% 1.11/0.98 (~c2_1(a300)),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[578, 135, 294, 572, 561, 293, 292, 550, 11])).
% 1.11/0.98 tff(580,assumption,(c0_1(a291)), introduced(assumption)).
% 1.11/0.98 tff(581,assumption,(c2_1(a341)), introduced(assumption)).
% 1.11/0.98 tff(582,plain,
% 1.11/0.98 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(583,plain,
% 1.11/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/0.98 inference(quant_intro,[status(thm)],[582])).
% 1.11/0.98 tff(584,plain,
% 1.11/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(585,plain,
% 1.11/0.98 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(586,plain,
% 1.11/0.98 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/0.98 inference(quant_intro,[status(thm)],[585])).
% 1.11/0.98 tff(587,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.11/0.98 tff(588,plain,
% 1.11/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[587, 586])).
% 1.11/0.98 tff(589,plain,
% 1.11/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[588, 584])).
% 1.11/0.98 tff(590,plain,(
% 1.11/0.98 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/0.98 inference(skolemize,[status(sab)],[589])).
% 1.11/0.98 tff(591,plain,
% 1.11/0.98 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[590, 583])).
% 1.11/0.98 tff(592,assumption,(~c3_1(a291)), introduced(assumption)).
% 1.11/0.98 tff(593,assumption,(~c2_1(a291)), introduced(assumption)).
% 1.11/0.98 tff(594,plain,
% 1.11/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a341)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(595,plain,
% 1.11/0.98 (((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a341)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(596,plain,
% 1.11/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a341))))),
% 1.11/0.98 inference(monotonicity,[status(thm)],[595])).
% 1.11/0.98 tff(597,plain,
% 1.11/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a341)))),
% 1.11/0.98 inference(transitivity,[status(thm)],[596, 594])).
% 1.11/0.98 tff(598,plain,
% 1.11/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 1.11/0.98 inference(quant_inst,[status(thm)],[])).
% 1.11/0.98 tff(599,plain,
% 1.11/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a341))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[598, 597])).
% 1.11/0.98 tff(600,plain,
% 1.11/0.98 ($false),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[599, 135, 572, 561, 293, 292, 593, 592, 591, 581, 580, 579])).
% 1.11/0.98 tff(601,plain,((~hskp8) | c0_1(a341) | c3_1(a341) | c2_1(a291) | c3_1(a291) | (~c2_1(a341)) | (~c0_1(a291)) | (~c1_1(a341))), inference(lemma,lemma(discharge,[]))).
% 1.11/0.98 tff(602,plain,
% 1.11/0.98 (~hskp8),
% 1.11/0.98 inference(unit_resolution,[status(thm)],[601, 518, 292, 293, 543, 487, 537, 294])).
% 1.11/0.98 tff(603,plain,
% 1.11/0.98 (^[U: $i] : refl((hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(604,plain,
% 1.11/0.98 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.11/0.98 inference(quant_intro,[status(thm)],[603])).
% 1.11/0.98 tff(605,plain,
% 1.11/0.98 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.11/0.98 inference(rewrite,[status(thm)],[])).
% 1.11/0.98 tff(606,plain,
% 1.11/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> ((hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp23))), rewrite(((hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp23) <=> (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 1.11/0.98 inference(bind,[status(th)],[])).
% 1.11/0.98 tff(607,plain,
% 1.11/0.98 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23) <=> ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.11/0.98 inference(quant_intro,[status(thm)],[606])).
% 1.11/0.98 tff(608,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 1.11/0.98 tff(609,plain,
% 1.11/0.98 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[608, 607])).
% 1.11/0.98 tff(610,plain,
% 1.11/0.98 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.11/0.98 inference(modus_ponens,[status(thm)],[609, 605])).
% 1.11/0.98 tff(611,plain,(
% 1.11/0.98 ![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.11/0.98 inference(skolemize,[status(sab)],[610])).
% 1.11/0.98 tff(612,plain,
% 1.11/0.98 (![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[611, 604])).
% 1.11/0.99 tff(613,assumption,(hskp12), introduced(assumption)).
% 1.11/0.99 tff(614,plain,
% 1.11/0.99 (((~hskp12) | (~c3_1(a307))) <=> ((~hskp12) | (~c3_1(a307)))),
% 1.11/0.99 inference(rewrite,[status(thm)],[])).
% 1.11/0.99 tff(615,plain,
% 1.11/0.99 (((~c3_1(a307)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a307)))),
% 1.11/0.99 inference(rewrite,[status(thm)],[])).
% 1.11/0.99 tff(616,axiom,((~c3_1(a307)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.11/0.99 tff(617,plain,
% 1.11/0.99 ((~hskp12) | (~c3_1(a307))),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[616, 615])).
% 1.11/0.99 tff(618,plain,
% 1.11/0.99 ((~hskp12) | (~c3_1(a307))),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[617, 614])).
% 1.11/0.99 tff(619,plain,
% 1.11/0.99 (~c3_1(a307)),
% 1.11/0.99 inference(unit_resolution,[status(thm)],[618, 613])).
% 1.11/0.99 tff(620,plain,
% 1.11/0.99 (((~hskp12) | (~c1_1(a307))) <=> ((~hskp12) | (~c1_1(a307)))),
% 1.11/0.99 inference(rewrite,[status(thm)],[])).
% 1.11/0.99 tff(621,plain,
% 1.11/0.99 (((~c1_1(a307)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a307)))),
% 1.11/0.99 inference(rewrite,[status(thm)],[])).
% 1.11/0.99 tff(622,axiom,((~c1_1(a307)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.11/0.99 tff(623,plain,
% 1.11/0.99 ((~hskp12) | (~c1_1(a307))),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[622, 621])).
% 1.11/0.99 tff(624,plain,
% 1.11/0.99 ((~hskp12) | (~c1_1(a307))),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[623, 620])).
% 1.11/0.99 tff(625,plain,
% 1.11/0.99 (~c1_1(a307)),
% 1.11/0.99 inference(unit_resolution,[status(thm)],[624, 613])).
% 1.11/0.99 tff(626,plain,
% 1.11/0.99 (((~hskp12) | c2_1(a307)) <=> ((~hskp12) | c2_1(a307))),
% 1.11/0.99 inference(rewrite,[status(thm)],[])).
% 1.11/0.99 tff(627,axiom,((~hskp12) | c2_1(a307)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 1.11/0.99 tff(628,plain,
% 1.11/0.99 ((~hskp12) | c2_1(a307)),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[627, 626])).
% 1.11/0.99 tff(629,plain,
% 1.11/0.99 ((~hskp12) | c2_1(a307)),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[628, 626])).
% 1.11/0.99 tff(630,plain,
% 1.11/0.99 ((~hskp12) | c2_1(a307)),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[629, 626])).
% 1.11/0.99 tff(631,plain,
% 1.11/0.99 ((~hskp12) | c2_1(a307)),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[630, 626])).
% 1.11/0.99 tff(632,plain,
% 1.11/0.99 ((~hskp12) | c2_1(a307)),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[631, 626])).
% 1.11/0.99 tff(633,plain,
% 1.11/0.99 ((~hskp12) | c2_1(a307)),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[632, 626])).
% 1.11/0.99 tff(634,plain,
% 1.11/0.99 ((~hskp12) | c2_1(a307)),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[633, 626])).
% 1.11/0.99 tff(635,plain,
% 1.11/0.99 ((~hskp12) | c2_1(a307)),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[634, 626])).
% 1.11/0.99 tff(636,plain,
% 1.11/0.99 (c2_1(a307)),
% 1.11/0.99 inference(unit_resolution,[status(thm)],[635, 613])).
% 1.11/0.99 tff(637,assumption,(~hskp8), introduced(assumption)).
% 1.11/0.99 tff(638,plain,
% 1.11/0.99 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | c1_1(a307) | c3_1(a307) | (~ndr1_0) | (~c2_1(a307)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a307) | c3_1(a307) | (~ndr1_0) | (~c2_1(a307)))),
% 1.11/0.99 inference(rewrite,[status(thm)],[])).
% 1.11/0.99 tff(639,plain,
% 1.11/0.99 ((hskp23 | hskp8 | (~ndr1_0) | c3_1(a307) | c1_1(a307) | (~c2_1(a307))) <=> (hskp23 | hskp8 | c1_1(a307) | c3_1(a307) | (~ndr1_0) | (~c2_1(a307)))),
% 1.11/0.99 inference(rewrite,[status(thm)],[])).
% 1.11/0.99 tff(640,plain,
% 1.11/0.99 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c3_1(a307) | c1_1(a307) | (~c2_1(a307)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | c1_1(a307) | c3_1(a307) | (~ndr1_0) | (~c2_1(a307))))),
% 1.11/0.99 inference(monotonicity,[status(thm)],[639])).
% 1.11/0.99 tff(641,plain,
% 1.11/0.99 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c3_1(a307) | c1_1(a307) | (~c2_1(a307)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a307) | c3_1(a307) | (~ndr1_0) | (~c2_1(a307)))),
% 1.11/0.99 inference(transitivity,[status(thm)],[640, 638])).
% 1.11/0.99 tff(642,plain,
% 1.11/0.99 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c3_1(a307) | c1_1(a307) | (~c2_1(a307)))),
% 1.11/0.99 inference(quant_inst,[status(thm)],[])).
% 1.11/0.99 tff(643,plain,
% 1.11/0.99 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a307) | c3_1(a307) | (~ndr1_0) | (~c2_1(a307))),
% 1.11/0.99 inference(modus_ponens,[status(thm)],[642, 641])).
% 1.11/0.99 tff(644,plain,
% 1.11/0.99 ($false),
% 1.11/0.99 inference(unit_resolution,[status(thm)],[643, 135, 336, 637, 636, 625, 619, 612])).
% 1.11/0.99 tff(645,plain,((~hskp12) | hskp23 | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.11/0.99 tff(646,plain,
% 1.11/0.99 (~hskp12),
% 1.11/0.99 inference(unit_resolution,[status(thm)],[645, 602, 336])).
% 1.11/0.99 tff(647,plain,
% 1.11/0.99 (^[U: $i] : refl((hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.11/0.99 inference(bind,[status(th)],[])).
% 1.11/0.99 tff(648,plain,
% 1.11/0.99 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.11/0.99 inference(quant_intro,[status(thm)],[647])).
% 1.11/0.99 tff(649,plain,
% 1.11/0.99 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.11/0.99 inference(rewrite,[status(thm)],[])).
% 1.11/0.99 tff(650,plain,
% 1.11/0.99 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> ((hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp12))), rewrite(((hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.18/0.99 inference(bind,[status(th)],[])).
% 1.18/0.99 tff(651,plain,
% 1.18/0.99 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) | hskp12) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.18/0.99 inference(quant_intro,[status(thm)],[650])).
% 1.18/0.99 tff(652,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp11) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.18/0.99 tff(653,plain,
% 1.18/0.99 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[652, 651])).
% 1.18/0.99 tff(654,plain,
% 1.18/0.99 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[653, 649])).
% 1.18/0.99 tff(655,plain,(
% 1.18/0.99 ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.18/0.99 inference(skolemize,[status(sab)],[654])).
% 1.18/0.99 tff(656,plain,
% 1.18/0.99 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[655, 648])).
% 1.18/0.99 tff(657,plain,
% 1.18/0.99 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c1_1(a341)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c1_1(a341)))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(658,plain,
% 1.18/0.99 ((hskp12 | hskp11 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (hskp12 | hskp11 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c1_1(a341)))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(659,plain,
% 1.18/0.99 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c1_1(a341))))),
% 1.18/0.99 inference(monotonicity,[status(thm)],[658])).
% 1.18/0.99 tff(660,plain,
% 1.18/0.99 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c1_1(a341)))),
% 1.18/0.99 inference(transitivity,[status(thm)],[659, 657])).
% 1.18/0.99 tff(661,plain,
% 1.18/0.99 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 1.18/0.99 inference(quant_inst,[status(thm)],[])).
% 1.18/0.99 tff(662,plain,
% 1.18/0.99 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c1_1(a341))),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[661, 660])).
% 1.18/0.99 tff(663,plain,
% 1.18/0.99 (hskp12 | hskp11),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[662, 135, 294, 293, 292, 656])).
% 1.18/0.99 tff(664,plain,
% 1.18/0.99 (hskp11),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[663, 646])).
% 1.18/0.99 tff(665,plain,
% 1.18/0.99 (((~hskp11) | (~c0_1(a306))) <=> ((~hskp11) | (~c0_1(a306)))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(666,plain,
% 1.18/0.99 (((~c0_1(a306)) | (~hskp11)) <=> ((~hskp11) | (~c0_1(a306)))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(667,axiom,((~c0_1(a306)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.18/0.99 tff(668,plain,
% 1.18/0.99 ((~hskp11) | (~c0_1(a306))),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[667, 666])).
% 1.18/0.99 tff(669,plain,
% 1.18/0.99 ((~hskp11) | (~c0_1(a306))),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[668, 665])).
% 1.18/0.99 tff(670,plain,
% 1.18/0.99 (~c0_1(a306)),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[669, 664])).
% 1.18/0.99 tff(671,plain,
% 1.18/0.99 (((~hskp11) | c3_1(a306)) <=> ((~hskp11) | c3_1(a306))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(672,axiom,((~hskp11) | c3_1(a306)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.18/0.99 tff(673,plain,
% 1.18/0.99 ((~hskp11) | c3_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[672, 671])).
% 1.18/0.99 tff(674,plain,
% 1.18/0.99 ((~hskp11) | c3_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[673, 671])).
% 1.18/0.99 tff(675,plain,
% 1.18/0.99 ((~hskp11) | c3_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[674, 671])).
% 1.18/0.99 tff(676,plain,
% 1.18/0.99 ((~hskp11) | c3_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[675, 671])).
% 1.18/0.99 tff(677,plain,
% 1.18/0.99 ((~hskp11) | c3_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[676, 671])).
% 1.18/0.99 tff(678,plain,
% 1.18/0.99 ((~hskp11) | c3_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[677, 671])).
% 1.18/0.99 tff(679,plain,
% 1.18/0.99 ((~hskp11) | c3_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[678, 671])).
% 1.18/0.99 tff(680,plain,
% 1.18/0.99 ((~hskp11) | c3_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[679, 671])).
% 1.18/0.99 tff(681,plain,
% 1.18/0.99 (c3_1(a306)),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[680, 664])).
% 1.18/0.99 tff(682,plain,
% 1.18/0.99 (((~hskp11) | c1_1(a306)) <=> ((~hskp11) | c1_1(a306))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(683,axiom,((~hskp11) | c1_1(a306)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.18/0.99 tff(684,plain,
% 1.18/0.99 ((~hskp11) | c1_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[683, 682])).
% 1.18/0.99 tff(685,plain,
% 1.18/0.99 ((~hskp11) | c1_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[684, 682])).
% 1.18/0.99 tff(686,plain,
% 1.18/0.99 ((~hskp11) | c1_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[685, 682])).
% 1.18/0.99 tff(687,plain,
% 1.18/0.99 ((~hskp11) | c1_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[686, 682])).
% 1.18/0.99 tff(688,plain,
% 1.18/0.99 ((~hskp11) | c1_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[687, 682])).
% 1.18/0.99 tff(689,plain,
% 1.18/0.99 ((~hskp11) | c1_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[688, 682])).
% 1.18/0.99 tff(690,plain,
% 1.18/0.99 ((~hskp11) | c1_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[689, 682])).
% 1.18/0.99 tff(691,plain,
% 1.18/0.99 ((~hskp11) | c1_1(a306)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[690, 682])).
% 1.18/0.99 tff(692,plain,
% 1.18/0.99 (c1_1(a306)),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[691, 664])).
% 1.18/0.99 tff(693,plain,
% 1.18/0.99 (~hskp12),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[645, 637, 336])).
% 1.18/0.99 tff(694,plain,
% 1.18/0.99 (hskp11),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[663, 693])).
% 1.18/0.99 tff(695,plain,
% 1.18/0.99 (~c0_1(a306)),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[669, 694])).
% 1.18/0.99 tff(696,plain,
% 1.18/0.99 (c1_1(a306)),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[691, 694])).
% 1.18/0.99 tff(697,plain,
% 1.18/0.99 (c3_1(a306)),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[680, 694])).
% 1.18/0.99 tff(698,assumption,(c3_1(a306)), introduced(assumption)).
% 1.18/0.99 tff(699,plain,
% 1.18/0.99 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 1.18/0.99 inference(bind,[status(th)],[])).
% 1.18/0.99 tff(700,plain,
% 1.18/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.18/0.99 inference(quant_intro,[status(thm)],[699])).
% 1.18/0.99 tff(701,plain,
% 1.18/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(702,plain,
% 1.18/0.99 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 1.18/0.99 inference(bind,[status(th)],[])).
% 1.18/0.99 tff(703,plain,
% 1.18/0.99 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.18/0.99 inference(quant_intro,[status(thm)],[702])).
% 1.18/0.99 tff(704,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.18/0.99 tff(705,plain,
% 1.18/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[704, 703])).
% 1.18/0.99 tff(706,plain,
% 1.18/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[705, 701])).
% 1.18/0.99 tff(707,plain,(
% 1.18/0.99 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.18/0.99 inference(skolemize,[status(sab)],[706])).
% 1.18/0.99 tff(708,plain,
% 1.18/0.99 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[707, 700])).
% 1.18/0.99 tff(709,assumption,(~c0_1(a306)), introduced(assumption)).
% 1.18/0.99 tff(710,plain,
% 1.18/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a341) | c3_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c2_1(a306)) | (~c1_1(a341)) | c2_1(a341))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a341) | c3_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c2_1(a306)) | (~c1_1(a341)) | c2_1(a341))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(711,plain,
% 1.18/0.99 (((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a306) | (~c3_1(a306)) | (~c2_1(a306)) | c3_1(a341) | c2_1(a341) | c0_1(a341)) <=> (c0_1(a341) | c3_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c2_1(a306)) | (~c1_1(a341)) | c2_1(a341))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(712,plain,
% 1.18/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a306) | (~c3_1(a306)) | (~c2_1(a306)) | c3_1(a341) | c2_1(a341) | c0_1(a341))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a341) | c3_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c2_1(a306)) | (~c1_1(a341)) | c2_1(a341)))),
% 1.18/0.99 inference(monotonicity,[status(thm)],[711])).
% 1.18/0.99 tff(713,plain,
% 1.18/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a306) | (~c3_1(a306)) | (~c2_1(a306)) | c3_1(a341) | c2_1(a341) | c0_1(a341))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a341) | c3_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c2_1(a306)) | (~c1_1(a341)) | c2_1(a341))),
% 1.18/0.99 inference(transitivity,[status(thm)],[712, 710])).
% 1.18/0.99 tff(714,plain,
% 1.18/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a306) | (~c3_1(a306)) | (~c2_1(a306)) | c3_1(a341) | c2_1(a341) | c0_1(a341))),
% 1.18/0.99 inference(quant_inst,[status(thm)],[])).
% 1.18/0.99 tff(715,plain,
% 1.18/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a341) | c3_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c2_1(a306)) | (~c1_1(a341)) | c2_1(a341)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[714, 713])).
% 1.18/0.99 tff(716,plain,
% 1.18/0.99 ((~c3_1(a306)) | (~c2_1(a306)) | c2_1(a341)),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[715, 135, 294, 293, 292, 709, 708])).
% 1.18/0.99 tff(717,plain,
% 1.18/0.99 (~c2_1(a306)),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[716, 305, 698])).
% 1.18/0.99 tff(718,assumption,(c1_1(a306)), introduced(assumption)).
% 1.18/0.99 tff(719,plain,
% 1.18/0.99 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c3_1(a306)) | c2_1(a306) | (~c1_1(a306)) | c2_1(a341))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c3_1(a306)) | c2_1(a306) | (~c1_1(a306)) | c2_1(a341))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(720,plain,
% 1.18/0.99 ((hskp8 | (~ndr1_0) | c2_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a341) | c0_1(a341) | c3_1(a341)) <=> (hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c3_1(a306)) | c2_1(a306) | (~c1_1(a306)) | c2_1(a341))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(721,plain,
% 1.18/0.99 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a341) | c0_1(a341) | c3_1(a341))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c3_1(a306)) | c2_1(a306) | (~c1_1(a306)) | c2_1(a341)))),
% 1.18/0.99 inference(monotonicity,[status(thm)],[720])).
% 1.18/0.99 tff(722,plain,
% 1.18/0.99 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a341) | c0_1(a341) | c3_1(a341))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c3_1(a306)) | c2_1(a306) | (~c1_1(a306)) | c2_1(a341))),
% 1.18/0.99 inference(transitivity,[status(thm)],[721, 719])).
% 1.18/0.99 tff(723,plain,
% 1.18/0.99 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a341) | c0_1(a341) | c3_1(a341))),
% 1.18/0.99 inference(quant_inst,[status(thm)],[])).
% 1.18/0.99 tff(724,plain,
% 1.18/0.99 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c3_1(a306)) | c2_1(a306) | (~c1_1(a306)) | c2_1(a341)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[723, 722])).
% 1.18/0.99 tff(725,plain,
% 1.18/0.99 ($false),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[724, 135, 637, 718, 698, 293, 292, 315, 305, 717])).
% 1.18/0.99 tff(726,plain,(c2_1(a341) | hskp8 | (~c1_1(a306)) | (~c3_1(a306)) | c0_1(a341) | c3_1(a341) | (~c1_1(a341)) | c0_1(a306)), inference(lemma,lemma(discharge,[]))).
% 1.18/0.99 tff(727,plain,
% 1.18/0.99 (c2_1(a341)),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[726, 697, 696, 637, 293, 292, 294, 695])).
% 1.18/0.99 tff(728,assumption,(c1_1(a291)), introduced(assumption)).
% 1.18/0.99 tff(729,plain,
% 1.18/0.99 (c0_1(a291) | (~c2_1(a341))),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[535, 135, 386, 294, 728, 293, 593, 63])).
% 1.18/0.99 tff(730,plain,
% 1.18/0.99 (c0_1(a291)),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[729, 727])).
% 1.18/0.99 tff(731,plain,
% 1.18/0.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | c0_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c0_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(732,plain,
% 1.18/0.99 ((hskp7 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341))) <=> (hskp7 | c0_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(733,plain,
% 1.18/0.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | c0_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 1.18/0.99 inference(monotonicity,[status(thm)],[732])).
% 1.18/0.99 tff(734,plain,
% 1.18/0.99 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c0_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/0.99 inference(transitivity,[status(thm)],[733, 731])).
% 1.18/0.99 tff(735,plain,
% 1.18/0.99 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)))),
% 1.18/0.99 inference(quant_inst,[status(thm)],[])).
% 1.18/0.99 tff(736,plain,
% 1.18/0.99 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c0_1(a341) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)) | (~c1_1(a341)) | (~c2_1(a341))),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[735, 734])).
% 1.18/0.99 tff(737,plain,
% 1.18/0.99 (hskp7),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[736, 135, 294, 696, 697, 293, 695, 497, 727])).
% 1.18/0.99 tff(738,plain,
% 1.18/0.99 (((~hskp7) | c0_1(a299)) <=> ((~hskp7) | c0_1(a299))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(739,axiom,((~hskp7) | c0_1(a299)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.18/0.99 tff(740,plain,
% 1.18/0.99 ((~hskp7) | c0_1(a299)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[739, 738])).
% 1.18/0.99 tff(741,plain,
% 1.18/0.99 ((~hskp7) | c0_1(a299)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[740, 738])).
% 1.18/0.99 tff(742,plain,
% 1.18/0.99 ((~hskp7) | c0_1(a299)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[741, 738])).
% 1.18/0.99 tff(743,plain,
% 1.18/0.99 ((~hskp7) | c0_1(a299)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[742, 738])).
% 1.18/0.99 tff(744,plain,
% 1.18/0.99 ((~hskp7) | c0_1(a299)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[743, 738])).
% 1.18/0.99 tff(745,plain,
% 1.18/0.99 ((~hskp7) | c0_1(a299)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[744, 738])).
% 1.18/0.99 tff(746,plain,
% 1.18/0.99 ((~hskp7) | c0_1(a299)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[745, 738])).
% 1.18/0.99 tff(747,plain,
% 1.18/0.99 ((~hskp7) | c0_1(a299)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[746, 738])).
% 1.18/0.99 tff(748,plain,
% 1.18/0.99 (c0_1(a299)),
% 1.18/0.99 inference(unit_resolution,[status(thm)],[747, 737])).
% 1.18/0.99 tff(749,plain,
% 1.18/0.99 (((~hskp7) | c3_1(a299)) <=> ((~hskp7) | c3_1(a299))),
% 1.18/0.99 inference(rewrite,[status(thm)],[])).
% 1.18/0.99 tff(750,axiom,((~hskp7) | c3_1(a299)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.18/0.99 tff(751,plain,
% 1.18/0.99 ((~hskp7) | c3_1(a299)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[750, 749])).
% 1.18/0.99 tff(752,plain,
% 1.18/0.99 ((~hskp7) | c3_1(a299)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[751, 749])).
% 1.18/0.99 tff(753,plain,
% 1.18/0.99 ((~hskp7) | c3_1(a299)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[752, 749])).
% 1.18/0.99 tff(754,plain,
% 1.18/0.99 ((~hskp7) | c3_1(a299)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[753, 749])).
% 1.18/0.99 tff(755,plain,
% 1.18/0.99 ((~hskp7) | c3_1(a299)),
% 1.18/0.99 inference(modus_ponens,[status(thm)],[754, 749])).
% 1.18/1.00 tff(756,plain,
% 1.18/1.00 ((~hskp7) | c3_1(a299)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[755, 749])).
% 1.18/1.00 tff(757,plain,
% 1.18/1.00 ((~hskp7) | c3_1(a299)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[756, 749])).
% 1.18/1.00 tff(758,plain,
% 1.18/1.00 ((~hskp7) | c3_1(a299)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[757, 749])).
% 1.18/1.00 tff(759,plain,
% 1.18/1.00 (c3_1(a299)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[758, 737])).
% 1.18/1.00 tff(760,assumption,(~c2_1(a299)), introduced(assumption)).
% 1.18/1.00 tff(761,plain,
% 1.18/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(762,plain,
% 1.18/1.00 (((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(763,plain,
% 1.18/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341))))),
% 1.18/1.00 inference(monotonicity,[status(thm)],[762])).
% 1.18/1.00 tff(764,plain,
% 1.18/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341)))),
% 1.18/1.00 inference(transitivity,[status(thm)],[763, 761])).
% 1.18/1.00 tff(765,plain,
% 1.18/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 1.18/1.00 inference(quant_inst,[status(thm)],[])).
% 1.18/1.00 tff(766,plain,
% 1.18/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341))),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[765, 764])).
% 1.18/1.00 tff(767,plain,
% 1.18/1.00 ((~c0_1(a291)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a341))),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[766, 135, 293, 292, 760, 593, 592, 591])).
% 1.18/1.00 tff(768,plain,
% 1.18/1.00 ($false),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[767, 759, 748, 727, 730])).
% 1.18/1.00 tff(769,plain,(hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a299) | c2_1(a291) | c3_1(a291) | (~c1_1(a341)) | (~c1_1(a291)) | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.18/1.00 tff(770,plain,
% 1.18/1.00 (c2_1(a299)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[769, 602, 292, 293, 518, 543, 294, 529, 336])).
% 1.18/1.00 tff(771,plain,
% 1.18/1.00 (((~hskp7) | (~c2_1(a299))) <=> ((~hskp7) | (~c2_1(a299)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(772,plain,
% 1.18/1.00 (((~c2_1(a299)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a299)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(773,axiom,((~c2_1(a299)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 1.18/1.00 tff(774,plain,
% 1.18/1.00 ((~hskp7) | (~c2_1(a299))),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[773, 772])).
% 1.18/1.00 tff(775,plain,
% 1.18/1.00 ((~hskp7) | (~c2_1(a299))),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[774, 771])).
% 1.18/1.00 tff(776,plain,
% 1.18/1.00 (~hskp7),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[775, 770])).
% 1.18/1.00 tff(777,plain,
% 1.18/1.00 ($false),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[736, 135, 776, 294, 692, 681, 293, 670, 497, 487])).
% 1.18/1.00 tff(778,plain,(hskp3 | (~c1_1(a341)) | c0_1(a341) | c3_1(a341) | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.18/1.00 tff(779,plain,
% 1.18/1.00 (hskp3),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[778, 336, 293, 292, 294])).
% 1.18/1.00 tff(780,plain,
% 1.18/1.00 (((~hskp3) | (~c1_1(a294))) <=> ((~hskp3) | (~c1_1(a294)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(781,plain,
% 1.18/1.00 (((~c1_1(a294)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a294)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(782,axiom,((~c1_1(a294)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause134')).
% 1.18/1.00 tff(783,plain,
% 1.18/1.00 ((~hskp3) | (~c1_1(a294))),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[782, 781])).
% 1.18/1.00 tff(784,plain,
% 1.18/1.00 ((~hskp3) | (~c1_1(a294))),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[783, 780])).
% 1.18/1.00 tff(785,plain,
% 1.18/1.00 (~c1_1(a294)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[784, 779])).
% 1.18/1.00 tff(786,plain,
% 1.18/1.00 (((~hskp3) | c2_1(a294)) <=> ((~hskp3) | c2_1(a294))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(787,axiom,((~hskp3) | c2_1(a294)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 1.18/1.00 tff(788,plain,
% 1.18/1.00 ((~hskp3) | c2_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[787, 786])).
% 1.18/1.00 tff(789,plain,
% 1.18/1.00 ((~hskp3) | c2_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[788, 786])).
% 1.18/1.00 tff(790,plain,
% 1.18/1.00 ((~hskp3) | c2_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[789, 786])).
% 1.18/1.00 tff(791,plain,
% 1.18/1.00 ((~hskp3) | c2_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[790, 786])).
% 1.18/1.00 tff(792,plain,
% 1.18/1.00 ((~hskp3) | c2_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[791, 786])).
% 1.18/1.00 tff(793,plain,
% 1.18/1.00 ((~hskp3) | c2_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[792, 786])).
% 1.18/1.00 tff(794,plain,
% 1.18/1.00 ((~hskp3) | c2_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[793, 786])).
% 1.18/1.00 tff(795,plain,
% 1.18/1.00 ((~hskp3) | c2_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[794, 786])).
% 1.18/1.00 tff(796,plain,
% 1.18/1.00 (c2_1(a294)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[795, 779])).
% 1.18/1.00 tff(797,plain,
% 1.18/1.00 (((~hskp3) | c0_1(a294)) <=> ((~hskp3) | c0_1(a294))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(798,axiom,((~hskp3) | c0_1(a294)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 1.18/1.00 tff(799,plain,
% 1.18/1.00 ((~hskp3) | c0_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[798, 797])).
% 1.18/1.00 tff(800,plain,
% 1.18/1.00 ((~hskp3) | c0_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[799, 797])).
% 1.18/1.00 tff(801,plain,
% 1.18/1.00 ((~hskp3) | c0_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[800, 797])).
% 1.18/1.00 tff(802,plain,
% 1.18/1.00 ((~hskp3) | c0_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[801, 797])).
% 1.18/1.00 tff(803,plain,
% 1.18/1.00 ((~hskp3) | c0_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[802, 797])).
% 1.18/1.00 tff(804,plain,
% 1.18/1.00 ((~hskp3) | c0_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[803, 797])).
% 1.18/1.00 tff(805,plain,
% 1.18/1.00 ((~hskp3) | c0_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[804, 797])).
% 1.18/1.00 tff(806,plain,
% 1.18/1.00 ((~hskp3) | c0_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[805, 797])).
% 1.18/1.00 tff(807,plain,
% 1.18/1.00 (c0_1(a294)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[806, 779])).
% 1.18/1.00 tff(808,plain,
% 1.18/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(809,plain,
% 1.18/1.00 (((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a294) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(810,plain,
% 1.18/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a294) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a341))))),
% 1.18/1.00 inference(monotonicity,[status(thm)],[809])).
% 1.18/1.00 tff(811,plain,
% 1.18/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a294) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)))),
% 1.18/1.00 inference(transitivity,[status(thm)],[810, 808])).
% 1.18/1.00 tff(812,plain,
% 1.18/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a294) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 1.18/1.00 inference(quant_inst,[status(thm)],[])).
% 1.18/1.00 tff(813,plain,
% 1.18/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a341))),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[812, 811])).
% 1.18/1.00 tff(814,plain,
% 1.18/1.00 (~c3_1(a294)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[813, 135, 294, 807, 796, 293, 292, 785, 11])).
% 1.18/1.00 tff(815,plain,
% 1.18/1.00 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(816,plain,
% 1.18/1.00 ((hskp23 | hskp8 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c2_1(a294))) <=> (hskp23 | hskp8 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(817,plain,
% 1.18/1.00 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c2_1(a294)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294)))),
% 1.18/1.00 inference(monotonicity,[status(thm)],[816])).
% 1.18/1.00 tff(818,plain,
% 1.18/1.00 (((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c2_1(a294)))) <=> ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294))),
% 1.18/1.00 inference(transitivity,[status(thm)],[817, 815])).
% 1.18/1.00 tff(819,plain,
% 1.18/1.00 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp23 | hskp8 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c2_1(a294)))),
% 1.18/1.00 inference(quant_inst,[status(thm)],[])).
% 1.18/1.00 tff(820,plain,
% 1.18/1.00 ((~![U: $i] : (hskp23 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp23 | hskp8 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[819, 818])).
% 1.18/1.00 tff(821,plain,
% 1.18/1.00 (hskp8 | c3_1(a294)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[820, 135, 336, 796, 785, 612])).
% 1.18/1.00 tff(822,plain,
% 1.18/1.00 (hskp8),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[821, 814])).
% 1.18/1.00 tff(823,plain,
% 1.18/1.00 (~c1_1(a300)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[549, 822])).
% 1.18/1.00 tff(824,plain,
% 1.18/1.00 (c3_1(a300)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[560, 822])).
% 1.18/1.00 tff(825,plain,
% 1.18/1.00 (c0_1(a300)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[571, 822])).
% 1.18/1.00 tff(826,plain,
% 1.18/1.00 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp15 | c1_1(a300) | (~ndr1_0) | (~c3_1(a300)) | (~c0_1(a300)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp29 | hskp15 | c1_1(a300) | (~ndr1_0) | (~c3_1(a300)) | (~c0_1(a300)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(827,plain,
% 1.18/1.00 ((hskp29 | hskp15 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300))) <=> (hskp29 | hskp15 | c1_1(a300) | (~ndr1_0) | (~c3_1(a300)) | (~c0_1(a300)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(828,plain,
% 1.18/1.00 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp15 | c1_1(a300) | (~ndr1_0) | (~c3_1(a300)) | (~c0_1(a300))))),
% 1.18/1.00 inference(monotonicity,[status(thm)],[827])).
% 1.18/1.00 tff(829,plain,
% 1.18/1.00 (((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)))) <=> ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp29 | hskp15 | c1_1(a300) | (~ndr1_0) | (~c3_1(a300)) | (~c0_1(a300)))),
% 1.18/1.00 inference(transitivity,[status(thm)],[828, 826])).
% 1.18/1.00 tff(830,plain,
% 1.18/1.00 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp29 | hskp15 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)))),
% 1.18/1.00 inference(quant_inst,[status(thm)],[])).
% 1.18/1.00 tff(831,plain,
% 1.18/1.00 ((~![U: $i] : (hskp29 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp29 | hskp15 | c1_1(a300) | (~ndr1_0) | (~c3_1(a300)) | (~c0_1(a300))),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[830, 829])).
% 1.18/1.00 tff(832,plain,
% 1.18/1.00 (hskp15),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[831, 135, 386, 825, 824, 823, 335])).
% 1.18/1.00 tff(833,plain,
% 1.18/1.00 (((~hskp15) | c1_1(a311)) <=> ((~hskp15) | c1_1(a311))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(834,axiom,((~hskp15) | c1_1(a311)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.18/1.00 tff(835,plain,
% 1.18/1.00 ((~hskp15) | c1_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[834, 833])).
% 1.18/1.00 tff(836,plain,
% 1.18/1.00 ((~hskp15) | c1_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[835, 833])).
% 1.18/1.00 tff(837,plain,
% 1.18/1.00 ((~hskp15) | c1_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[836, 833])).
% 1.18/1.00 tff(838,plain,
% 1.18/1.00 ((~hskp15) | c1_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[837, 833])).
% 1.18/1.00 tff(839,plain,
% 1.18/1.00 ((~hskp15) | c1_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[838, 833])).
% 1.18/1.00 tff(840,plain,
% 1.18/1.00 ((~hskp15) | c1_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[839, 833])).
% 1.18/1.00 tff(841,plain,
% 1.18/1.00 ((~hskp15) | c1_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[840, 833])).
% 1.18/1.00 tff(842,plain,
% 1.18/1.00 ((~hskp15) | c1_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[841, 833])).
% 1.18/1.00 tff(843,plain,
% 1.18/1.00 (c1_1(a311)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[842, 832])).
% 1.18/1.00 tff(844,plain,
% 1.18/1.00 (((~hskp15) | c0_1(a311)) <=> ((~hskp15) | c0_1(a311))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(845,axiom,((~hskp15) | c0_1(a311)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.18/1.00 tff(846,plain,
% 1.18/1.00 ((~hskp15) | c0_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[845, 844])).
% 1.18/1.00 tff(847,plain,
% 1.18/1.00 ((~hskp15) | c0_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[846, 844])).
% 1.18/1.00 tff(848,plain,
% 1.18/1.00 ((~hskp15) | c0_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[847, 844])).
% 1.18/1.00 tff(849,plain,
% 1.18/1.00 ((~hskp15) | c0_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[848, 844])).
% 1.18/1.00 tff(850,plain,
% 1.18/1.00 ((~hskp15) | c0_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[849, 844])).
% 1.18/1.00 tff(851,plain,
% 1.18/1.00 ((~hskp15) | c0_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[850, 844])).
% 1.18/1.00 tff(852,plain,
% 1.18/1.00 ((~hskp15) | c0_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[851, 844])).
% 1.18/1.00 tff(853,plain,
% 1.18/1.00 ((~hskp15) | c0_1(a311)),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[852, 844])).
% 1.18/1.00 tff(854,plain,
% 1.18/1.00 (c0_1(a311)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[853, 832])).
% 1.18/1.00 tff(855,plain,
% 1.18/1.00 (((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | (~c0_1(a311)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(856,plain,
% 1.18/1.00 ((hskp23 | (~ndr1_0) | (~c2_1(a311)) | (~c1_1(a311)) | (~c0_1(a311))) <=> (hskp23 | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(857,plain,
% 1.18/1.00 (((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c2_1(a311)) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | (~c0_1(a311))))),
% 1.18/1.00 inference(monotonicity,[status(thm)],[856])).
% 1.18/1.00 tff(858,plain,
% 1.18/1.00 (((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c2_1(a311)) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 1.18/1.00 inference(transitivity,[status(thm)],[857, 855])).
% 1.18/1.00 tff(859,plain,
% 1.18/1.00 ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | (~ndr1_0) | (~c2_1(a311)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 1.18/1.00 inference(quant_inst,[status(thm)],[])).
% 1.18/1.00 tff(860,plain,
% 1.18/1.00 ((~![U: $i] : (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | (~c0_1(a311))),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[859, 858])).
% 1.18/1.00 tff(861,plain,
% 1.18/1.00 (~c2_1(a311)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[860, 135, 336, 854, 843, 325])).
% 1.18/1.00 tff(862,plain,
% 1.18/1.00 (((~hskp15) | (~c3_1(a311))) <=> ((~hskp15) | (~c3_1(a311)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(863,plain,
% 1.18/1.00 (((~c3_1(a311)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a311)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(864,axiom,((~c3_1(a311)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.18/1.00 tff(865,plain,
% 1.18/1.00 ((~hskp15) | (~c3_1(a311))),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[864, 863])).
% 1.18/1.00 tff(866,plain,
% 1.18/1.00 ((~hskp15) | (~c3_1(a311))),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[865, 862])).
% 1.18/1.00 tff(867,plain,
% 1.18/1.00 (~c3_1(a311)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[866, 832])).
% 1.18/1.00 tff(868,plain,
% 1.18/1.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a311) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a311) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(869,plain,
% 1.18/1.00 ((hskp7 | (~ndr1_0) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294))) <=> (hskp7 | c3_1(a311) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(870,plain,
% 1.18/1.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c3_1(a311) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311))))),
% 1.18/1.00 inference(monotonicity,[status(thm)],[869])).
% 1.18/1.00 tff(871,plain,
% 1.18/1.00 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a311) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 1.18/1.00 inference(transitivity,[status(thm)],[870, 868])).
% 1.18/1.00 tff(872,plain,
% 1.18/1.00 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))),
% 1.18/1.00 inference(quant_inst,[status(thm)],[])).
% 1.18/1.00 tff(873,plain,
% 1.18/1.00 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c3_1(a311) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311))),
% 1.18/1.00 inference(modus_ponens,[status(thm)],[872, 871])).
% 1.18/1.00 tff(874,plain,
% 1.18/1.00 (hskp7),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[873, 135, 854, 843, 807, 796, 867, 785, 52])).
% 1.18/1.00 tff(875,plain,
% 1.18/1.00 (~c2_1(a299)),
% 1.18/1.00 inference(unit_resolution,[status(thm)],[775, 874])).
% 1.18/1.00 tff(876,plain,
% 1.18/1.00 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a300) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c3_1(a300)) | (~c0_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a300) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(877,plain,
% 1.18/1.00 ((hskp16 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294))) <=> (hskp16 | c1_1(a300) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 1.18/1.00 inference(rewrite,[status(thm)],[])).
% 1.18/1.00 tff(878,plain,
% 1.18/1.00 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | c1_1(a300) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c3_1(a300)) | (~c0_1(a300))))),
% 1.18/1.00 inference(monotonicity,[status(thm)],[877])).
% 1.18/1.00 tff(879,plain,
% 1.18/1.00 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a300) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 1.18/1.00 inference(transitivity,[status(thm)],[878, 876])).
% 1.18/1.00 tff(880,plain,
% 1.18/1.00 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))),
% 1.18/1.01 inference(quant_inst,[status(thm)],[])).
% 1.18/1.01 tff(881,plain,
% 1.18/1.01 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp16 | c1_1(a300) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c3_1(a300)) | (~c0_1(a300))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[880, 879])).
% 1.18/1.01 tff(882,plain,
% 1.18/1.01 (hskp16),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[881, 135, 825, 824, 807, 796, 823, 785, 291])).
% 1.18/1.01 tff(883,plain,
% 1.18/1.01 (~c3_1(a315)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[477, 882])).
% 1.18/1.01 tff(884,plain,
% 1.18/1.01 (~c0_1(a315)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[459, 882])).
% 1.18/1.01 tff(885,plain,
% 1.18/1.01 (c3_1(a299)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[758, 874])).
% 1.18/1.01 tff(886,plain,
% 1.18/1.01 (c0_1(a299)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[747, 874])).
% 1.18/1.01 tff(887,plain,
% 1.18/1.01 (c2_1(a315)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[453, 882])).
% 1.18/1.01 tff(888,plain,
% 1.18/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(889,plain,
% 1.18/1.01 (((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(890,plain,
% 1.18/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315))))),
% 1.18/1.01 inference(monotonicity,[status(thm)],[889])).
% 1.18/1.01 tff(891,plain,
% 1.18/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))),
% 1.18/1.01 inference(transitivity,[status(thm)],[890, 888])).
% 1.18/1.01 tff(892,plain,
% 1.18/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 1.18/1.01 inference(quant_inst,[status(thm)],[])).
% 1.18/1.01 tff(893,plain,
% 1.18/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[892, 891])).
% 1.18/1.01 tff(894,plain,
% 1.18/1.01 ($false),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[893, 135, 887, 854, 886, 885, 884, 883, 867, 875, 591, 861])).
% 1.18/1.01 tff(895,plain,(hskp23 | (~c1_1(a341)) | c0_1(a341) | c3_1(a341)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.01 tff(896,plain,
% 1.18/1.01 (hskp23),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[895, 294, 293, 292])).
% 1.18/1.01 tff(897,plain,
% 1.18/1.01 (((~hskp23) | (~c2_1(a337))) <=> ((~hskp23) | (~c2_1(a337)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(898,plain,
% 1.18/1.01 (((~c2_1(a337)) | (~hskp23)) <=> ((~hskp23) | (~c2_1(a337)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(899,axiom,((~c2_1(a337)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.18/1.01 tff(900,plain,
% 1.18/1.01 ((~hskp23) | (~c2_1(a337))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[899, 898])).
% 1.18/1.01 tff(901,plain,
% 1.18/1.01 ((~hskp23) | (~c2_1(a337))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[900, 897])).
% 1.18/1.01 tff(902,plain,
% 1.18/1.01 (~c2_1(a337)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[901, 896])).
% 1.18/1.01 tff(903,plain,
% 1.18/1.01 (((~hskp23) | c3_1(a337)) <=> ((~hskp23) | c3_1(a337))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(904,axiom,((~hskp23) | c3_1(a337)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.18/1.01 tff(905,plain,
% 1.18/1.01 ((~hskp23) | c3_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[904, 903])).
% 1.18/1.01 tff(906,plain,
% 1.18/1.01 ((~hskp23) | c3_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[905, 903])).
% 1.18/1.01 tff(907,plain,
% 1.18/1.01 ((~hskp23) | c3_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[906, 903])).
% 1.18/1.01 tff(908,plain,
% 1.18/1.01 ((~hskp23) | c3_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[907, 903])).
% 1.18/1.01 tff(909,plain,
% 1.18/1.01 ((~hskp23) | c3_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[908, 903])).
% 1.18/1.01 tff(910,plain,
% 1.18/1.01 ((~hskp23) | c3_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[909, 903])).
% 1.18/1.01 tff(911,plain,
% 1.18/1.01 ((~hskp23) | c3_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[910, 903])).
% 1.18/1.01 tff(912,plain,
% 1.18/1.01 ((~hskp23) | c3_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[911, 903])).
% 1.18/1.01 tff(913,plain,
% 1.18/1.01 (c3_1(a337)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[912, 896])).
% 1.18/1.01 tff(914,plain,
% 1.18/1.01 (((~hskp23) | c1_1(a337)) <=> ((~hskp23) | c1_1(a337))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(915,axiom,((~hskp23) | c1_1(a337)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.18/1.01 tff(916,plain,
% 1.18/1.01 ((~hskp23) | c1_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[915, 914])).
% 1.18/1.01 tff(917,plain,
% 1.18/1.01 ((~hskp23) | c1_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[916, 914])).
% 1.18/1.01 tff(918,plain,
% 1.18/1.01 ((~hskp23) | c1_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[917, 914])).
% 1.18/1.01 tff(919,plain,
% 1.18/1.01 ((~hskp23) | c1_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[918, 914])).
% 1.18/1.01 tff(920,plain,
% 1.18/1.01 ((~hskp23) | c1_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[919, 914])).
% 1.18/1.01 tff(921,plain,
% 1.18/1.01 ((~hskp23) | c1_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[920, 914])).
% 1.18/1.01 tff(922,plain,
% 1.18/1.01 ((~hskp23) | c1_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[921, 914])).
% 1.18/1.01 tff(923,plain,
% 1.18/1.01 ((~hskp23) | c1_1(a337)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[922, 914])).
% 1.18/1.01 tff(924,plain,
% 1.18/1.01 (c1_1(a337)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[923, 896])).
% 1.18/1.01 tff(925,plain,
% 1.18/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(926,plain,
% 1.18/1.01 ((hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341) | c0_1(a341) | c3_1(a341)) <=> (hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(927,plain,
% 1.18/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341) | c0_1(a341) | c3_1(a341))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341)))),
% 1.18/1.01 inference(monotonicity,[status(thm)],[926])).
% 1.18/1.01 tff(928,plain,
% 1.18/1.01 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341) | c0_1(a341) | c3_1(a341))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341))),
% 1.18/1.01 inference(transitivity,[status(thm)],[927, 925])).
% 1.18/1.01 tff(929,plain,
% 1.18/1.01 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341) | c0_1(a341) | c3_1(a341))),
% 1.18/1.01 inference(quant_inst,[status(thm)],[])).
% 1.18/1.01 tff(930,plain,
% 1.18/1.01 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c0_1(a341) | c3_1(a341) | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a341)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[929, 928])).
% 1.18/1.01 tff(931,plain,
% 1.18/1.01 (hskp8),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[930, 135, 924, 913, 293, 292, 902, 315, 305])).
% 1.18/1.01 tff(932,plain,
% 1.18/1.01 (~c1_1(a300)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[549, 931])).
% 1.18/1.01 tff(933,plain,
% 1.18/1.01 (c3_1(a300)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[560, 931])).
% 1.18/1.01 tff(934,plain,
% 1.18/1.01 (c0_1(a300)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[571, 931])).
% 1.18/1.01 tff(935,plain,
% 1.18/1.01 (~c2_1(a300)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[578, 135, 294, 934, 933, 293, 292, 932, 11])).
% 1.18/1.01 tff(936,plain,
% 1.18/1.01 (hskp29),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[486, 305, 294, 64, 293])).
% 1.18/1.01 tff(937,plain,
% 1.18/1.01 (c3_1(a301)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[376, 936])).
% 1.18/1.01 tff(938,plain,
% 1.18/1.01 (c2_1(a301)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[347, 936])).
% 1.18/1.01 tff(939,plain,
% 1.18/1.01 (c0_1(a301)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[358, 936])).
% 1.18/1.01 tff(940,assumption,(~hskp22), introduced(assumption)).
% 1.18/1.01 tff(941,plain,
% 1.18/1.01 (hskp5),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[442, 32, 940])).
% 1.18/1.01 tff(942,plain,
% 1.18/1.01 (~c0_1(a297)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[392, 941])).
% 1.18/1.01 tff(943,plain,
% 1.18/1.01 (c2_1(a297)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[414, 941])).
% 1.18/1.01 tff(944,plain,
% 1.18/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a341) | c3_1(a341) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a341)) | c2_1(a341))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a341) | c3_1(a341) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a341)) | c2_1(a341))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(945,plain,
% 1.18/1.01 (((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a297) | (~c3_1(a297)) | (~c2_1(a297)) | c3_1(a341) | c2_1(a341) | c0_1(a341)) <=> (c0_1(a341) | c3_1(a341) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a341)) | c2_1(a341))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(946,plain,
% 1.18/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a297) | (~c3_1(a297)) | (~c2_1(a297)) | c3_1(a341) | c2_1(a341) | c0_1(a341))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a341) | c3_1(a341) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a341)) | c2_1(a341)))),
% 1.18/1.01 inference(monotonicity,[status(thm)],[945])).
% 1.18/1.01 tff(947,plain,
% 1.18/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a297) | (~c3_1(a297)) | (~c2_1(a297)) | c3_1(a341) | c2_1(a341) | c0_1(a341))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a341) | c3_1(a341) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a341)) | c2_1(a341))),
% 1.18/1.01 inference(transitivity,[status(thm)],[946, 944])).
% 1.18/1.01 tff(948,plain,
% 1.18/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a341) | c2_1(a341) | (~c1_1(a341)) | c0_1(a297) | (~c3_1(a297)) | (~c2_1(a297)) | c3_1(a341) | c2_1(a341) | c0_1(a341))),
% 1.18/1.01 inference(quant_inst,[status(thm)],[])).
% 1.18/1.01 tff(949,plain,
% 1.18/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a341) | c3_1(a341) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a341)) | c2_1(a341)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[948, 947])).
% 1.18/1.01 tff(950,plain,
% 1.18/1.01 (~c3_1(a297)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[949, 135, 294, 943, 293, 292, 942, 708, 305])).
% 1.18/1.01 tff(951,plain,
% 1.18/1.01 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.18/1.01 inference(bind,[status(th)],[])).
% 1.18/1.01 tff(952,plain,
% 1.18/1.01 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.18/1.01 inference(quant_intro,[status(thm)],[951])).
% 1.18/1.01 tff(953,plain,
% 1.18/1.01 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(954,plain,
% 1.18/1.01 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp4) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp4))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.18/1.01 inference(bind,[status(th)],[])).
% 1.18/1.01 tff(955,plain,
% 1.18/1.01 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.18/1.01 inference(quant_intro,[status(thm)],[954])).
% 1.18/1.01 tff(956,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)) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 1.18/1.01 tff(957,plain,
% 1.18/1.01 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[956, 955])).
% 1.18/1.01 tff(958,plain,
% 1.18/1.01 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[957, 953])).
% 1.18/1.01 tff(959,plain,(
% 1.18/1.01 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.18/1.01 inference(skolemize,[status(sab)],[958])).
% 1.18/1.01 tff(960,plain,
% 1.18/1.01 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[959, 952])).
% 1.18/1.01 tff(961,plain,
% 1.18/1.01 ((hskp22 | hskp16 | hskp9) <=> (hskp22 | hskp16 | hskp9)),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(962,plain,
% 1.18/1.01 (((hskp16 | hskp9) | hskp22) <=> (hskp22 | hskp16 | hskp9)),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(963,plain,
% 1.18/1.01 ((hskp9 | hskp16) <=> (hskp16 | hskp9)),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(964,plain,
% 1.18/1.01 (((hskp9 | hskp16) | hskp22) <=> ((hskp16 | hskp9) | hskp22)),
% 1.18/1.01 inference(monotonicity,[status(thm)],[963])).
% 1.18/1.01 tff(965,plain,
% 1.18/1.01 (((hskp9 | hskp16) | hskp22) <=> (hskp22 | hskp16 | hskp9)),
% 1.18/1.01 inference(transitivity,[status(thm)],[964, 962])).
% 1.18/1.01 tff(966,axiom,((hskp9 | hskp16) | hskp22), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 1.18/1.01 tff(967,plain,
% 1.18/1.01 (hskp22 | hskp16 | hskp9),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[966, 965])).
% 1.18/1.01 tff(968,plain,
% 1.18/1.01 (hskp22 | hskp16 | hskp9),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[967, 961])).
% 1.18/1.01 tff(969,plain,
% 1.18/1.01 (hskp22 | hskp16 | hskp9),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[968, 961])).
% 1.18/1.01 tff(970,plain,
% 1.18/1.01 (hskp22 | hskp16 | hskp9),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[969, 961])).
% 1.18/1.01 tff(971,plain,
% 1.18/1.01 (hskp22 | hskp16 | hskp9),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[970, 961])).
% 1.18/1.01 tff(972,plain,
% 1.18/1.01 (hskp22 | hskp16 | hskp9),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[971, 961])).
% 1.18/1.01 tff(973,plain,
% 1.18/1.01 (hskp22 | hskp16 | hskp9),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[972, 961])).
% 1.18/1.01 tff(974,plain,
% 1.18/1.01 (hskp22 | hskp16 | hskp9),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[973, 961])).
% 1.18/1.01 tff(975,plain,
% 1.18/1.01 (hskp9),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[974, 32, 940])).
% 1.18/1.01 tff(976,plain,
% 1.18/1.01 (((~hskp9) | (~c2_1(a304))) <=> ((~hskp9) | (~c2_1(a304)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(977,plain,
% 1.18/1.01 (((~c2_1(a304)) | (~hskp9)) <=> ((~hskp9) | (~c2_1(a304)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(978,axiom,((~c2_1(a304)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.18/1.01 tff(979,plain,
% 1.18/1.01 ((~hskp9) | (~c2_1(a304))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[978, 977])).
% 1.18/1.01 tff(980,plain,
% 1.18/1.01 ((~hskp9) | (~c2_1(a304))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[979, 976])).
% 1.18/1.01 tff(981,plain,
% 1.18/1.01 (~c2_1(a304)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[980, 975])).
% 1.18/1.01 tff(982,plain,
% 1.18/1.01 (((~hskp9) | c1_1(a304)) <=> ((~hskp9) | c1_1(a304))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(983,axiom,((~hskp9) | c1_1(a304)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.18/1.01 tff(984,plain,
% 1.18/1.01 ((~hskp9) | c1_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[983, 982])).
% 1.18/1.01 tff(985,plain,
% 1.18/1.01 ((~hskp9) | c1_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[984, 982])).
% 1.18/1.01 tff(986,plain,
% 1.18/1.01 ((~hskp9) | c1_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[985, 982])).
% 1.18/1.01 tff(987,plain,
% 1.18/1.01 ((~hskp9) | c1_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[986, 982])).
% 1.18/1.01 tff(988,plain,
% 1.18/1.01 ((~hskp9) | c1_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[987, 982])).
% 1.18/1.01 tff(989,plain,
% 1.18/1.01 ((~hskp9) | c1_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[988, 982])).
% 1.18/1.01 tff(990,plain,
% 1.18/1.01 ((~hskp9) | c1_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[989, 982])).
% 1.18/1.01 tff(991,plain,
% 1.18/1.01 ((~hskp9) | c1_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[990, 982])).
% 1.18/1.01 tff(992,plain,
% 1.18/1.01 (c1_1(a304)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[991, 975])).
% 1.18/1.01 tff(993,plain,
% 1.18/1.01 (((~hskp9) | c0_1(a304)) <=> ((~hskp9) | c0_1(a304))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(994,axiom,((~hskp9) | c0_1(a304)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.18/1.01 tff(995,plain,
% 1.18/1.01 ((~hskp9) | c0_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[994, 993])).
% 1.18/1.01 tff(996,plain,
% 1.18/1.01 ((~hskp9) | c0_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[995, 993])).
% 1.18/1.01 tff(997,plain,
% 1.18/1.01 ((~hskp9) | c0_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[996, 993])).
% 1.18/1.01 tff(998,plain,
% 1.18/1.01 ((~hskp9) | c0_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[997, 993])).
% 1.18/1.01 tff(999,plain,
% 1.18/1.01 ((~hskp9) | c0_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[998, 993])).
% 1.18/1.01 tff(1000,plain,
% 1.18/1.01 ((~hskp9) | c0_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[999, 993])).
% 1.18/1.01 tff(1001,plain,
% 1.18/1.01 ((~hskp9) | c0_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[1000, 993])).
% 1.18/1.01 tff(1002,plain,
% 1.18/1.01 ((~hskp9) | c0_1(a304)),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[1001, 993])).
% 1.18/1.01 tff(1003,plain,
% 1.18/1.01 (c0_1(a304)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[1002, 975])).
% 1.18/1.01 tff(1004,assumption,(c3_1(a301)), introduced(assumption)).
% 1.18/1.01 tff(1005,assumption,(c2_1(a301)), introduced(assumption)).
% 1.18/1.01 tff(1006,assumption,(c0_1(a301)), introduced(assumption)).
% 1.18/1.01 tff(1007,plain,
% 1.18/1.01 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | c2_1(a304) | (~ndr1_0) | (~c1_1(a304)) | (~c0_1(a304)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp4 | c2_1(a304) | (~ndr1_0) | (~c1_1(a304)) | (~c0_1(a304)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(1008,plain,
% 1.18/1.01 ((hskp4 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a304) | (~c1_1(a304)) | (~c0_1(a304))) <=> (hskp4 | c2_1(a304) | (~ndr1_0) | (~c1_1(a304)) | (~c0_1(a304)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(1009,plain,
% 1.18/1.01 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a304) | (~c1_1(a304)) | (~c0_1(a304)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | c2_1(a304) | (~ndr1_0) | (~c1_1(a304)) | (~c0_1(a304)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 1.18/1.01 inference(monotonicity,[status(thm)],[1008])).
% 1.18/1.01 tff(1010,plain,
% 1.18/1.01 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a304) | (~c1_1(a304)) | (~c0_1(a304)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp4 | c2_1(a304) | (~ndr1_0) | (~c1_1(a304)) | (~c0_1(a304)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.18/1.01 inference(transitivity,[status(thm)],[1009, 1007])).
% 1.18/1.01 tff(1011,plain,
% 1.18/1.01 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a304) | (~c1_1(a304)) | (~c0_1(a304)))),
% 1.18/1.01 inference(quant_inst,[status(thm)],[])).
% 1.18/1.01 tff(1012,plain,
% 1.18/1.01 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp4 | c2_1(a304) | (~ndr1_0) | (~c1_1(a304)) | (~c0_1(a304)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 1.18/1.01 tff(1013,plain,
% 1.18/1.01 (hskp4),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[1012, 135, 1006, 1005, 1004, 1003, 992, 981, 960])).
% 1.18/1.01 tff(1014,plain,
% 1.18/1.01 (((~hskp4) | (~c3_1(a295))) <=> ((~hskp4) | (~c3_1(a295)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(1015,plain,
% 1.18/1.01 (((~c3_1(a295)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a295)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(1016,axiom,((~c3_1(a295)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.18/1.01 tff(1017,plain,
% 1.18/1.01 ((~hskp4) | (~c3_1(a295))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 1.18/1.01 tff(1018,plain,
% 1.18/1.01 ((~hskp4) | (~c3_1(a295))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[1017, 1014])).
% 1.18/1.01 tff(1019,plain,
% 1.18/1.01 (~c3_1(a295)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[1018, 1013])).
% 1.18/1.01 tff(1020,plain,
% 1.18/1.01 (((~hskp4) | (~c2_1(a295))) <=> ((~hskp4) | (~c2_1(a295)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(1021,plain,
% 1.18/1.01 (((~c2_1(a295)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a295)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(1022,axiom,((~c2_1(a295)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.18/1.01 tff(1023,plain,
% 1.18/1.01 ((~hskp4) | (~c2_1(a295))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 1.18/1.01 tff(1024,plain,
% 1.18/1.01 ((~hskp4) | (~c2_1(a295))),
% 1.18/1.01 inference(modus_ponens,[status(thm)],[1023, 1020])).
% 1.18/1.01 tff(1025,plain,
% 1.18/1.01 (~c2_1(a295)),
% 1.18/1.01 inference(unit_resolution,[status(thm)],[1024, 1013])).
% 1.18/1.01 tff(1026,plain,
% 1.18/1.01 (^[U: $i] : refl((hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.18/1.01 inference(bind,[status(th)],[])).
% 1.18/1.01 tff(1027,plain,
% 1.18/1.01 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.18/1.01 inference(quant_intro,[status(thm)],[1026])).
% 1.18/1.01 tff(1028,plain,
% 1.18/1.01 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.18/1.01 inference(rewrite,[status(thm)],[])).
% 1.18/1.01 tff(1029,plain,
% 1.18/1.01 (^[U: $i] : 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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp13))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp16) <=> ((hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp16))), rewrite(((hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp16) <=> (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp16) <=> (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.18/1.02 inference(bind,[status(th)],[])).
% 1.18/1.02 tff(1030,plain,
% 1.18/1.02 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp16) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.18/1.02 inference(quant_intro,[status(thm)],[1029])).
% 1.18/1.02 tff(1031,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.18/1.02 tff(1032,plain,
% 1.18/1.02 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 1.18/1.02 tff(1033,plain,
% 1.18/1.02 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1032, 1028])).
% 1.18/1.02 tff(1034,plain,(
% 1.18/1.02 ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.18/1.02 inference(skolemize,[status(sab)],[1033])).
% 1.18/1.02 tff(1035,plain,
% 1.18/1.02 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1034, 1027])).
% 1.18/1.02 tff(1036,plain,
% 1.18/1.02 (c1_1(a297)),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[403, 941])).
% 1.18/1.02 tff(1037,plain,
% 1.18/1.02 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp13 | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1038,plain,
% 1.18/1.02 ((hskp16 | hskp13 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297))) <=> (hskp16 | hskp13 | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1039,plain,
% 1.18/1.02 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp13 | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297))))),
% 1.18/1.02 inference(monotonicity,[status(thm)],[1038])).
% 1.18/1.02 tff(1040,plain,
% 1.18/1.02 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)))),
% 1.18/1.02 inference(transitivity,[status(thm)],[1039, 1037])).
% 1.18/1.02 tff(1041,plain,
% 1.18/1.02 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)))),
% 1.18/1.02 inference(quant_inst,[status(thm)],[])).
% 1.18/1.02 tff(1042,plain,
% 1.18/1.02 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 1.18/1.02 tff(1043,plain,
% 1.18/1.02 (hskp13),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[1042, 135, 32, 1036, 943, 942, 1035])).
% 1.18/1.02 tff(1044,plain,
% 1.18/1.02 (((~hskp13) | (~c2_1(a308))) <=> ((~hskp13) | (~c2_1(a308)))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1045,plain,
% 1.18/1.02 (((~c2_1(a308)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a308)))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1046,axiom,((~c2_1(a308)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.18/1.02 tff(1047,plain,
% 1.18/1.02 ((~hskp13) | (~c2_1(a308))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 1.18/1.02 tff(1048,plain,
% 1.18/1.02 ((~hskp13) | (~c2_1(a308))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1047, 1044])).
% 1.18/1.02 tff(1049,plain,
% 1.18/1.02 (~c2_1(a308)),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[1048, 1043])).
% 1.18/1.02 tff(1050,plain,
% 1.18/1.02 (((~hskp4) | c0_1(a295)) <=> ((~hskp4) | c0_1(a295))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1051,axiom,((~hskp4) | c0_1(a295)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 1.18/1.02 tff(1052,plain,
% 1.18/1.02 ((~hskp4) | c0_1(a295)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 1.18/1.02 tff(1053,plain,
% 1.18/1.02 ((~hskp4) | c0_1(a295)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1052, 1050])).
% 1.18/1.02 tff(1054,plain,
% 1.18/1.02 ((~hskp4) | c0_1(a295)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1053, 1050])).
% 1.18/1.02 tff(1055,plain,
% 1.18/1.02 ((~hskp4) | c0_1(a295)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1054, 1050])).
% 1.18/1.02 tff(1056,plain,
% 1.18/1.02 ((~hskp4) | c0_1(a295)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1055, 1050])).
% 1.18/1.02 tff(1057,plain,
% 1.18/1.02 ((~hskp4) | c0_1(a295)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1056, 1050])).
% 1.18/1.02 tff(1058,plain,
% 1.18/1.02 ((~hskp4) | c0_1(a295)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1057, 1050])).
% 1.18/1.02 tff(1059,plain,
% 1.18/1.02 ((~hskp4) | c0_1(a295)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1058, 1050])).
% 1.18/1.02 tff(1060,plain,
% 1.18/1.02 (c0_1(a295)),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[1059, 1013])).
% 1.18/1.02 tff(1061,plain,
% 1.18/1.02 (((~hskp13) | c0_1(a308)) <=> ((~hskp13) | c0_1(a308))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1062,axiom,((~hskp13) | c0_1(a308)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.18/1.02 tff(1063,plain,
% 1.18/1.02 ((~hskp13) | c0_1(a308)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 1.18/1.02 tff(1064,plain,
% 1.18/1.02 ((~hskp13) | c0_1(a308)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1063, 1061])).
% 1.18/1.02 tff(1065,plain,
% 1.18/1.02 ((~hskp13) | c0_1(a308)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1064, 1061])).
% 1.18/1.02 tff(1066,plain,
% 1.18/1.02 ((~hskp13) | c0_1(a308)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1065, 1061])).
% 1.18/1.02 tff(1067,plain,
% 1.18/1.02 ((~hskp13) | c0_1(a308)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1066, 1061])).
% 1.18/1.02 tff(1068,plain,
% 1.18/1.02 ((~hskp13) | c0_1(a308)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1067, 1061])).
% 1.18/1.02 tff(1069,plain,
% 1.18/1.02 ((~hskp13) | c0_1(a308)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1068, 1061])).
% 1.18/1.02 tff(1070,plain,
% 1.18/1.02 ((~hskp13) | c0_1(a308)),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1069, 1061])).
% 1.18/1.02 tff(1071,plain,
% 1.18/1.02 (c0_1(a308)),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[1070, 1043])).
% 1.18/1.02 tff(1072,plain,
% 1.18/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a308) | c0_1(a297) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | c3_1(a297) | (~c2_1(a297)) | (~c3_1(a308)) | (~c0_1(a308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a308) | c0_1(a297) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | c3_1(a297) | (~c2_1(a297)) | (~c3_1(a308)) | (~c0_1(a308)))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1073,plain,
% 1.18/1.02 (((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297))) <=> (c2_1(a308) | c0_1(a297) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | c3_1(a297) | (~c2_1(a297)) | (~c3_1(a308)) | (~c0_1(a308)))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1074,plain,
% 1.18/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a308) | c0_1(a297) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | c3_1(a297) | (~c2_1(a297)) | (~c3_1(a308)) | (~c0_1(a308))))),
% 1.18/1.02 inference(monotonicity,[status(thm)],[1073])).
% 1.18/1.02 tff(1075,plain,
% 1.18/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a308) | c0_1(a297) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | c3_1(a297) | (~c2_1(a297)) | (~c3_1(a308)) | (~c0_1(a308)))),
% 1.18/1.02 inference(transitivity,[status(thm)],[1074, 1072])).
% 1.18/1.02 tff(1076,plain,
% 1.18/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297)))),
% 1.18/1.02 inference(quant_inst,[status(thm)],[])).
% 1.18/1.02 tff(1077,plain,
% 1.18/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a308) | c0_1(a297) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | c3_1(a297) | (~c2_1(a297)) | (~c3_1(a308)) | (~c0_1(a308))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 1.18/1.02 tff(1078,plain,
% 1.18/1.02 (~c3_1(a308)),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[1077, 135, 1071, 943, 1060, 1049, 942, 1025, 1019, 591, 950])).
% 1.18/1.02 tff(1079,plain,
% 1.18/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a308) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a308) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1080,plain,
% 1.18/1.02 (((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297))) <=> (c2_1(a308) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1081,plain,
% 1.18/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a308) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308))))),
% 1.18/1.02 inference(monotonicity,[status(thm)],[1080])).
% 1.18/1.02 tff(1082,plain,
% 1.18/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a308) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)))),
% 1.18/1.02 inference(transitivity,[status(thm)],[1081, 1079])).
% 1.18/1.02 tff(1083,plain,
% 1.18/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a297) | c0_1(a297) | (~c2_1(a297)))),
% 1.18/1.02 inference(quant_inst,[status(thm)],[])).
% 1.18/1.02 tff(1084,plain,
% 1.18/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a308) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1083, 1082])).
% 1.18/1.02 tff(1085,plain,
% 1.18/1.02 ($false),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[1084, 135, 1071, 934, 933, 943, 1049, 942, 591, 935, 950, 1078])).
% 1.18/1.02 tff(1086,plain,(hskp16 | (~c1_1(a341)) | c0_1(a341) | c3_1(a341) | c2_1(a341) | (~c0_1(a301)) | (~c2_1(a301)) | (~c3_1(a301)) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.18/1.02 tff(1087,plain,
% 1.18/1.02 (hskp16),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[1086, 305, 293, 292, 294, 939, 938, 937, 166])).
% 1.18/1.02 tff(1088,plain,
% 1.18/1.02 (~c3_1(a315)),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[477, 1087])).
% 1.18/1.02 tff(1089,plain,
% 1.18/1.02 (~c0_1(a315)),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[459, 1087])).
% 1.18/1.02 tff(1090,plain,
% 1.18/1.02 (c1_1(a315)),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[484, 135, 64, 1089, 1088, 93])).
% 1.18/1.02 tff(1091,plain,
% 1.18/1.02 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)))),
% 1.18/1.02 inference(bind,[status(th)],[])).
% 1.18/1.02 tff(1092,plain,
% 1.18/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.18/1.02 inference(quant_intro,[status(thm)],[1091])).
% 1.18/1.02 tff(1093,plain,
% 1.18/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1094,plain,
% 1.18/1.02 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | c1_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))))),
% 1.18/1.02 inference(bind,[status(th)],[])).
% 1.18/1.02 tff(1095,plain,
% 1.18/1.02 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.18/1.02 inference(quant_intro,[status(thm)],[1094])).
% 1.18/1.02 tff(1096,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c3_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.18/1.02 tff(1097,plain,
% 1.18/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 1.18/1.02 tff(1098,plain,
% 1.18/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1097, 1093])).
% 1.18/1.02 tff(1099,plain,(
% 1.18/1.02 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.18/1.02 inference(skolemize,[status(sab)],[1098])).
% 1.18/1.02 tff(1100,plain,
% 1.18/1.02 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1099, 1092])).
% 1.18/1.02 tff(1101,plain,
% 1.18/1.02 (c2_1(a315)),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[453, 1087])).
% 1.18/1.02 tff(1102,plain,
% 1.18/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a315) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c1_1(a315)) | (~c2_1(a315)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c1_1(a315)) | (~c2_1(a315)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1103,plain,
% 1.18/1.02 (((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300)) <=> (c3_1(a315) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c1_1(a315)) | (~c2_1(a315)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1104,plain,
% 1.18/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a315) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c1_1(a315)) | (~c2_1(a315)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301))))),
% 1.18/1.02 inference(monotonicity,[status(thm)],[1103])).
% 1.18/1.02 tff(1105,plain,
% 1.18/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c1_1(a315)) | (~c2_1(a315)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 1.18/1.02 inference(transitivity,[status(thm)],[1104, 1102])).
% 1.18/1.02 tff(1106,plain,
% 1.18/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))),
% 1.18/1.02 inference(quant_inst,[status(thm)],[])).
% 1.18/1.02 tff(1107,plain,
% 1.18/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c1_1(a315)) | (~c2_1(a315)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 1.18/1.02 tff(1108,plain,
% 1.18/1.02 (~c1_1(a301)),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[1107, 135, 938, 937, 1101, 933, 1088, 932, 1100, 1090, 935])).
% 1.18/1.02 tff(1109,plain,
% 1.18/1.02 ($false),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[383, 135, 939, 938, 937, 294, 293, 292, 11, 1108])).
% 1.18/1.02 tff(1110,plain,(c2_1(a341) | (~c1_1(a341)) | c0_1(a341) | c3_1(a341) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.18/1.02 tff(1111,plain,
% 1.18/1.02 (c2_1(a341)),
% 1.18/1.02 inference(unit_resolution,[status(thm)],[1110, 64, 293, 292, 294])).
% 1.18/1.02 tff(1112,plain,
% 1.18/1.02 (^[U: $i] : refl((hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.18/1.02 inference(bind,[status(th)],[])).
% 1.18/1.02 tff(1113,plain,
% 1.18/1.02 (![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.18/1.02 inference(quant_intro,[status(thm)],[1112])).
% 1.18/1.02 tff(1114,plain,
% 1.18/1.02 (![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1115,plain,
% 1.18/1.02 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp8) <=> ((hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp8))), rewrite(((hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp8) <=> (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp8) <=> (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.18/1.02 inference(bind,[status(th)],[])).
% 1.18/1.02 tff(1116,plain,
% 1.18/1.02 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp8) <=> ![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.18/1.02 inference(quant_intro,[status(thm)],[1115])).
% 1.18/1.02 tff(1117,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp15) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 1.18/1.02 tff(1118,plain,
% 1.18/1.02 (![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 1.18/1.02 tff(1119,plain,
% 1.18/1.02 (![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1118, 1114])).
% 1.18/1.02 tff(1120,plain,(
% 1.18/1.02 ![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.18/1.02 inference(skolemize,[status(sab)],[1119])).
% 1.18/1.02 tff(1121,plain,
% 1.18/1.02 (![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.18/1.02 inference(modus_ponens,[status(thm)],[1120, 1113])).
% 1.18/1.02 tff(1122,plain,
% 1.18/1.02 (((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c2_1(a341)))) <=> ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp15 | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c2_1(a341)))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1123,plain,
% 1.18/1.02 ((hskp15 | hskp8 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (hskp15 | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c2_1(a341)))),
% 1.18/1.02 inference(rewrite,[status(thm)],[])).
% 1.18/1.02 tff(1124,plain,
% 1.18/1.02 (((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c2_1(a341))))),
% 1.18/1.02 inference(monotonicity,[status(thm)],[1123])).
% 1.18/1.02 tff(1125,plain,
% 1.18/1.02 (((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp15 | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c2_1(a341)))),
% 1.18/1.03 inference(transitivity,[status(thm)],[1124, 1122])).
% 1.18/1.03 tff(1126,plain,
% 1.18/1.03 ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | (~ndr1_0) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 1.18/1.03 inference(quant_inst,[status(thm)],[])).
% 1.18/1.03 tff(1127,plain,
% 1.18/1.03 ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp15 | hskp8 | c0_1(a341) | c3_1(a341) | (~ndr1_0) | (~c2_1(a341))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 1.18/1.03 tff(1128,plain,
% 1.18/1.03 (hskp15 | hskp8 | (~c2_1(a341))),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1127, 135, 293, 292, 1121])).
% 1.18/1.03 tff(1129,plain,
% 1.18/1.03 (hskp15),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1128, 637, 1111])).
% 1.18/1.03 tff(1130,plain,
% 1.18/1.03 (~c3_1(a311)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[866, 1129])).
% 1.18/1.03 tff(1131,plain,
% 1.18/1.03 (c1_1(a311)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[842, 1129])).
% 1.18/1.03 tff(1132,plain,
% 1.18/1.03 (c0_1(a311)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[853, 1129])).
% 1.18/1.03 tff(1133,plain,
% 1.18/1.03 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c2_1(a337) | (~ndr1_0) | c0_1(a337) | (~c1_1(a337)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c2_1(a337) | (~ndr1_0) | c0_1(a337) | (~c1_1(a337)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1134,plain,
% 1.18/1.03 ((hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a337) | c0_1(a337) | (~c1_1(a337))) <=> (hskp29 | c0_1(a341) | c2_1(a337) | (~ndr1_0) | c0_1(a337) | (~c1_1(a337)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1135,plain,
% 1.18/1.03 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a337) | c0_1(a337) | (~c1_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a341) | c2_1(a337) | (~ndr1_0) | c0_1(a337) | (~c1_1(a337)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 1.18/1.03 inference(monotonicity,[status(thm)],[1134])).
% 1.18/1.03 tff(1136,plain,
% 1.18/1.03 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a337) | c0_1(a337) | (~c1_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c2_1(a337) | (~ndr1_0) | c0_1(a337) | (~c1_1(a337)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/1.03 inference(transitivity,[status(thm)],[1135, 1133])).
% 1.18/1.03 tff(1137,plain,
% 1.18/1.03 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a337) | c0_1(a337) | (~c1_1(a337)))),
% 1.18/1.03 inference(quant_inst,[status(thm)],[])).
% 1.18/1.03 tff(1138,plain,
% 1.18/1.03 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a341) | c2_1(a337) | (~ndr1_0) | c0_1(a337) | (~c1_1(a337)) | (~c1_1(a341)) | (~c2_1(a341))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 1.18/1.03 tff(1139,plain,
% 1.18/1.03 (hskp29 | c0_1(a337) | (~c2_1(a341))),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1138, 135, 294, 924, 293, 902, 63])).
% 1.18/1.03 tff(1140,plain,
% 1.18/1.03 (c0_1(a337)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1139, 53, 1111])).
% 1.18/1.03 tff(1141,plain,
% 1.18/1.03 (^[U: $i] : refl((hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))),
% 1.18/1.03 inference(bind,[status(th)],[])).
% 1.18/1.03 tff(1142,plain,
% 1.18/1.03 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.18/1.03 inference(quant_intro,[status(thm)],[1141])).
% 1.18/1.03 tff(1143,plain,
% 1.18/1.03 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1144,plain,
% 1.18/1.03 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp8))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp28) <=> ((hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite(((hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp28) <=> (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))))),
% 1.18/1.03 inference(bind,[status(th)],[])).
% 1.18/1.03 tff(1145,plain,
% 1.18/1.03 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp28) <=> ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.18/1.03 inference(quant_intro,[status(thm)],[1144])).
% 1.18/1.03 tff(1146,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp8) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 1.18/1.03 tff(1147,plain,
% 1.18/1.03 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 1.18/1.03 tff(1148,plain,
% 1.18/1.03 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1147, 1143])).
% 1.18/1.03 tff(1149,plain,(
% 1.18/1.03 ![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.18/1.03 inference(skolemize,[status(sab)],[1148])).
% 1.18/1.03 tff(1150,plain,
% 1.18/1.03 (![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1149, 1142])).
% 1.18/1.03 tff(1151,plain,
% 1.18/1.03 (((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)))) <=> ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp8 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1152,plain,
% 1.18/1.03 ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c0_1(a337)))),
% 1.18/1.03 inference(quant_inst,[status(thm)],[])).
% 1.18/1.03 tff(1153,plain,
% 1.18/1.03 ((~![U: $i] : (hskp28 | hskp8 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp8 | (~ndr1_0) | (~c1_1(a337)) | (~c3_1(a337)) | (~c0_1(a337))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 1.18/1.03 tff(1154,plain,
% 1.18/1.03 (hskp28 | hskp8 | (~c0_1(a337))),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1153, 135, 924, 913, 1150])).
% 1.18/1.03 tff(1155,plain,
% 1.18/1.03 (hskp28),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1154, 1140, 637])).
% 1.18/1.03 tff(1156,plain,
% 1.18/1.03 (((~hskp28) | c3_1(a296)) <=> ((~hskp28) | c3_1(a296))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1157,axiom,((~hskp28) | c3_1(a296)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 1.18/1.03 tff(1158,plain,
% 1.18/1.03 ((~hskp28) | c3_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 1.18/1.03 tff(1159,plain,
% 1.18/1.03 ((~hskp28) | c3_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1158, 1156])).
% 1.18/1.03 tff(1160,plain,
% 1.18/1.03 ((~hskp28) | c3_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1159, 1156])).
% 1.18/1.03 tff(1161,plain,
% 1.18/1.03 ((~hskp28) | c3_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1160, 1156])).
% 1.18/1.03 tff(1162,plain,
% 1.18/1.03 ((~hskp28) | c3_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1161, 1156])).
% 1.18/1.03 tff(1163,plain,
% 1.18/1.03 ((~hskp28) | c3_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1162, 1156])).
% 1.18/1.03 tff(1164,plain,
% 1.18/1.03 ((~hskp28) | c3_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1163, 1156])).
% 1.18/1.03 tff(1165,plain,
% 1.18/1.03 ((~hskp28) | c3_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1164, 1156])).
% 1.18/1.03 tff(1166,plain,
% 1.18/1.03 (c3_1(a296)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1165, 1155])).
% 1.18/1.03 tff(1167,plain,
% 1.18/1.03 (((~hskp28) | c2_1(a296)) <=> ((~hskp28) | c2_1(a296))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1168,axiom,((~hskp28) | c2_1(a296)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 1.18/1.03 tff(1169,plain,
% 1.18/1.03 ((~hskp28) | c2_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1168, 1167])).
% 1.18/1.03 tff(1170,plain,
% 1.18/1.03 ((~hskp28) | c2_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1169, 1167])).
% 1.18/1.03 tff(1171,plain,
% 1.18/1.03 ((~hskp28) | c2_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1170, 1167])).
% 1.18/1.03 tff(1172,plain,
% 1.18/1.03 ((~hskp28) | c2_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1171, 1167])).
% 1.18/1.03 tff(1173,plain,
% 1.18/1.03 ((~hskp28) | c2_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1172, 1167])).
% 1.18/1.03 tff(1174,plain,
% 1.18/1.03 ((~hskp28) | c2_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1173, 1167])).
% 1.18/1.03 tff(1175,plain,
% 1.18/1.03 ((~hskp28) | c2_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1174, 1167])).
% 1.18/1.03 tff(1176,plain,
% 1.18/1.03 ((~hskp28) | c2_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1175, 1167])).
% 1.18/1.03 tff(1177,plain,
% 1.18/1.03 (c2_1(a296)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1176, 1155])).
% 1.18/1.03 tff(1178,plain,
% 1.18/1.03 (((~hskp28) | c1_1(a296)) <=> ((~hskp28) | c1_1(a296))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1179,axiom,((~hskp28) | c1_1(a296)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 1.18/1.03 tff(1180,plain,
% 1.18/1.03 ((~hskp28) | c1_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 1.18/1.03 tff(1181,plain,
% 1.18/1.03 ((~hskp28) | c1_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1180, 1178])).
% 1.18/1.03 tff(1182,plain,
% 1.18/1.03 ((~hskp28) | c1_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1181, 1178])).
% 1.18/1.03 tff(1183,plain,
% 1.18/1.03 ((~hskp28) | c1_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1182, 1178])).
% 1.18/1.03 tff(1184,plain,
% 1.18/1.03 ((~hskp28) | c1_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1183, 1178])).
% 1.18/1.03 tff(1185,plain,
% 1.18/1.03 ((~hskp28) | c1_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1184, 1178])).
% 1.18/1.03 tff(1186,plain,
% 1.18/1.03 ((~hskp28) | c1_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1185, 1178])).
% 1.18/1.03 tff(1187,plain,
% 1.18/1.03 ((~hskp28) | c1_1(a296)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1186, 1178])).
% 1.18/1.03 tff(1188,plain,
% 1.18/1.03 (c1_1(a296)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1187, 1155])).
% 1.18/1.03 tff(1189,assumption,(hskp2), introduced(assumption)).
% 1.18/1.03 tff(1190,plain,
% 1.18/1.03 (((~hskp2) | (~c2_1(a293))) <=> ((~hskp2) | (~c2_1(a293)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1191,plain,
% 1.18/1.03 (((~c2_1(a293)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a293)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1192,axiom,((~c2_1(a293)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.18/1.03 tff(1193,plain,
% 1.18/1.03 ((~hskp2) | (~c2_1(a293))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 1.18/1.03 tff(1194,plain,
% 1.18/1.03 ((~hskp2) | (~c2_1(a293))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1193, 1190])).
% 1.18/1.03 tff(1195,plain,
% 1.18/1.03 (~c2_1(a293)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1194, 1189])).
% 1.18/1.03 tff(1196,plain,
% 1.18/1.03 (((~hskp2) | (~c1_1(a293))) <=> ((~hskp2) | (~c1_1(a293)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1197,plain,
% 1.18/1.03 (((~c1_1(a293)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a293)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1198,axiom,((~c1_1(a293)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.18/1.03 tff(1199,plain,
% 1.18/1.03 ((~hskp2) | (~c1_1(a293))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 1.18/1.03 tff(1200,plain,
% 1.18/1.03 ((~hskp2) | (~c1_1(a293))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1199, 1196])).
% 1.18/1.03 tff(1201,plain,
% 1.18/1.03 (~c1_1(a293)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1200, 1189])).
% 1.18/1.03 tff(1202,plain,
% 1.18/1.03 (((~hskp2) | c3_1(a293)) <=> ((~hskp2) | c3_1(a293))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1203,axiom,((~hskp2) | c3_1(a293)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 1.18/1.03 tff(1204,plain,
% 1.18/1.03 ((~hskp2) | c3_1(a293)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 1.18/1.03 tff(1205,plain,
% 1.18/1.03 ((~hskp2) | c3_1(a293)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1204, 1202])).
% 1.18/1.03 tff(1206,plain,
% 1.18/1.03 ((~hskp2) | c3_1(a293)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1205, 1202])).
% 1.18/1.03 tff(1207,plain,
% 1.18/1.03 ((~hskp2) | c3_1(a293)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1206, 1202])).
% 1.18/1.03 tff(1208,plain,
% 1.18/1.03 ((~hskp2) | c3_1(a293)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1207, 1202])).
% 1.18/1.03 tff(1209,plain,
% 1.18/1.03 ((~hskp2) | c3_1(a293)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1208, 1202])).
% 1.18/1.03 tff(1210,plain,
% 1.18/1.03 ((~hskp2) | c3_1(a293)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1209, 1202])).
% 1.18/1.03 tff(1211,plain,
% 1.18/1.03 ((~hskp2) | c3_1(a293)),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1210, 1202])).
% 1.18/1.03 tff(1212,plain,
% 1.18/1.03 (c3_1(a293)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1211, 1189])).
% 1.18/1.03 tff(1213,assumption,(c3_1(a296)), introduced(assumption)).
% 1.18/1.03 tff(1214,assumption,(c2_1(a296)), introduced(assumption)).
% 1.18/1.03 tff(1215,assumption,(c1_1(a296)), introduced(assumption)).
% 1.18/1.03 tff(1216,plain,
% 1.18/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a341) | c1_1(a293) | c2_1(a293) | (~ndr1_0) | (~c3_1(a293)) | (~c1_1(a341)) | (~c2_1(a341)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a293) | c2_1(a293) | (~ndr1_0) | (~c3_1(a293)) | (~c1_1(a341)) | (~c2_1(a341)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1217,plain,
% 1.18/1.03 (((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a293) | (~c3_1(a293)) | c1_1(a293)) <=> (c3_1(a341) | c1_1(a293) | c2_1(a293) | (~ndr1_0) | (~c3_1(a293)) | (~c1_1(a341)) | (~c2_1(a341)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1218,plain,
% 1.18/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a293) | (~c3_1(a293)) | c1_1(a293))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a341) | c1_1(a293) | c2_1(a293) | (~ndr1_0) | (~c3_1(a293)) | (~c1_1(a341)) | (~c2_1(a341)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296))))),
% 1.18/1.03 inference(monotonicity,[status(thm)],[1217])).
% 1.18/1.03 tff(1219,plain,
% 1.18/1.03 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a293) | (~c3_1(a293)) | c1_1(a293))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a293) | c2_1(a293) | (~ndr1_0) | (~c3_1(a293)) | (~c1_1(a341)) | (~c2_1(a341)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))),
% 1.18/1.03 inference(transitivity,[status(thm)],[1218, 1216])).
% 1.18/1.03 tff(1220,plain,
% 1.18/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a293) | (~c3_1(a293)) | c1_1(a293))),
% 1.18/1.03 inference(quant_inst,[status(thm)],[])).
% 1.18/1.03 tff(1221,plain,
% 1.18/1.03 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a293) | c2_1(a293) | (~ndr1_0) | (~c3_1(a293)) | (~c1_1(a341)) | (~c2_1(a341)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 1.18/1.03 tff(1222,plain,
% 1.18/1.03 ($false),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1221, 135, 1215, 1214, 1213, 294, 1212, 292, 1201, 1195, 1100, 581])).
% 1.18/1.03 tff(1223,plain,((~hskp2) | (~c1_1(a296)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a341)) | c3_1(a341) | (~c2_1(a341))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.03 tff(1224,plain,
% 1.18/1.03 (~hskp2),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1223, 1188, 1177, 1166, 294, 292, 1111])).
% 1.18/1.03 tff(1225,plain,
% 1.18/1.03 (^[U: $i] : refl((hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))),
% 1.18/1.03 inference(bind,[status(th)],[])).
% 1.18/1.03 tff(1226,plain,
% 1.18/1.03 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.18/1.03 inference(quant_intro,[status(thm)],[1225])).
% 1.18/1.03 tff(1227,plain,
% 1.18/1.03 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1228,plain,
% 1.18/1.03 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp2) <=> ((hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp2))), rewrite(((hskp3 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U))) | hskp2) <=> (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp2) <=> (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.18/1.03 inference(bind,[status(th)],[])).
% 1.18/1.03 tff(1229,plain,
% 1.18/1.03 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp2) <=> ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.18/1.03 inference(quant_intro,[status(thm)],[1228])).
% 1.18/1.03 tff(1230,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause156')).
% 1.18/1.03 tff(1231,plain,
% 1.18/1.03 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1230, 1229])).
% 1.18/1.03 tff(1232,plain,
% 1.18/1.03 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1231, 1227])).
% 1.18/1.03 tff(1233,plain,(
% 1.18/1.03 ![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.18/1.03 inference(skolemize,[status(sab)],[1232])).
% 1.18/1.03 tff(1234,plain,
% 1.18/1.03 (![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1233, 1226])).
% 1.18/1.03 tff(1235,plain,
% 1.18/1.03 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c3_1(a296)) | (~c1_1(a296)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c3_1(a296)) | (~c1_1(a296)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1236,plain,
% 1.18/1.03 ((hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c1_1(a296)) | (~c3_1(a296))) <=> (hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c3_1(a296)) | (~c1_1(a296)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1237,plain,
% 1.18/1.03 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c1_1(a296)) | (~c3_1(a296)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c3_1(a296)) | (~c1_1(a296))))),
% 1.18/1.03 inference(monotonicity,[status(thm)],[1236])).
% 1.18/1.03 tff(1238,plain,
% 1.18/1.03 (((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c1_1(a296)) | (~c3_1(a296)))) <=> ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c3_1(a296)) | (~c1_1(a296)))),
% 1.18/1.03 inference(transitivity,[status(thm)],[1237, 1235])).
% 1.18/1.03 tff(1239,plain,
% 1.18/1.03 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | (hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c1_1(a296)) | (~c3_1(a296)))),
% 1.18/1.03 inference(quant_inst,[status(thm)],[])).
% 1.18/1.03 tff(1240,plain,
% 1.18/1.03 ((~![U: $i] : (hskp3 | hskp2 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)))) | hskp3 | hskp2 | (~ndr1_0) | c0_1(a296) | (~c3_1(a296)) | (~c1_1(a296))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1239, 1238])).
% 1.18/1.03 tff(1241,plain,
% 1.18/1.03 (hskp2 | c0_1(a296)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1240, 135, 64, 1188, 1166, 1234])).
% 1.18/1.03 tff(1242,plain,
% 1.18/1.03 (c0_1(a296)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1241, 1224])).
% 1.18/1.03 tff(1243,plain,
% 1.18/1.03 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c0_1(a296)) | (~c2_1(a296)) | (~c3_1(a296)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp4 | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c0_1(a296)) | (~c2_1(a296)) | (~c3_1(a296)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1244,plain,
% 1.18/1.03 ((hskp4 | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337))) <=> (hskp4 | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c0_1(a296)) | (~c2_1(a296)) | (~c3_1(a296)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1245,plain,
% 1.18/1.03 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c0_1(a296)) | (~c2_1(a296)) | (~c3_1(a296))))),
% 1.18/1.03 inference(monotonicity,[status(thm)],[1244])).
% 1.18/1.03 tff(1246,plain,
% 1.18/1.03 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp4 | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c0_1(a296)) | (~c2_1(a296)) | (~c3_1(a296)))),
% 1.18/1.03 inference(transitivity,[status(thm)],[1245, 1243])).
% 1.18/1.03 tff(1247,plain,
% 1.18/1.03 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp4 | (~ndr1_0) | (~c2_1(a296)) | (~c3_1(a296)) | (~c0_1(a296)) | c2_1(a337) | (~c1_1(a337)) | (~c0_1(a337)))),
% 1.18/1.03 inference(quant_inst,[status(thm)],[])).
% 1.18/1.03 tff(1248,plain,
% 1.18/1.03 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp4 | c2_1(a337) | (~ndr1_0) | (~c1_1(a337)) | (~c0_1(a337)) | (~c0_1(a296)) | (~c2_1(a296)) | (~c3_1(a296))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 1.18/1.03 tff(1249,plain,
% 1.18/1.03 (hskp4 | (~c0_1(a296))),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1248, 135, 1177, 1166, 924, 902, 960, 1140])).
% 1.18/1.03 tff(1250,plain,
% 1.18/1.03 (hskp4),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1249, 1242])).
% 1.18/1.03 tff(1251,plain,
% 1.18/1.03 (~c2_1(a295)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1024, 1250])).
% 1.18/1.03 tff(1252,plain,
% 1.18/1.03 (~c3_1(a295)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1018, 1250])).
% 1.18/1.03 tff(1253,assumption,(~c3_1(a295)), introduced(assumption)).
% 1.18/1.03 tff(1254,assumption,(~c2_1(a295)), introduced(assumption)).
% 1.18/1.03 tff(1255,assumption,(~c0_1(a295)), introduced(assumption)).
% 1.18/1.03 tff(1256,plain,
% 1.18/1.03 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a295) | c0_1(a341) | c2_1(a295) | (~ndr1_0) | (~c1_1(a295)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a295) | c0_1(a341) | c2_1(a295) | (~ndr1_0) | (~c1_1(a295)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1257,plain,
% 1.18/1.03 ((hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a295) | c0_1(a295) | (~c1_1(a295))) <=> (hskp29 | c0_1(a295) | c0_1(a341) | c2_1(a295) | (~ndr1_0) | (~c1_1(a295)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/1.03 inference(rewrite,[status(thm)],[])).
% 1.18/1.03 tff(1258,plain,
% 1.18/1.03 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a295) | c0_1(a295) | (~c1_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a295) | c0_1(a341) | c2_1(a295) | (~ndr1_0) | (~c1_1(a295)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 1.18/1.03 inference(monotonicity,[status(thm)],[1257])).
% 1.18/1.03 tff(1259,plain,
% 1.18/1.03 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a295) | c0_1(a295) | (~c1_1(a295)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a295) | c0_1(a341) | c2_1(a295) | (~ndr1_0) | (~c1_1(a295)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/1.03 inference(transitivity,[status(thm)],[1258, 1256])).
% 1.18/1.03 tff(1260,plain,
% 1.18/1.03 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a295) | c0_1(a295) | (~c1_1(a295)))),
% 1.18/1.03 inference(quant_inst,[status(thm)],[])).
% 1.18/1.03 tff(1261,plain,
% 1.18/1.03 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a295) | c0_1(a341) | c2_1(a295) | (~ndr1_0) | (~c1_1(a295)) | (~c1_1(a341)) | (~c2_1(a341))),
% 1.18/1.03 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 1.18/1.03 tff(1262,plain,
% 1.18/1.03 (c0_1(a295) | (~c1_1(a295)) | (~c2_1(a341))),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1261, 135, 53, 294, 293, 1254, 63])).
% 1.18/1.03 tff(1263,plain,
% 1.18/1.03 (~c1_1(a295)),
% 1.18/1.03 inference(unit_resolution,[status(thm)],[1262, 1255, 581])).
% 1.18/1.04 tff(1264,plain,
% 1.18/1.04 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c0_1(a295) | c3_1(a295) | (~ndr1_0) | c1_1(a295))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a295) | c3_1(a295) | (~ndr1_0) | c1_1(a295))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1265,plain,
% 1.18/1.04 ((hskp3 | (~ndr1_0) | c3_1(a295) | c1_1(a295) | c0_1(a295)) <=> (hskp3 | c0_1(a295) | c3_1(a295) | (~ndr1_0) | c1_1(a295))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1266,plain,
% 1.18/1.04 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a295) | c1_1(a295) | c0_1(a295))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | c0_1(a295) | c3_1(a295) | (~ndr1_0) | c1_1(a295)))),
% 1.18/1.04 inference(monotonicity,[status(thm)],[1265])).
% 1.18/1.04 tff(1267,plain,
% 1.18/1.04 (((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a295) | c1_1(a295) | c0_1(a295))) <=> ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a295) | c3_1(a295) | (~ndr1_0) | c1_1(a295))),
% 1.18/1.04 inference(transitivity,[status(thm)],[1266, 1264])).
% 1.18/1.04 tff(1268,plain,
% 1.18/1.04 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp3 | (~ndr1_0) | c3_1(a295) | c1_1(a295) | c0_1(a295))),
% 1.18/1.04 inference(quant_inst,[status(thm)],[])).
% 1.18/1.04 tff(1269,plain,
% 1.18/1.04 ((~![U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp3 | c0_1(a295) | c3_1(a295) | (~ndr1_0) | c1_1(a295)),
% 1.18/1.04 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 1.18/1.04 tff(1270,plain,
% 1.18/1.04 (c0_1(a295) | c1_1(a295)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1269, 135, 64, 1253, 93])).
% 1.18/1.04 tff(1271,plain,
% 1.18/1.04 ($false),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1270, 1263, 1255])).
% 1.18/1.04 tff(1272,plain,(c0_1(a295) | hskp3 | c3_1(a295) | (~c2_1(a341)) | hskp29 | (~c1_1(a341)) | c0_1(a341) | c2_1(a295)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.04 tff(1273,plain,
% 1.18/1.04 (c0_1(a295)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1272, 1254, 1111, 64, 53, 294, 293, 1253])).
% 1.18/1.04 tff(1274,plain,
% 1.18/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1275,plain,
% 1.18/1.04 (((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1276,plain,
% 1.18/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341))))),
% 1.18/1.04 inference(monotonicity,[status(thm)],[1275])).
% 1.18/1.04 tff(1277,plain,
% 1.18/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 1.18/1.04 inference(transitivity,[status(thm)],[1276, 1274])).
% 1.18/1.04 tff(1278,plain,
% 1.18/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 1.18/1.04 inference(quant_inst,[status(thm)],[])).
% 1.18/1.04 tff(1279,plain,
% 1.18/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341))),
% 1.18/1.04 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 1.18/1.04 tff(1280,plain,
% 1.18/1.04 ($false),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1279, 135, 913, 1273, 293, 292, 902, 1254, 1253, 591, 1111, 1140])).
% 1.18/1.04 tff(1281,plain,(c2_1(a295) | c0_1(a341) | c3_1(a341) | c3_1(a295) | hskp3 | hskp29 | (~c1_1(a341))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.04 tff(1282,plain,
% 1.18/1.04 ($false),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1281, 1252, 1251, 292, 293, 64, 53, 294])).
% 1.18/1.04 tff(1283,plain,(hskp29 | c3_1(a341) | c0_1(a341) | hskp3 | (~c1_1(a341)) | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.18/1.04 tff(1284,plain,
% 1.18/1.04 (hskp29),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1283, 637, 293, 64, 294, 292])).
% 1.18/1.04 tff(1285,plain,
% 1.18/1.04 (c3_1(a301)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[376, 1284])).
% 1.18/1.04 tff(1286,plain,
% 1.18/1.04 (c2_1(a301)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[347, 1284])).
% 1.18/1.04 tff(1287,plain,
% 1.18/1.04 (c0_1(a301)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[358, 1284])).
% 1.18/1.04 tff(1288,plain,
% 1.18/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c0_1(a311)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c0_1(a311)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1289,plain,
% 1.18/1.04 ((hskp13 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311))) <=> (hskp13 | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c0_1(a311)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1290,plain,
% 1.18/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c0_1(a311)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 1.18/1.04 inference(monotonicity,[status(thm)],[1289])).
% 1.18/1.04 tff(1291,plain,
% 1.18/1.04 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c0_1(a311)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.18/1.04 inference(transitivity,[status(thm)],[1290, 1288])).
% 1.18/1.04 tff(1292,plain,
% 1.18/1.04 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)))),
% 1.18/1.04 inference(quant_inst,[status(thm)],[])).
% 1.18/1.04 tff(1293,plain,
% 1.18/1.04 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c0_1(a311)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 1.18/1.04 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 1.18/1.04 tff(1294,plain,
% 1.18/1.04 (hskp13),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1293, 135, 1287, 1286, 1285, 1132, 1131, 1130, 304])).
% 1.18/1.04 tff(1295,plain,
% 1.18/1.04 (~c2_1(a308)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1048, 1294])).
% 1.18/1.04 tff(1296,plain,
% 1.18/1.04 (((~hskp13) | (~c1_1(a308))) <=> ((~hskp13) | (~c1_1(a308)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1297,plain,
% 1.18/1.04 (((~c1_1(a308)) | (~hskp13)) <=> ((~hskp13) | (~c1_1(a308)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1298,axiom,((~c1_1(a308)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.18/1.04 tff(1299,plain,
% 1.18/1.04 ((~hskp13) | (~c1_1(a308))),
% 1.18/1.04 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 1.18/1.04 tff(1300,plain,
% 1.18/1.04 ((~hskp13) | (~c1_1(a308))),
% 1.18/1.04 inference(modus_ponens,[status(thm)],[1299, 1296])).
% 1.18/1.04 tff(1301,plain,
% 1.18/1.04 (~c1_1(a308)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1300, 1294])).
% 1.18/1.04 tff(1302,plain,
% 1.18/1.04 (c0_1(a308)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1070, 1294])).
% 1.18/1.04 tff(1303,assumption,(~c3_1(a308)), introduced(assumption)).
% 1.18/1.04 tff(1304,assumption,(~c2_1(a308)), introduced(assumption)).
% 1.18/1.04 tff(1305,assumption,(~c1_1(a308)), introduced(assumption)).
% 1.18/1.04 tff(1306,assumption,(c0_1(a308)), introduced(assumption)).
% 1.18/1.04 tff(1307,plain,
% 1.18/1.04 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a308) | (~c0_1(a308)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a308) | (~c0_1(a308)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1308,plain,
% 1.18/1.04 ((hskp3 | (~ndr1_0) | c3_1(a308) | c1_1(a308) | (~c0_1(a308)) | c2_1(a308) | c1_1(a308) | c3_1(a308)) <=> (hskp3 | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a308) | (~c0_1(a308)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1309,plain,
% 1.18/1.04 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a308) | c1_1(a308) | (~c0_1(a308)) | c2_1(a308) | c1_1(a308) | c3_1(a308))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a308) | (~c0_1(a308))))),
% 1.18/1.04 inference(monotonicity,[status(thm)],[1308])).
% 1.18/1.04 tff(1310,plain,
% 1.18/1.04 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a308) | c1_1(a308) | (~c0_1(a308)) | c2_1(a308) | c1_1(a308) | c3_1(a308))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a308) | (~c0_1(a308)))),
% 1.18/1.04 inference(transitivity,[status(thm)],[1309, 1307])).
% 1.18/1.04 tff(1311,plain,
% 1.18/1.04 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp3 | (~ndr1_0) | c3_1(a308) | c1_1(a308) | (~c0_1(a308)) | c2_1(a308) | c1_1(a308) | c3_1(a308))),
% 1.18/1.04 inference(quant_inst,[status(thm)],[])).
% 1.18/1.04 tff(1312,plain,
% 1.18/1.04 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp3 | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a308) | (~c0_1(a308))),
% 1.18/1.04 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 1.18/1.04 tff(1313,plain,
% 1.18/1.04 ($false),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1312, 135, 64, 1306, 1305, 1304, 153, 1303])).
% 1.18/1.04 tff(1314,plain,(c3_1(a308) | hskp3 | (~c0_1(a308)) | c1_1(a308) | c2_1(a308)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.04 tff(1315,plain,
% 1.18/1.04 (c3_1(a308)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1314, 1302, 64, 1301, 1295])).
% 1.18/1.04 tff(1316,plain,
% 1.18/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a341) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1317,plain,
% 1.18/1.04 (((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308)) <=> (c3_1(a341) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1318,plain,
% 1.18/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a341) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 1.18/1.04 inference(monotonicity,[status(thm)],[1317])).
% 1.18/1.04 tff(1319,plain,
% 1.18/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/1.04 inference(transitivity,[status(thm)],[1318, 1316])).
% 1.18/1.04 tff(1320,plain,
% 1.18/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308))),
% 1.18/1.04 inference(quant_inst,[status(thm)],[])).
% 1.18/1.04 tff(1321,plain,
% 1.18/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341))),
% 1.18/1.04 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 1.18/1.04 tff(1322,plain,
% 1.18/1.04 ((~c3_1(a308)) | (~c1_1(a301))),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1321, 135, 1286, 1285, 294, 292, 1301, 1295, 1100, 1111])).
% 1.18/1.04 tff(1323,plain,
% 1.18/1.04 (~c1_1(a301)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1322, 1315])).
% 1.18/1.04 tff(1324,plain,
% 1.18/1.04 ($false),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[383, 135, 1287, 1286, 1285, 294, 293, 292, 11, 1323])).
% 1.18/1.04 tff(1325,plain,(hskp8 | (~c1_1(a341)) | c0_1(a341) | c3_1(a341) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.18/1.04 tff(1326,plain,
% 1.18/1.04 (hskp8),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1325, 64, 293, 292, 294])).
% 1.18/1.04 tff(1327,plain,
% 1.18/1.04 (~c1_1(a300)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[549, 1326])).
% 1.18/1.04 tff(1328,plain,
% 1.18/1.04 (c3_1(a300)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[560, 1326])).
% 1.18/1.04 tff(1329,plain,
% 1.18/1.04 (c0_1(a300)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[571, 1326])).
% 1.18/1.04 tff(1330,plain,
% 1.18/1.04 (~c2_1(a300)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[578, 135, 294, 1329, 1328, 293, 292, 1327, 11])).
% 1.18/1.04 tff(1331,assumption,(~c1_1(a300)), introduced(assumption)).
% 1.18/1.04 tff(1332,assumption,(c3_1(a300)), introduced(assumption)).
% 1.18/1.04 tff(1333,assumption,(c0_1(a300)), introduced(assumption)).
% 1.18/1.04 tff(1334,plain,
% 1.18/1.04 (~c2_1(a300)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[578, 135, 294, 1333, 1332, 293, 292, 1331, 11])).
% 1.18/1.04 tff(1335,plain,
% 1.18/1.04 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.18/1.04 inference(bind,[status(th)],[])).
% 1.18/1.04 tff(1336,plain,
% 1.18/1.04 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.04 inference(quant_intro,[status(thm)],[1335])).
% 1.18/1.04 tff(1337,plain,
% 1.18/1.04 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1338,plain,
% 1.18/1.04 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.18/1.04 inference(bind,[status(th)],[])).
% 1.18/1.04 tff(1339,plain,
% 1.18/1.04 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.04 inference(quant_intro,[status(thm)],[1338])).
% 1.18/1.04 tff(1340,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.18/1.04 tff(1341,plain,
% 1.18/1.04 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.04 inference(modus_ponens,[status(thm)],[1340, 1339])).
% 1.18/1.04 tff(1342,plain,
% 1.18/1.04 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.04 inference(modus_ponens,[status(thm)],[1341, 1337])).
% 1.18/1.04 tff(1343,plain,(
% 1.18/1.04 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.04 inference(skolemize,[status(sab)],[1342])).
% 1.18/1.04 tff(1344,plain,
% 1.18/1.04 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.04 inference(modus_ponens,[status(thm)],[1343, 1336])).
% 1.18/1.04 tff(1345,plain,
% 1.18/1.04 (hskp29 | hskp15),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[831, 135, 1333, 1332, 1331, 335])).
% 1.18/1.04 tff(1346,plain,
% 1.18/1.04 (hskp15),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1345, 53])).
% 1.18/1.04 tff(1347,plain,
% 1.18/1.04 (~c3_1(a311)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[866, 1346])).
% 1.18/1.04 tff(1348,plain,
% 1.18/1.04 (c0_1(a311)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[853, 1346])).
% 1.18/1.04 tff(1349,plain,
% 1.18/1.04 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c3_1(a311) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c2_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c3_1(a311) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1350,plain,
% 1.18/1.04 ((hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300))) <=> (hskp22 | c3_1(a311) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1351,plain,
% 1.18/1.04 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c3_1(a311) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c2_1(a311)) | (~c0_1(a311))))),
% 1.18/1.04 inference(monotonicity,[status(thm)],[1350])).
% 1.18/1.04 tff(1352,plain,
% 1.18/1.04 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c3_1(a311) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 1.18/1.04 inference(transitivity,[status(thm)],[1351, 1349])).
% 1.18/1.04 tff(1353,plain,
% 1.18/1.04 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))),
% 1.18/1.04 inference(quant_inst,[status(thm)],[])).
% 1.18/1.04 tff(1354,plain,
% 1.18/1.04 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c3_1(a311) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c2_1(a311)) | (~c0_1(a311))),
% 1.18/1.04 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 1.18/1.04 tff(1355,plain,
% 1.18/1.04 (~c2_1(a311)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1354, 135, 940, 1348, 1332, 1347, 1331, 1344, 1334])).
% 1.18/1.04 tff(1356,plain,
% 1.18/1.04 (c0_1(a337)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1139, 53, 581])).
% 1.18/1.04 tff(1357,plain,
% 1.18/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a337) | c3_1(a311) | (~ndr1_0) | c2_1(a311) | (~c0_1(a311)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c3_1(a311) | (~ndr1_0) | c2_1(a311) | (~c0_1(a311)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1358,plain,
% 1.18/1.04 (((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a337) | c3_1(a311) | (~ndr1_0) | c2_1(a311) | (~c0_1(a311)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 1.18/1.04 inference(rewrite,[status(thm)],[])).
% 1.18/1.04 tff(1359,plain,
% 1.18/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a337) | c3_1(a311) | (~ndr1_0) | c2_1(a311) | (~c0_1(a311)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341))))),
% 1.18/1.04 inference(monotonicity,[status(thm)],[1358])).
% 1.18/1.04 tff(1360,plain,
% 1.18/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c3_1(a311) | (~ndr1_0) | c2_1(a311) | (~c0_1(a311)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 1.18/1.04 inference(transitivity,[status(thm)],[1359, 1357])).
% 1.18/1.04 tff(1361,plain,
% 1.18/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 1.18/1.04 inference(quant_inst,[status(thm)],[])).
% 1.18/1.04 tff(1362,plain,
% 1.18/1.04 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c3_1(a311) | (~ndr1_0) | c2_1(a311) | (~c0_1(a311)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341))),
% 1.18/1.04 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 1.18/1.04 tff(1363,plain,
% 1.18/1.04 ($false),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1362, 135, 913, 1348, 293, 292, 902, 1347, 591, 581, 1356, 1355])).
% 1.18/1.04 tff(1364,plain,(hskp29 | c0_1(a341) | c3_1(a341) | (~c2_1(a341)) | hskp22 | (~c3_1(a300)) | c1_1(a300) | (~c0_1(a300)) | (~c1_1(a341))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.04 tff(1365,plain,
% 1.18/1.04 (hskp29),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[1364, 1111, 292, 293, 166, 1328, 1327, 1329, 294])).
% 1.18/1.04 tff(1366,plain,
% 1.18/1.04 (c3_1(a301)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[376, 1365])).
% 1.18/1.04 tff(1367,plain,
% 1.18/1.04 (c2_1(a301)),
% 1.18/1.04 inference(unit_resolution,[status(thm)],[347, 1365])).
% 1.18/1.04 tff(1368,plain,
% 1.18/1.04 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a341) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1369,plain,
% 1.18/1.05 (((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300)) <=> (c3_1(a341) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1370,plain,
% 1.18/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c3_1(a341) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 1.18/1.05 inference(monotonicity,[status(thm)],[1369])).
% 1.18/1.05 tff(1371,plain,
% 1.18/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.18/1.05 inference(transitivity,[status(thm)],[1370, 1368])).
% 1.18/1.05 tff(1372,plain,
% 1.18/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))),
% 1.18/1.05 inference(quant_inst,[status(thm)],[])).
% 1.18/1.05 tff(1373,plain,
% 1.18/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c3_1(a341) | c1_1(a300) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)) | (~c1_1(a341)) | (~c2_1(a341))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1372, 1371])).
% 1.18/1.05 tff(1374,plain,
% 1.18/1.05 (~c1_1(a301)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[1373, 135, 1367, 1366, 294, 1328, 292, 1327, 1100, 1111, 1330])).
% 1.18/1.05 tff(1375,plain,
% 1.18/1.05 (c0_1(a301)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[358, 1365])).
% 1.18/1.05 tff(1376,plain,
% 1.18/1.05 ($false),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[383, 135, 1375, 1367, 1366, 294, 293, 292, 11, 1374])).
% 1.18/1.05 tff(1377,plain,(hskp3 | (~c1_1(a341)) | c0_1(a341) | c3_1(a341)), inference(lemma,lemma(discharge,[]))).
% 1.18/1.05 tff(1378,plain,
% 1.18/1.05 (hskp3),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[1377, 294, 293, 292])).
% 1.18/1.05 tff(1379,plain,
% 1.18/1.05 (~c1_1(a294)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[784, 1378])).
% 1.18/1.05 tff(1380,plain,
% 1.18/1.05 (c2_1(a294)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[795, 1378])).
% 1.18/1.05 tff(1381,plain,
% 1.18/1.05 (c0_1(a294)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[806, 1378])).
% 1.18/1.05 tff(1382,plain,
% 1.18/1.05 (hskp16),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[881, 135, 934, 933, 1381, 1380, 932, 1379, 291])).
% 1.18/1.05 tff(1383,plain,
% 1.18/1.05 (~c3_1(a315)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[477, 1382])).
% 1.18/1.05 tff(1384,plain,
% 1.18/1.05 (~c0_1(a315)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[459, 1382])).
% 1.18/1.05 tff(1385,plain,
% 1.18/1.05 (c2_1(a315)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[453, 1382])).
% 1.18/1.05 tff(1386,plain,
% 1.18/1.05 (~c3_1(a294)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[813, 135, 294, 1381, 1380, 293, 292, 1379, 11])).
% 1.18/1.05 tff(1387,plain,
% 1.18/1.05 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.18/1.05 inference(bind,[status(th)],[])).
% 1.18/1.05 tff(1388,plain,
% 1.18/1.05 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.18/1.05 inference(quant_intro,[status(thm)],[1387])).
% 1.18/1.05 tff(1389,plain,
% 1.18/1.05 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1390,plain,
% 1.18/1.05 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.18/1.05 inference(bind,[status(th)],[])).
% 1.18/1.05 tff(1391,plain,
% 1.18/1.05 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.18/1.05 inference(quant_intro,[status(thm)],[1390])).
% 1.18/1.05 tff(1392,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 1.18/1.05 tff(1393,plain,
% 1.18/1.05 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1392, 1391])).
% 1.18/1.05 tff(1394,plain,
% 1.18/1.05 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1393, 1389])).
% 1.18/1.05 tff(1395,plain,(
% 1.18/1.05 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.18/1.05 inference(skolemize,[status(sab)],[1394])).
% 1.18/1.05 tff(1396,plain,
% 1.18/1.05 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1395, 1388])).
% 1.18/1.05 tff(1397,plain,
% 1.18/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | c0_1(a315) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a315) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a315)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1398,plain,
% 1.18/1.05 ((hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315))) <=> (hskp13 | c0_1(a315) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a315)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1399,plain,
% 1.18/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | c0_1(a315) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a315))))),
% 1.18/1.05 inference(monotonicity,[status(thm)],[1398])).
% 1.18/1.05 tff(1400,plain,
% 1.18/1.05 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a315) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a315)))),
% 1.18/1.05 inference(transitivity,[status(thm)],[1399, 1397])).
% 1.18/1.05 tff(1401,plain,
% 1.18/1.05 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))),
% 1.18/1.05 inference(quant_inst,[status(thm)],[])).
% 1.18/1.05 tff(1402,plain,
% 1.18/1.05 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a315) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a315))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 1.18/1.05 tff(1403,plain,
% 1.18/1.05 (hskp13),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[1402, 135, 1385, 1381, 1384, 1383, 1379, 1396, 1386])).
% 1.18/1.05 tff(1404,plain,
% 1.18/1.05 (~c2_1(a308)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[1048, 1403])).
% 1.18/1.05 tff(1405,plain,
% 1.18/1.05 (c0_1(a308)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[1070, 1403])).
% 1.18/1.05 tff(1406,plain,
% 1.18/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a308) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a308) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1407,plain,
% 1.18/1.05 (((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c2_1(a308) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1408,plain,
% 1.18/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a308) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315))))),
% 1.18/1.05 inference(monotonicity,[status(thm)],[1407])).
% 1.18/1.05 tff(1409,plain,
% 1.18/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a308) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))),
% 1.18/1.05 inference(transitivity,[status(thm)],[1408, 1406])).
% 1.18/1.05 tff(1410,plain,
% 1.18/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 1.18/1.05 inference(quant_inst,[status(thm)],[])).
% 1.18/1.05 tff(1411,plain,
% 1.18/1.05 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a308) | (~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1410, 1409])).
% 1.18/1.05 tff(1412,plain,
% 1.18/1.05 (c3_1(a308)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[1411, 135, 1385, 1405, 934, 933, 1384, 1383, 1404, 591, 935])).
% 1.18/1.05 tff(1413,plain,
% 1.18/1.05 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.18/1.05 inference(bind,[status(th)],[])).
% 1.18/1.05 tff(1414,plain,
% 1.18/1.05 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.05 inference(quant_intro,[status(thm)],[1413])).
% 1.18/1.05 tff(1415,plain,
% 1.18/1.05 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1416,plain,
% 1.18/1.05 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp21))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.18/1.05 inference(bind,[status(th)],[])).
% 1.18/1.05 tff(1417,plain,
% 1.18/1.05 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.05 inference(quant_intro,[status(thm)],[1416])).
% 1.18/1.05 tff(1418,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.18/1.05 tff(1419,plain,
% 1.18/1.05 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 1.18/1.05 tff(1420,plain,
% 1.18/1.05 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1419, 1415])).
% 1.18/1.05 tff(1421,plain,(
% 1.18/1.05 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.05 inference(skolemize,[status(sab)],[1420])).
% 1.18/1.05 tff(1422,plain,
% 1.18/1.05 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1421, 1414])).
% 1.18/1.05 tff(1423,plain,
% 1.18/1.05 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1424,plain,
% 1.18/1.05 ((hskp21 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300))) <=> (hskp21 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1425,plain,
% 1.18/1.05 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300))))),
% 1.18/1.05 inference(monotonicity,[status(thm)],[1424])).
% 1.18/1.05 tff(1426,plain,
% 1.18/1.05 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))),
% 1.18/1.05 inference(transitivity,[status(thm)],[1425, 1423])).
% 1.18/1.05 tff(1427,plain,
% 1.18/1.05 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))),
% 1.18/1.05 inference(quant_inst,[status(thm)],[])).
% 1.18/1.05 tff(1428,plain,
% 1.18/1.05 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1427, 1426])).
% 1.18/1.05 tff(1429,plain,
% 1.18/1.05 (hskp21),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[1428, 135, 933, 1381, 1380, 932, 1422, 1386, 935])).
% 1.18/1.05 tff(1430,plain,
% 1.18/1.05 (((~hskp21) | (~c0_1(a330))) <=> ((~hskp21) | (~c0_1(a330)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1431,plain,
% 1.18/1.05 (((~c0_1(a330)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a330)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1432,axiom,((~c0_1(a330)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.18/1.05 tff(1433,plain,
% 1.18/1.05 ((~hskp21) | (~c0_1(a330))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 1.18/1.05 tff(1434,plain,
% 1.18/1.05 ((~hskp21) | (~c0_1(a330))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1433, 1430])).
% 1.18/1.05 tff(1435,plain,
% 1.18/1.05 (~c0_1(a330)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[1434, 1429])).
% 1.18/1.05 tff(1436,plain,
% 1.18/1.05 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1437,plain,
% 1.18/1.05 ((hskp22 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300))) <=> (hskp22 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1438,plain,
% 1.18/1.05 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300))))),
% 1.18/1.05 inference(monotonicity,[status(thm)],[1437])).
% 1.18/1.05 tff(1439,plain,
% 1.18/1.05 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300)))),
% 1.18/1.05 inference(transitivity,[status(thm)],[1438, 1436])).
% 1.18/1.05 tff(1440,plain,
% 1.18/1.05 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)) | c2_1(a300) | c1_1(a300) | (~c3_1(a300)))),
% 1.18/1.05 inference(quant_inst,[status(thm)],[])).
% 1.18/1.05 tff(1441,plain,
% 1.18/1.05 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c1_1(a300) | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)) | c2_1(a300) | (~c3_1(a300))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1440, 1439])).
% 1.18/1.05 tff(1442,plain,
% 1.18/1.05 (hskp22),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[1441, 135, 933, 1381, 1380, 932, 1344, 1386, 935])).
% 1.18/1.05 tff(1443,plain,
% 1.18/1.05 (~c3_1(a331)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[82, 1442])).
% 1.18/1.05 tff(1444,plain,
% 1.18/1.05 (~c2_1(a331)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[70, 1442])).
% 1.18/1.05 tff(1445,plain,
% 1.18/1.05 (~c1_1(a331)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[76, 1442])).
% 1.18/1.05 tff(1446,plain,
% 1.18/1.05 (((~hskp21) | (~c2_1(a330))) <=> ((~hskp21) | (~c2_1(a330)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1447,plain,
% 1.18/1.05 (((~c2_1(a330)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a330)))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1448,axiom,((~c2_1(a330)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.18/1.05 tff(1449,plain,
% 1.18/1.05 ((~hskp21) | (~c2_1(a330))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1448, 1447])).
% 1.18/1.05 tff(1450,plain,
% 1.18/1.05 ((~hskp21) | (~c2_1(a330))),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1449, 1446])).
% 1.18/1.05 tff(1451,plain,
% 1.18/1.05 (~c2_1(a330)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[1450, 1429])).
% 1.18/1.05 tff(1452,plain,
% 1.18/1.05 (((~hskp21) | c3_1(a330)) <=> ((~hskp21) | c3_1(a330))),
% 1.18/1.05 inference(rewrite,[status(thm)],[])).
% 1.18/1.05 tff(1453,axiom,((~hskp21) | c3_1(a330)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 1.18/1.05 tff(1454,plain,
% 1.18/1.05 ((~hskp21) | c3_1(a330)),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1453, 1452])).
% 1.18/1.05 tff(1455,plain,
% 1.18/1.05 ((~hskp21) | c3_1(a330)),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1454, 1452])).
% 1.18/1.05 tff(1456,plain,
% 1.18/1.05 ((~hskp21) | c3_1(a330)),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1455, 1452])).
% 1.18/1.05 tff(1457,plain,
% 1.18/1.05 ((~hskp21) | c3_1(a330)),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1456, 1452])).
% 1.18/1.05 tff(1458,plain,
% 1.18/1.05 ((~hskp21) | c3_1(a330)),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1457, 1452])).
% 1.18/1.05 tff(1459,plain,
% 1.18/1.05 ((~hskp21) | c3_1(a330)),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1458, 1452])).
% 1.18/1.05 tff(1460,plain,
% 1.18/1.05 ((~hskp21) | c3_1(a330)),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1459, 1452])).
% 1.18/1.05 tff(1461,plain,
% 1.18/1.05 ((~hskp21) | c3_1(a330)),
% 1.18/1.05 inference(modus_ponens,[status(thm)],[1460, 1452])).
% 1.18/1.05 tff(1462,plain,
% 1.18/1.05 (c3_1(a330)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[1461, 1429])).
% 1.18/1.05 tff(1463,assumption,(~c1_1(a294)), introduced(assumption)).
% 1.18/1.05 tff(1464,assumption,(c2_1(a294)), introduced(assumption)).
% 1.18/1.05 tff(1465,assumption,(c0_1(a294)), introduced(assumption)).
% 1.18/1.05 tff(1466,plain,
% 1.18/1.05 (hskp16),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[881, 135, 1333, 1332, 1465, 1464, 1331, 1463, 291])).
% 1.18/1.05 tff(1467,plain,
% 1.18/1.05 (~c3_1(a315)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[477, 1466])).
% 1.18/1.05 tff(1468,plain,
% 1.18/1.05 (~c0_1(a315)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[459, 1466])).
% 1.18/1.05 tff(1469,plain,
% 1.18/1.05 (c2_1(a315)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[453, 1466])).
% 1.18/1.05 tff(1470,plain,
% 1.18/1.05 (~c1_1(a315)),
% 1.18/1.05 inference(unit_resolution,[status(thm)],[471, 53, 294, 305, 293, 1468, 1469])).
% 1.18/1.05 tff(1471,assumption,(~c0_1(a330)), introduced(assumption)).
% 1.18/1.05 tff(1472,assumption,(c3_1(a308)), introduced(assumption)).
% 1.18/1.05 tff(1473,assumption,(~c2_1(a311)), introduced(assumption)).
% 1.18/1.05 tff(1474,assumption,(~c3_1(a311)), introduced(assumption)).
% 1.18/1.05 tff(1475,assumption,(~c3_1(a315)), introduced(assumption)).
% 1.18/1.05 tff(1476,assumption,(c0_1(a311)), introduced(assumption)).
% 1.18/1.05 tff(1477,plain,
% 1.18/1.05 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))),
% 1.18/1.06 inference(rewrite,[status(thm)],[])).
% 1.18/1.06 tff(1478,plain,
% 1.18/1.06 (((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))),
% 1.18/1.06 inference(rewrite,[status(thm)],[])).
% 1.18/1.06 tff(1479,plain,
% 1.18/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315))))),
% 1.18/1.06 inference(monotonicity,[status(thm)],[1478])).
% 1.18/1.06 tff(1480,plain,
% 1.18/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315)))),
% 1.18/1.06 inference(transitivity,[status(thm)],[1479, 1477])).
% 1.18/1.06 tff(1481,plain,
% 1.18/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | c3_1(a311) | (~c0_1(a311)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 1.18/1.06 inference(quant_inst,[status(thm)],[])).
% 1.18/1.06 tff(1482,plain,
% 1.18/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a311) | (~c0_1(a311)) | (~c2_1(a315))),
% 1.18/1.06 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 1.18/1.06 tff(1483,plain,
% 1.18/1.06 ($false),
% 1.18/1.06 inference(unit_resolution,[status(thm)],[1482, 135, 463, 1476, 1306, 462, 1475, 1474, 1304, 591, 1472, 1473])).
% 1.18/1.06 tff(1484,plain,(c2_1(a311) | (~c2_1(a315)) | (~c0_1(a311)) | (~c0_1(a308)) | c0_1(a315) | c3_1(a315) | c3_1(a311) | c2_1(a308) | (~c3_1(a308))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.06 tff(1485,plain,
% 1.18/1.06 (c2_1(a311)),
% 1.18/1.06 inference(unit_resolution,[status(thm)],[1484, 1348, 1469, 1306, 1468, 1467, 1347, 1304, 1472])).
% 1.18/1.06 tff(1486,assumption,(~c2_1(a330)), introduced(assumption)).
% 1.18/1.06 tff(1487,assumption,(c3_1(a330)), introduced(assumption)).
% 1.18/1.06 tff(1488,plain,
% 1.18/1.06 (c1_1(a311)),
% 1.18/1.06 inference(unit_resolution,[status(thm)],[842, 1346])).
% 1.18/1.06 tff(1489,assumption,(c2_1(a311)), introduced(assumption)).
% 1.18/1.06 tff(1490,assumption,(~hskp4), introduced(assumption)).
% 1.18/1.06 tff(1491,plain,
% 1.18/1.06 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~ndr1_0) | (~c1_1(a330)) | (~c3_1(a330)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~ndr1_0) | (~c1_1(a330)) | (~c3_1(a330)))),
% 1.18/1.06 inference(rewrite,[status(thm)],[])).
% 1.18/1.06 tff(1492,plain,
% 1.18/1.06 ((hskp4 | (~ndr1_0) | c0_1(a330) | (~c1_1(a330)) | (~c3_1(a330)) | c2_1(a331) | c1_1(a331) | c3_1(a331)) <=> (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~ndr1_0) | (~c1_1(a330)) | (~c3_1(a330)))),
% 1.18/1.06 inference(rewrite,[status(thm)],[])).
% 1.18/1.06 tff(1493,plain,
% 1.18/1.06 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a330) | (~c1_1(a330)) | (~c3_1(a330)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~ndr1_0) | (~c1_1(a330)) | (~c3_1(a330))))),
% 1.18/1.06 inference(monotonicity,[status(thm)],[1492])).
% 1.18/1.06 tff(1494,plain,
% 1.18/1.06 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a330) | (~c1_1(a330)) | (~c3_1(a330)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~ndr1_0) | (~c1_1(a330)) | (~c3_1(a330)))),
% 1.18/1.06 inference(transitivity,[status(thm)],[1493, 1491])).
% 1.18/1.06 tff(1495,plain,
% 1.18/1.06 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a330) | (~c1_1(a330)) | (~c3_1(a330)) | c2_1(a331) | c1_1(a331) | c3_1(a331))),
% 1.18/1.06 inference(quant_inst,[status(thm)],[])).
% 1.18/1.06 tff(1496,plain,
% 1.18/1.06 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~ndr1_0) | (~c1_1(a330)) | (~c3_1(a330))),
% 1.18/1.06 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 1.18/1.06 tff(1497,plain,
% 1.18/1.06 (hskp4 | (~c1_1(a330))),
% 1.18/1.06 inference(unit_resolution,[status(thm)],[1496, 135, 1487, 95, 154, 94, 1471, 42])).
% 1.18/1.06 tff(1498,plain,
% 1.18/1.06 (~c1_1(a330)),
% 1.18/1.06 inference(unit_resolution,[status(thm)],[1497, 1490])).
% 1.18/1.06 tff(1499,assumption,(c1_1(a311)), introduced(assumption)).
% 1.18/1.06 tff(1500,assumption,(~c1_1(a315)), introduced(assumption)).
% 1.18/1.06 tff(1501,plain,
% 1.18/1.06 (^[U: $i] : refl((hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.18/1.06 inference(bind,[status(th)],[])).
% 1.18/1.06 tff(1502,plain,
% 1.18/1.06 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.18/1.06 inference(quant_intro,[status(thm)],[1501])).
% 1.18/1.06 tff(1503,plain,
% 1.18/1.06 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.18/1.06 inference(rewrite,[status(thm)],[])).
% 1.18/1.06 tff(1504,plain,
% 1.18/1.06 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp28) <=> ((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp28))), rewrite(((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp28) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp28) <=> (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.25/1.06 inference(bind,[status(th)],[])).
% 1.25/1.06 tff(1505,plain,
% 1.25/1.06 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp28) <=> ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.25/1.06 inference(quant_intro,[status(thm)],[1504])).
% 1.25/1.06 tff(1506,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.25/1.06 tff(1507,plain,
% 1.25/1.06 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.25/1.06 inference(modus_ponens,[status(thm)],[1506, 1505])).
% 1.25/1.06 tff(1508,plain,
% 1.25/1.06 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.25/1.06 inference(modus_ponens,[status(thm)],[1507, 1503])).
% 1.25/1.06 tff(1509,plain,(
% 1.25/1.06 ![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.25/1.06 inference(skolemize,[status(sab)],[1508])).
% 1.25/1.06 tff(1510,plain,
% 1.25/1.06 (![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.25/1.06 inference(modus_ponens,[status(thm)],[1509, 1502])).
% 1.25/1.06 tff(1511,plain,
% 1.25/1.06 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp4 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp28 | hskp4 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))),
% 1.25/1.06 inference(rewrite,[status(thm)],[])).
% 1.25/1.06 tff(1512,plain,
% 1.25/1.06 ((hskp28 | hskp4 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315)) <=> (hskp28 | hskp4 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))),
% 1.25/1.06 inference(rewrite,[status(thm)],[])).
% 1.25/1.06 tff(1513,plain,
% 1.25/1.06 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp4 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315)))),
% 1.25/1.06 inference(monotonicity,[status(thm)],[1512])).
% 1.25/1.06 tff(1514,plain,
% 1.25/1.06 (((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315))) <=> ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp28 | hskp4 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315))),
% 1.25/1.06 inference(transitivity,[status(thm)],[1513, 1511])).
% 1.25/1.06 tff(1515,plain,
% 1.25/1.06 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp4 | (~ndr1_0) | c3_1(a315) | c1_1(a315) | c0_1(a315))),
% 1.25/1.06 inference(quant_inst,[status(thm)],[])).
% 1.25/1.06 tff(1516,plain,
% 1.25/1.06 ((~![U: $i] : (hskp28 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp28 | hskp4 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | c1_1(a315)),
% 1.25/1.06 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 1.25/1.06 tff(1517,plain,
% 1.25/1.06 (hskp28 | hskp4 | c1_1(a315)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1516, 135, 462, 1475, 1510])).
% 1.25/1.06 tff(1518,plain,
% 1.25/1.06 (hskp28),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1517, 1490, 1500])).
% 1.25/1.06 tff(1519,plain,
% 1.25/1.06 (c3_1(a296)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1165, 1518])).
% 1.25/1.06 tff(1520,plain,
% 1.25/1.06 (c2_1(a296)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1176, 1518])).
% 1.25/1.06 tff(1521,plain,
% 1.25/1.06 (c1_1(a296)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1187, 1518])).
% 1.25/1.06 tff(1522,plain,
% 1.25/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c2_1(a330) | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | c1_1(a330) | (~c3_1(a330)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c2_1(a330) | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | c1_1(a330) | (~c3_1(a330)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))),
% 1.25/1.06 inference(rewrite,[status(thm)],[])).
% 1.25/1.06 tff(1523,plain,
% 1.25/1.06 (((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a311) | (~c2_1(a311)) | (~c1_1(a311)) | c2_1(a330) | (~c3_1(a330)) | c1_1(a330)) <=> (c2_1(a330) | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | c1_1(a330) | (~c3_1(a330)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))),
% 1.25/1.06 inference(rewrite,[status(thm)],[])).
% 1.25/1.06 tff(1524,plain,
% 1.25/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a311) | (~c2_1(a311)) | (~c1_1(a311)) | c2_1(a330) | (~c3_1(a330)) | c1_1(a330))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c2_1(a330) | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | c1_1(a330) | (~c3_1(a330)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296))))),
% 1.25/1.06 inference(monotonicity,[status(thm)],[1523])).
% 1.25/1.06 tff(1525,plain,
% 1.25/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a311) | (~c2_1(a311)) | (~c1_1(a311)) | c2_1(a330) | (~c3_1(a330)) | c1_1(a330))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c2_1(a330) | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | c1_1(a330) | (~c3_1(a330)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296)))),
% 1.25/1.06 inference(transitivity,[status(thm)],[1524, 1522])).
% 1.25/1.06 tff(1526,plain,
% 1.25/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a296)) | (~c1_1(a296)) | (~c3_1(a296)) | c3_1(a311) | (~c2_1(a311)) | (~c1_1(a311)) | c2_1(a330) | (~c3_1(a330)) | c1_1(a330))),
% 1.25/1.06 inference(quant_inst,[status(thm)],[])).
% 1.25/1.06 tff(1527,plain,
% 1.25/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c2_1(a330) | c3_1(a311) | (~ndr1_0) | (~c1_1(a311)) | (~c2_1(a311)) | c1_1(a330) | (~c3_1(a330)) | (~c2_1(a296)) | (~c3_1(a296)) | (~c1_1(a296))),
% 1.25/1.06 inference(modus_ponens,[status(thm)],[1526, 1525])).
% 1.25/1.06 tff(1528,plain,
% 1.25/1.06 ($false),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1527, 135, 1521, 1520, 1519, 1487, 1499, 1486, 1474, 1100, 1498, 1489])).
% 1.25/1.06 tff(1529,plain,(hskp4 | (~c3_1(a330)) | (~c1_1(a311)) | c2_1(a330) | c3_1(a311) | (~c2_1(a311)) | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | c1_1(a315) | c0_1(a315) | c3_1(a315)), inference(lemma,lemma(discharge,[]))).
% 1.25/1.06 tff(1530,plain,
% 1.25/1.06 (hskp4),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1529, 1488, 1487, 1486, 1347, 1485, 95, 154, 94, 1471, 1470, 1468, 1467])).
% 1.25/1.06 tff(1531,plain,
% 1.25/1.06 (~c3_1(a295)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1018, 1530])).
% 1.25/1.06 tff(1532,plain,
% 1.25/1.06 (hskp7),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[873, 135, 1348, 1488, 1465, 1464, 1347, 1463, 52])).
% 1.25/1.06 tff(1533,plain,
% 1.25/1.06 (c3_1(a299)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[758, 1532])).
% 1.25/1.06 tff(1534,plain,
% 1.25/1.06 (~c2_1(a299)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[775, 1532])).
% 1.25/1.06 tff(1535,plain,
% 1.25/1.06 (c0_1(a299)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[747, 1532])).
% 1.25/1.06 tff(1536,plain,
% 1.25/1.06 (c0_1(a295)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1059, 1530])).
% 1.25/1.06 tff(1537,plain,
% 1.25/1.06 (~c2_1(a295)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1024, 1530])).
% 1.25/1.06 tff(1538,assumption,(hskp16), introduced(assumption)).
% 1.25/1.06 tff(1539,plain,
% 1.25/1.06 (~c3_1(a315)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[477, 1538])).
% 1.25/1.06 tff(1540,plain,
% 1.25/1.06 (~c0_1(a315)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[459, 1538])).
% 1.25/1.06 tff(1541,assumption,(c0_1(a295)), introduced(assumption)).
% 1.25/1.06 tff(1542,assumption,(c3_1(a299)), introduced(assumption)).
% 1.25/1.06 tff(1543,assumption,(c0_1(a299)), introduced(assumption)).
% 1.25/1.06 tff(1544,plain,
% 1.25/1.06 (c2_1(a315)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[453, 1538])).
% 1.25/1.06 tff(1545,plain,
% 1.25/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a299) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a299) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)))),
% 1.25/1.06 inference(rewrite,[status(thm)],[])).
% 1.25/1.06 tff(1546,plain,
% 1.25/1.06 (((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c2_1(a299) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)))),
% 1.25/1.06 inference(rewrite,[status(thm)],[])).
% 1.25/1.06 tff(1547,plain,
% 1.25/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a299) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315))))),
% 1.25/1.06 inference(monotonicity,[status(thm)],[1546])).
% 1.25/1.06 tff(1548,plain,
% 1.25/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a299) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)))),
% 1.25/1.06 inference(transitivity,[status(thm)],[1547, 1545])).
% 1.25/1.06 tff(1549,plain,
% 1.25/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 1.25/1.06 inference(quant_inst,[status(thm)],[])).
% 1.25/1.06 tff(1550,plain,
% 1.25/1.06 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a299) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315))),
% 1.25/1.06 inference(modus_ponens,[status(thm)],[1549, 1548])).
% 1.25/1.06 tff(1551,plain,
% 1.25/1.06 ($false),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1550, 135, 1544, 1543, 1542, 1541, 1540, 1539, 760, 1254, 1253, 591])).
% 1.25/1.06 tff(1552,plain,((~hskp16) | (~c0_1(a299)) | (~c3_1(a299)) | (~c0_1(a295)) | c2_1(a299) | c2_1(a295) | c3_1(a295)), inference(lemma,lemma(discharge,[]))).
% 1.25/1.06 tff(1553,plain,
% 1.25/1.06 ($false),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1552, 1537, 1536, 1466, 1535, 1534, 1533, 1531])).
% 1.25/1.06 tff(1554,plain,(hskp29 | (~c3_1(a330)) | c2_1(a330) | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a330) | (~c0_1(a308)) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a294)) | (~c2_1(a294)) | c1_1(a294) | (~c0_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c1_1(a341)) | c2_1(a341) | c0_1(a341)), inference(lemma,lemma(discharge,[]))).
% 1.25/1.06 tff(1555,plain,
% 1.25/1.06 (hskp29),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1554, 1462, 1451, 1445, 1444, 1443, 1435, 1405, 1404, 1412, 1381, 1380, 1379, 934, 933, 932, 294, 305, 293])).
% 1.25/1.06 tff(1556,plain,
% 1.25/1.06 (c3_1(a301)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[376, 1555])).
% 1.25/1.06 tff(1557,plain,
% 1.25/1.06 (c2_1(a301)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[347, 1555])).
% 1.25/1.06 tff(1558,plain,
% 1.25/1.06 (c0_1(a301)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[358, 1555])).
% 1.25/1.06 tff(1559,plain,
% 1.25/1.06 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.25/1.06 inference(rewrite,[status(thm)],[])).
% 1.25/1.06 tff(1560,plain,
% 1.25/1.06 ((hskp5 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315))) <=> (hskp5 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.25/1.06 inference(rewrite,[status(thm)],[])).
% 1.25/1.06 tff(1561,plain,
% 1.25/1.06 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 1.25/1.06 inference(monotonicity,[status(thm)],[1560])).
% 1.25/1.06 tff(1562,plain,
% 1.25/1.06 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.25/1.06 inference(transitivity,[status(thm)],[1561, 1559])).
% 1.25/1.06 tff(1563,plain,
% 1.25/1.06 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))),
% 1.25/1.06 inference(quant_inst,[status(thm)],[])).
% 1.25/1.06 tff(1564,plain,
% 1.25/1.06 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 1.25/1.06 inference(modus_ponens,[status(thm)],[1563, 1562])).
% 1.25/1.06 tff(1565,plain,
% 1.25/1.06 (hskp5),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[1564, 135, 1558, 1557, 1556, 1385, 1384, 1383, 21])).
% 1.25/1.06 tff(1566,plain,
% 1.25/1.06 (~c0_1(a297)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[392, 1565])).
% 1.25/1.06 tff(1567,plain,
% 1.25/1.06 (c2_1(a297)),
% 1.25/1.06 inference(unit_resolution,[status(thm)],[414, 1565])).
% 1.25/1.06 tff(1568,plain,
% 1.25/1.06 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c2_1(a315)) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c2_1(a315)) | (~c1_1(a341)))),
% 1.25/1.06 inference(rewrite,[status(thm)],[])).
% 1.25/1.06 tff(1569,plain,
% 1.25/1.06 (((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c2_1(a315)) | (~c1_1(a341)))),
% 1.25/1.06 inference(rewrite,[status(thm)],[])).
% 1.25/1.06 tff(1570,plain,
% 1.25/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a341) | c3_1(a341) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c2_1(a315)) | (~c1_1(a341))))),
% 1.25/1.07 inference(monotonicity,[status(thm)],[1569])).
% 1.25/1.07 tff(1571,plain,
% 1.25/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c2_1(a315)) | (~c1_1(a341)))),
% 1.25/1.07 inference(transitivity,[status(thm)],[1570, 1568])).
% 1.25/1.07 tff(1572,plain,
% 1.25/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a341) | c0_1(a341) | (~c1_1(a341)))),
% 1.25/1.07 inference(quant_inst,[status(thm)],[])).
% 1.25/1.07 tff(1573,plain,
% 1.25/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a341) | c3_1(a341) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c2_1(a315)) | (~c1_1(a341))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 1.25/1.07 tff(1574,plain,
% 1.25/1.07 (~c3_1(a297)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1573, 135, 294, 1385, 1567, 293, 292, 1384, 1383, 1566, 281])).
% 1.25/1.07 tff(1575,plain,
% 1.25/1.07 (~c1_1(a308)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1300, 1403])).
% 1.25/1.07 tff(1576,plain,
% 1.25/1.07 (c1_1(a297)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[403, 1565])).
% 1.25/1.07 tff(1577,plain,
% 1.25/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1578,plain,
% 1.25/1.07 (((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308)) <=> (c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1579,plain,
% 1.25/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301))))),
% 1.25/1.07 inference(monotonicity,[status(thm)],[1578])).
% 1.25/1.07 tff(1580,plain,
% 1.25/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 1.25/1.07 inference(transitivity,[status(thm)],[1579, 1577])).
% 1.25/1.07 tff(1581,plain,
% 1.25/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a308) | (~c3_1(a308)) | c1_1(a308))),
% 1.25/1.07 inference(quant_inst,[status(thm)],[])).
% 1.25/1.07 tff(1582,plain,
% 1.25/1.07 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | (~c3_1(a308)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1581, 1580])).
% 1.25/1.07 tff(1583,plain,
% 1.25/1.07 (~c1_1(a301)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1582, 135, 1557, 1556, 1576, 1567, 1575, 1404, 1100, 1412, 1574])).
% 1.25/1.07 tff(1584,plain,
% 1.25/1.07 ($false),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[383, 135, 1558, 1557, 1556, 294, 293, 292, 11, 1583])).
% 1.25/1.07 tff(1585,plain,(c2_1(a341) | (~c1_1(a341)) | c0_1(a341) | c3_1(a341)), inference(lemma,lemma(discharge,[]))).
% 1.25/1.07 tff(1586,plain,
% 1.25/1.07 (c2_1(a341)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1585, 271, 260, 254])).
% 1.25/1.07 tff(1587,plain,
% 1.25/1.07 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 1.25/1.07 inference(bind,[status(th)],[])).
% 1.25/1.07 tff(1588,plain,
% 1.25/1.07 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.25/1.07 inference(quant_intro,[status(thm)],[1587])).
% 1.25/1.07 tff(1589,plain,
% 1.25/1.07 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1590,plain,
% 1.25/1.07 (^[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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp9) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp9))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 1.25/1.07 inference(bind,[status(th)],[])).
% 1.25/1.07 tff(1591,plain,
% 1.25/1.07 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.25/1.07 inference(quant_intro,[status(thm)],[1590])).
% 1.25/1.07 tff(1592,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 1.25/1.07 tff(1593,plain,
% 1.25/1.07 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 1.25/1.07 tff(1594,plain,
% 1.25/1.07 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1593, 1589])).
% 1.25/1.07 tff(1595,plain,(
% 1.25/1.07 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.25/1.07 inference(skolemize,[status(sab)],[1594])).
% 1.25/1.07 tff(1596,plain,
% 1.25/1.07 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1595, 1588])).
% 1.25/1.07 tff(1597,plain,
% 1.25/1.07 (hskp3),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1377, 271, 260, 254])).
% 1.25/1.07 tff(1598,plain,
% 1.25/1.07 (~c1_1(a294)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[784, 1597])).
% 1.25/1.07 tff(1599,plain,
% 1.25/1.07 (c2_1(a294)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[795, 1597])).
% 1.25/1.07 tff(1600,plain,
% 1.25/1.07 (c0_1(a294)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[806, 1597])).
% 1.25/1.07 tff(1601,plain,
% 1.25/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp9 | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1602,plain,
% 1.25/1.07 ((hskp9 | (~ndr1_0) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294))) <=> (hskp9 | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1603,plain,
% 1.25/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)) | (~c2_1(a341))))),
% 1.25/1.07 inference(monotonicity,[status(thm)],[1602])).
% 1.25/1.07 tff(1604,plain,
% 1.25/1.07 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp9 | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)) | (~c2_1(a341)))),
% 1.25/1.07 inference(transitivity,[status(thm)],[1603, 1601])).
% 1.25/1.07 tff(1605,plain,
% 1.25/1.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c3_1(a341) | (~c2_1(a341)) | (~c1_1(a341)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))),
% 1.25/1.07 inference(quant_inst,[status(thm)],[])).
% 1.25/1.07 tff(1606,plain,
% 1.25/1.07 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp9 | c3_1(a341) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a341)) | (~c2_1(a341))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1605, 1604])).
% 1.25/1.07 tff(1607,plain,
% 1.25/1.07 (hskp9 | (~c2_1(a341))),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1606, 135, 271, 1600, 1599, 254, 1598, 1596])).
% 1.25/1.07 tff(1608,plain,
% 1.25/1.07 (hskp9),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1607, 1586])).
% 1.25/1.07 tff(1609,plain,
% 1.25/1.07 (~c2_1(a304)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[980, 1608])).
% 1.25/1.07 tff(1610,plain,
% 1.25/1.07 (c1_1(a304)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[991, 1608])).
% 1.25/1.07 tff(1611,plain,
% 1.25/1.07 (c0_1(a304)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1002, 1608])).
% 1.25/1.07 tff(1612,plain,
% 1.25/1.07 (c2_1(a341)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1585, 294, 293, 292])).
% 1.25/1.07 tff(1613,plain,
% 1.25/1.07 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.25/1.07 inference(bind,[status(th)],[])).
% 1.25/1.07 tff(1614,plain,
% 1.25/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.25/1.07 inference(quant_intro,[status(thm)],[1613])).
% 1.25/1.07 tff(1615,plain,
% 1.25/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1616,plain,
% 1.25/1.07 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(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) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.25/1.07 inference(bind,[status(th)],[])).
% 1.25/1.07 tff(1617,plain,
% 1.25/1.07 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.25/1.07 inference(quant_intro,[status(thm)],[1616])).
% 1.25/1.07 tff(1618,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 1.25/1.07 tff(1619,plain,
% 1.25/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1618, 1617])).
% 1.25/1.07 tff(1620,plain,
% 1.25/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1619, 1615])).
% 1.25/1.07 tff(1621,plain,(
% 1.25/1.07 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.25/1.07 inference(skolemize,[status(sab)],[1620])).
% 1.25/1.07 tff(1622,plain,
% 1.25/1.07 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1621, 1614])).
% 1.25/1.07 tff(1623,plain,
% 1.25/1.07 (^[U: $i] : refl((hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 1.25/1.07 inference(bind,[status(th)],[])).
% 1.25/1.07 tff(1624,plain,
% 1.25/1.07 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.25/1.07 inference(quant_intro,[status(thm)],[1623])).
% 1.25/1.07 tff(1625,plain,
% 1.25/1.07 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1626,plain,
% 1.25/1.07 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.25/1.07 inference(bind,[status(th)],[])).
% 1.25/1.07 tff(1627,plain,
% 1.25/1.07 (![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp20) <=> ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.25/1.07 inference(quant_intro,[status(thm)],[1626])).
% 1.25/1.07 tff(1628,axiom,(![U: $i] : (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.25/1.07 tff(1629,plain,
% 1.25/1.07 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 1.25/1.07 tff(1630,plain,
% 1.25/1.07 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1629, 1625])).
% 1.25/1.07 tff(1631,plain,(
% 1.25/1.07 ![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.25/1.07 inference(skolemize,[status(sab)],[1630])).
% 1.25/1.07 tff(1632,plain,
% 1.25/1.07 (![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1631, 1624])).
% 1.25/1.07 tff(1633,plain,
% 1.25/1.07 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1634,plain,
% 1.25/1.07 ((hskp20 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294))) <=> (hskp20 | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1635,plain,
% 1.25/1.07 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294))))),
% 1.25/1.07 inference(monotonicity,[status(thm)],[1634])).
% 1.25/1.07 tff(1636,plain,
% 1.25/1.07 (((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294)))),
% 1.25/1.07 inference(transitivity,[status(thm)],[1635, 1633])).
% 1.25/1.07 tff(1637,plain,
% 1.25/1.07 ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | (~ndr1_0) | c3_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))),
% 1.25/1.07 inference(quant_inst,[status(thm)],[])).
% 1.25/1.07 tff(1638,plain,
% 1.25/1.07 ((~![U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | (~ndr1_0) | (~c2_1(a294)) | c3_1(a294) | (~c0_1(a294))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1637, 1636])).
% 1.25/1.07 tff(1639,plain,
% 1.25/1.07 (hskp20 | c3_1(a294)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1638, 135, 1381, 1380, 1632])).
% 1.25/1.07 tff(1640,plain,
% 1.25/1.07 (hskp20),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1639, 1386])).
% 1.25/1.07 tff(1641,plain,
% 1.25/1.07 (((~hskp20) | (~c2_1(a329))) <=> ((~hskp20) | (~c2_1(a329)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1642,plain,
% 1.25/1.07 (((~c2_1(a329)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a329)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1643,axiom,((~c2_1(a329)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.25/1.07 tff(1644,plain,
% 1.25/1.07 ((~hskp20) | (~c2_1(a329))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1643, 1642])).
% 1.25/1.07 tff(1645,plain,
% 1.25/1.07 ((~hskp20) | (~c2_1(a329))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1644, 1641])).
% 1.25/1.07 tff(1646,plain,
% 1.25/1.07 (~c2_1(a329)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1645, 1640])).
% 1.25/1.07 tff(1647,plain,
% 1.25/1.07 (((~hskp20) | (~c1_1(a329))) <=> ((~hskp20) | (~c1_1(a329)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1648,plain,
% 1.25/1.07 (((~c1_1(a329)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a329)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1649,axiom,((~c1_1(a329)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.25/1.07 tff(1650,plain,
% 1.25/1.07 ((~hskp20) | (~c1_1(a329))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 1.25/1.07 tff(1651,plain,
% 1.25/1.07 ((~hskp20) | (~c1_1(a329))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1650, 1647])).
% 1.25/1.07 tff(1652,plain,
% 1.25/1.07 (~c1_1(a329)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1651, 1640])).
% 1.25/1.07 tff(1653,plain,
% 1.25/1.07 (((~hskp20) | (~c0_1(a329))) <=> ((~hskp20) | (~c0_1(a329)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1654,plain,
% 1.25/1.07 (((~c0_1(a329)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a329)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1655,axiom,((~c0_1(a329)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.25/1.07 tff(1656,plain,
% 1.25/1.07 ((~hskp20) | (~c0_1(a329))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1655, 1654])).
% 1.25/1.07 tff(1657,plain,
% 1.25/1.07 ((~hskp20) | (~c0_1(a329))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1656, 1653])).
% 1.25/1.07 tff(1658,plain,
% 1.25/1.07 (~c0_1(a329)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1657, 1640])).
% 1.25/1.07 tff(1659,plain,
% 1.25/1.07 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a329) | c1_1(a329) | c2_1(a329) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a329) | c1_1(a329) | c2_1(a329) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1660,plain,
% 1.25/1.07 ((hskp0 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c2_1(a329) | c1_1(a329) | c0_1(a329)) <=> (hskp0 | c0_1(a329) | c1_1(a329) | c2_1(a329) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)))),
% 1.25/1.07 inference(rewrite,[status(thm)],[])).
% 1.25/1.07 tff(1661,plain,
% 1.25/1.07 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c2_1(a329) | c1_1(a329) | c0_1(a329))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a329) | c1_1(a329) | c2_1(a329) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294))))),
% 1.25/1.07 inference(monotonicity,[status(thm)],[1660])).
% 1.25/1.07 tff(1662,plain,
% 1.25/1.07 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c2_1(a329) | c1_1(a329) | c0_1(a329))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a329) | c1_1(a329) | c2_1(a329) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)))),
% 1.25/1.07 inference(transitivity,[status(thm)],[1661, 1659])).
% 1.25/1.07 tff(1663,plain,
% 1.25/1.07 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c2_1(a329) | c1_1(a329) | c0_1(a329))),
% 1.25/1.07 inference(quant_inst,[status(thm)],[])).
% 1.25/1.07 tff(1664,plain,
% 1.25/1.07 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a329) | c1_1(a329) | c2_1(a329) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294))),
% 1.25/1.07 inference(modus_ponens,[status(thm)],[1663, 1662])).
% 1.25/1.07 tff(1665,plain,
% 1.25/1.07 (hskp0),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1664, 135, 1381, 1658, 1652, 1646, 1379, 1622, 1386])).
% 1.25/1.07 tff(1666,plain,
% 1.25/1.07 (~c2_1(a291)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[517, 1665])).
% 1.25/1.07 tff(1667,plain,
% 1.25/1.07 (c1_1(a291)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[528, 1665])).
% 1.25/1.07 tff(1668,plain,
% 1.25/1.07 (hskp29 | c0_1(a291) | (~c2_1(a341))),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[535, 135, 294, 1667, 293, 1666, 63])).
% 1.25/1.07 tff(1669,plain,
% 1.25/1.07 (c0_1(a291)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1668, 53, 1612])).
% 1.25/1.07 tff(1670,plain,
% 1.25/1.07 (c0_1(a337)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[1139, 53, 1612])).
% 1.25/1.07 tff(1671,plain,
% 1.25/1.07 (~c3_1(a291)),
% 1.25/1.07 inference(unit_resolution,[status(thm)],[542, 1665])).
% 1.25/1.07 tff(1672,plain,
% 1.25/1.07 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 1.25/1.08 inference(rewrite,[status(thm)],[])).
% 1.25/1.08 tff(1673,plain,
% 1.25/1.08 (((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 1.25/1.08 inference(rewrite,[status(thm)],[])).
% 1.25/1.08 tff(1674,plain,
% 1.25/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341))))),
% 1.25/1.08 inference(monotonicity,[status(thm)],[1673])).
% 1.25/1.08 tff(1675,plain,
% 1.25/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341)))),
% 1.25/1.08 inference(transitivity,[status(thm)],[1674, 1672])).
% 1.25/1.08 tff(1676,plain,
% 1.25/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a337) | (~c3_1(a337)) | (~c0_1(a337)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 1.25/1.08 inference(quant_inst,[status(thm)],[])).
% 1.25/1.08 tff(1677,plain,
% 1.25/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a337) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | (~c3_1(a337)) | (~c0_1(a337)) | (~c2_1(a341))),
% 1.25/1.08 inference(modus_ponens,[status(thm)],[1676, 1675])).
% 1.25/1.08 tff(1678,plain,
% 1.25/1.08 ((~c0_1(a291)) | (~c0_1(a337)) | (~c2_1(a341))),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[1677, 135, 913, 293, 292, 902, 1666, 1671, 591])).
% 1.25/1.08 tff(1679,plain,
% 1.25/1.08 ($false),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[1678, 1670, 1669, 1612])).
% 1.25/1.08 tff(1680,plain,(hskp29 | c0_1(a341) | c3_1(a341) | (~c1_1(a341))), inference(lemma,lemma(discharge,[]))).
% 1.25/1.08 tff(1681,plain,
% 1.25/1.08 (hskp29),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[1680, 260, 254, 271])).
% 1.25/1.08 tff(1682,plain,
% 1.25/1.08 (c3_1(a301)),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[376, 1681])).
% 1.25/1.08 tff(1683,plain,
% 1.25/1.08 (c2_1(a301)),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[347, 1681])).
% 1.25/1.08 tff(1684,plain,
% 1.25/1.08 (c0_1(a301)),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[358, 1681])).
% 1.25/1.08 tff(1685,plain,
% 1.25/1.08 (hskp4),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[1012, 135, 1684, 1683, 1682, 1611, 1610, 1609, 960])).
% 1.25/1.08 tff(1686,plain,
% 1.25/1.08 (~c3_1(a295)),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[1018, 1685])).
% 1.25/1.08 tff(1687,plain,
% 1.25/1.08 (~c2_1(a295)),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[1024, 1685])).
% 1.25/1.08 tff(1688,plain,
% 1.25/1.08 (~c3_1(a294)),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[813, 135, 271, 1600, 1599, 260, 254, 1598, 11])).
% 1.25/1.08 tff(1689,plain,
% 1.25/1.08 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a341)))),
% 1.25/1.08 inference(rewrite,[status(thm)],[])).
% 1.25/1.08 tff(1690,plain,
% 1.25/1.08 ((hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a341) | c3_1(a341) | (~c2_1(a341))) <=> (hskp13 | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a341)))),
% 1.25/1.08 inference(rewrite,[status(thm)],[])).
% 1.25/1.08 tff(1691,plain,
% 1.25/1.08 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a341) | c3_1(a341) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a341))))),
% 1.25/1.08 inference(monotonicity,[status(thm)],[1690])).
% 1.25/1.08 tff(1692,plain,
% 1.25/1.08 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a341) | c3_1(a341) | (~c2_1(a341)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a341)))),
% 1.25/1.08 inference(transitivity,[status(thm)],[1691, 1689])).
% 1.25/1.08 tff(1693,plain,
% 1.25/1.08 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a294) | c1_1(a294) | (~c0_1(a294)) | c0_1(a341) | c3_1(a341) | (~c2_1(a341)))),
% 1.25/1.08 inference(quant_inst,[status(thm)],[])).
% 1.25/1.08 tff(1694,plain,
% 1.25/1.08 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c0_1(a341) | c3_1(a341) | c1_1(a294) | (~ndr1_0) | c3_1(a294) | (~c0_1(a294)) | (~c2_1(a341))),
% 1.25/1.08 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 1.25/1.08 tff(1695,plain,
% 1.25/1.08 (hskp13 | (~c2_1(a341))),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[1694, 135, 1600, 260, 254, 1598, 1396, 1688])).
% 1.25/1.08 tff(1696,plain,
% 1.25/1.08 (hskp13),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[1695, 1586])).
% 1.25/1.08 tff(1697,plain,
% 1.25/1.08 (~c2_1(a308)),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[1048, 1696])).
% 1.25/1.08 tff(1698,plain,
% 1.25/1.08 (c0_1(a295)),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[1059, 1685])).
% 1.25/1.08 tff(1699,plain,
% 1.25/1.08 (c0_1(a308)),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[1070, 1696])).
% 1.25/1.08 tff(1700,plain,
% 1.25/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a308)) | (~c0_1(a308)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a308)) | (~c0_1(a308)) | (~c2_1(a341)))),
% 1.25/1.08 inference(rewrite,[status(thm)],[])).
% 1.25/1.08 tff(1701,plain,
% 1.25/1.08 (((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a308)) | (~c0_1(a308)) | (~c2_1(a341)))),
% 1.25/1.08 inference(rewrite,[status(thm)],[])).
% 1.25/1.08 tff(1702,plain,
% 1.25/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a308)) | (~c0_1(a308)) | (~c2_1(a341))))),
% 1.25/1.08 inference(monotonicity,[status(thm)],[1701])).
% 1.25/1.08 tff(1703,plain,
% 1.25/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a308)) | (~c0_1(a308)) | (~c2_1(a341)))),
% 1.25/1.08 inference(transitivity,[status(thm)],[1702, 1700])).
% 1.25/1.08 tff(1704,plain,
% 1.25/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a308) | (~c3_1(a308)) | (~c0_1(a308)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 1.25/1.08 inference(quant_inst,[status(thm)],[])).
% 1.25/1.08 tff(1705,plain,
% 1.25/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a308)) | (~c0_1(a308)) | (~c2_1(a341))),
% 1.25/1.08 inference(modus_ponens,[status(thm)],[1704, 1703])).
% 1.25/1.08 tff(1706,plain,
% 1.25/1.08 (~c3_1(a308)),
% 1.25/1.08 inference(unit_resolution,[status(thm)],[1705, 135, 1699, 1698, 260, 254, 1697, 1687, 1686, 591, 1586])).
% 1.25/1.08 tff(1707,plain,
% 1.25/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a304) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a304)) | (~c0_1(a304)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a304) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a304)) | (~c0_1(a304)) | (~c2_1(a341)))),
% 1.25/1.08 inference(rewrite,[status(thm)],[])).
% 1.25/1.08 tff(1708,plain,
% 1.25/1.08 (((~ndr1_0) | c2_1(a304) | (~c3_1(a304)) | (~c0_1(a304)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a304) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a304)) | (~c0_1(a304)) | (~c2_1(a341)))),
% 1.25/1.08 inference(rewrite,[status(thm)],[])).
% 1.25/1.08 tff(1709,plain,
% 1.25/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a304) | (~c3_1(a304)) | (~c0_1(a304)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a304) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a304)) | (~c0_1(a304)) | (~c2_1(a341))))),
% 1.25/1.08 inference(monotonicity,[status(thm)],[1708])).
% 1.25/1.08 tff(1710,plain,
% 1.25/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a304) | (~c3_1(a304)) | (~c0_1(a304)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a304) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a304)) | (~c0_1(a304)) | (~c2_1(a341)))),
% 1.27/1.08 inference(transitivity,[status(thm)],[1709, 1707])).
% 1.27/1.08 tff(1711,plain,
% 1.27/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a304) | (~c3_1(a304)) | (~c0_1(a304)) | c2_1(a295) | c3_1(a295) | (~c0_1(a295)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 1.27/1.08 inference(quant_inst,[status(thm)],[])).
% 1.27/1.08 tff(1712,plain,
% 1.27/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a304) | c2_1(a295) | c3_1(a295) | (~ndr1_0) | (~c0_1(a295)) | (~c3_1(a304)) | (~c0_1(a304)) | (~c2_1(a341))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 1.27/1.08 tff(1713,plain,
% 1.27/1.08 (~c3_1(a304)),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[1712, 135, 1611, 1698, 260, 254, 1609, 1687, 1686, 591, 1586])).
% 1.27/1.08 tff(1714,plain,
% 1.27/1.08 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a304)) | c3_1(a304) | (~c0_1(a304)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a304)) | c3_1(a304) | (~c0_1(a304)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(1715,plain,
% 1.27/1.08 ((hskp7 | (~ndr1_0) | c3_1(a304) | (~c1_1(a304)) | (~c0_1(a304)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294))) <=> (hskp7 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a304)) | c3_1(a304) | (~c0_1(a304)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(1716,plain,
% 1.27/1.08 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a304) | (~c1_1(a304)) | (~c0_1(a304)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a304)) | c3_1(a304) | (~c0_1(a304))))),
% 1.27/1.08 inference(monotonicity,[status(thm)],[1715])).
% 1.27/1.08 tff(1717,plain,
% 1.27/1.08 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a304) | (~c1_1(a304)) | (~c0_1(a304)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a304)) | c3_1(a304) | (~c0_1(a304)))),
% 1.27/1.08 inference(transitivity,[status(thm)],[1716, 1714])).
% 1.27/1.08 tff(1718,plain,
% 1.27/1.08 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a304) | (~c1_1(a304)) | (~c0_1(a304)) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))),
% 1.27/1.08 inference(quant_inst,[status(thm)],[])).
% 1.27/1.08 tff(1719,plain,
% 1.27/1.08 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp7 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)) | (~c1_1(a304)) | c3_1(a304) | (~c0_1(a304))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1718, 1717])).
% 1.27/1.08 tff(1720,plain,
% 1.27/1.08 (hskp7),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[1719, 135, 1611, 1610, 1600, 1599, 1598, 52, 1713])).
% 1.27/1.08 tff(1721,plain,
% 1.27/1.08 (~c2_1(a299)),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[775, 1720])).
% 1.27/1.08 tff(1722,plain,
% 1.27/1.08 (c3_1(a299)),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[758, 1720])).
% 1.27/1.08 tff(1723,plain,
% 1.27/1.08 (c0_1(a299)),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[747, 1720])).
% 1.27/1.08 tff(1724,plain,
% 1.27/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a341)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(1725,plain,
% 1.27/1.08 (((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341))) <=> (c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a341)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(1726,plain,
% 1.27/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a341))))),
% 1.27/1.08 inference(monotonicity,[status(thm)],[1725])).
% 1.27/1.08 tff(1727,plain,
% 1.27/1.08 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a341)))),
% 1.27/1.08 inference(transitivity,[status(thm)],[1726, 1724])).
% 1.27/1.08 tff(1728,plain,
% 1.27/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a341) | c0_1(a341) | (~c2_1(a341)))),
% 1.27/1.08 inference(quant_inst,[status(thm)],[])).
% 1.27/1.08 tff(1729,plain,
% 1.27/1.08 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a341) | c3_1(a341) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a341))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1728, 1727])).
% 1.27/1.08 tff(1730,plain,
% 1.27/1.08 ($false),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[1729, 135, 1699, 1723, 1722, 260, 254, 1697, 1721, 591, 1586, 1706])).
% 1.27/1.08 tff(1731,plain,(~hskp24), inference(lemma,lemma(discharge,[]))).
% 1.27/1.08 tff(1732,plain,
% 1.27/1.08 (hskp31 | hskp27),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[133, 1731])).
% 1.27/1.08 tff(1733,plain,
% 1.27/1.08 (hskp27),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[1732, 247])).
% 1.27/1.08 tff(1734,plain,
% 1.27/1.08 (((~hskp27) | (~c2_1(a368))) <=> ((~hskp27) | (~c2_1(a368)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(1735,plain,
% 1.27/1.08 (((~c2_1(a368)) | (~hskp27)) <=> ((~hskp27) | (~c2_1(a368)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(1736,axiom,((~c2_1(a368)) | (~hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 1.27/1.08 tff(1737,plain,
% 1.27/1.08 ((~hskp27) | (~c2_1(a368))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 1.27/1.08 tff(1738,plain,
% 1.27/1.08 ((~hskp27) | (~c2_1(a368))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1737, 1734])).
% 1.27/1.08 tff(1739,plain,
% 1.27/1.08 (~c2_1(a368)),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[1738, 1733])).
% 1.27/1.08 tff(1740,plain,
% 1.27/1.08 (((~hskp27) | (~c0_1(a368))) <=> ((~hskp27) | (~c0_1(a368)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(1741,plain,
% 1.27/1.08 (((~c0_1(a368)) | (~hskp27)) <=> ((~hskp27) | (~c0_1(a368)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(1742,axiom,((~c0_1(a368)) | (~hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.27/1.08 tff(1743,plain,
% 1.27/1.08 ((~hskp27) | (~c0_1(a368))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 1.27/1.08 tff(1744,plain,
% 1.27/1.08 ((~hskp27) | (~c0_1(a368))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1743, 1740])).
% 1.27/1.08 tff(1745,plain,
% 1.27/1.08 (~c0_1(a368)),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[1744, 1733])).
% 1.27/1.08 tff(1746,plain,
% 1.27/1.08 (((~hskp27) | c1_1(a368)) <=> ((~hskp27) | c1_1(a368))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(1747,axiom,((~hskp27) | c1_1(a368)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.27/1.08 tff(1748,plain,
% 1.27/1.08 ((~hskp27) | c1_1(a368)),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1747, 1746])).
% 1.27/1.08 tff(1749,plain,
% 1.27/1.08 ((~hskp27) | c1_1(a368)),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1748, 1746])).
% 1.27/1.08 tff(1750,plain,
% 1.27/1.08 ((~hskp27) | c1_1(a368)),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1749, 1746])).
% 1.27/1.08 tff(1751,plain,
% 1.27/1.08 ((~hskp27) | c1_1(a368)),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1750, 1746])).
% 1.27/1.08 tff(1752,plain,
% 1.27/1.08 ((~hskp27) | c1_1(a368)),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1751, 1746])).
% 1.27/1.08 tff(1753,plain,
% 1.27/1.08 ((~hskp27) | c1_1(a368)),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1752, 1746])).
% 1.27/1.08 tff(1754,plain,
% 1.27/1.08 ((~hskp27) | c1_1(a368)),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1753, 1746])).
% 1.27/1.08 tff(1755,plain,
% 1.27/1.08 ((~hskp27) | c1_1(a368)),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1754, 1746])).
% 1.27/1.08 tff(1756,plain,
% 1.27/1.08 (c1_1(a368)),
% 1.27/1.08 inference(unit_resolution,[status(thm)],[1755, 1733])).
% 1.27/1.08 tff(1757,assumption,(~c2_1(a368)), introduced(assumption)).
% 1.27/1.08 tff(1758,assumption,(~c0_1(a368)), introduced(assumption)).
% 1.27/1.08 tff(1759,assumption,(c1_1(a368)), introduced(assumption)).
% 1.27/1.08 tff(1760,plain,
% 1.27/1.08 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a368)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a368)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(1761,plain,
% 1.27/1.08 ((hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368))) <=> (hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a368)))),
% 1.27/1.08 inference(rewrite,[status(thm)],[])).
% 1.27/1.08 tff(1762,plain,
% 1.27/1.08 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a368))))),
% 1.27/1.08 inference(monotonicity,[status(thm)],[1761])).
% 1.27/1.08 tff(1763,plain,
% 1.27/1.08 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a368)))),
% 1.27/1.08 inference(transitivity,[status(thm)],[1762, 1760])).
% 1.27/1.08 tff(1764,plain,
% 1.27/1.08 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368)))),
% 1.27/1.08 inference(quant_inst,[status(thm)],[])).
% 1.27/1.08 tff(1765,plain,
% 1.27/1.08 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a297) | (~ndr1_0) | (~c2_1(a297)) | (~c1_1(a297)) | (~c1_1(a368))),
% 1.27/1.08 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 1.27/1.09 tff(1766,plain,
% 1.27/1.09 ($false),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1765, 135, 53, 1759, 404, 415, 1758, 1757, 393, 63])).
% 1.27/1.09 tff(1767,plain,((~hskp5) | hskp29 | (~c1_1(a368)) | c0_1(a368) | c2_1(a368)), inference(lemma,lemma(discharge,[]))).
% 1.27/1.09 tff(1768,plain,
% 1.27/1.09 (~hskp5),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1767, 1756, 53, 1745, 1739])).
% 1.27/1.09 tff(1769,plain,
% 1.27/1.09 (hskp16),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[442, 1768, 166])).
% 1.27/1.09 tff(1770,plain,
% 1.27/1.09 (~c0_1(a315)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[459, 1769])).
% 1.27/1.09 tff(1771,plain,
% 1.27/1.09 (c2_1(a315)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[453, 1769])).
% 1.27/1.09 tff(1772,plain,
% 1.27/1.09 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a368)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a368)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1773,plain,
% 1.27/1.09 ((hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368))) <=> (hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a368)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1774,plain,
% 1.27/1.09 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a368))))),
% 1.27/1.09 inference(monotonicity,[status(thm)],[1773])).
% 1.27/1.09 tff(1775,plain,
% 1.27/1.09 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a368)))),
% 1.27/1.09 inference(transitivity,[status(thm)],[1774, 1772])).
% 1.27/1.09 tff(1776,plain,
% 1.27/1.09 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp29 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)) | c2_1(a368) | c0_1(a368) | (~c1_1(a368)))),
% 1.27/1.09 inference(quant_inst,[status(thm)],[])).
% 1.27/1.09 tff(1777,plain,
% 1.27/1.09 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp29 | c0_1(a368) | c2_1(a368) | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)) | (~c1_1(a368))),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1776, 1775])).
% 1.27/1.09 tff(1778,plain,
% 1.27/1.09 (~c1_1(a315)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1777, 135, 53, 1756, 1771, 1745, 1739, 1770, 63])).
% 1.27/1.09 tff(1779,plain,
% 1.27/1.09 (~c3_1(a315)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[477, 1769])).
% 1.27/1.09 tff(1780,plain,
% 1.27/1.09 ($false),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[484, 135, 64, 1770, 1779, 93, 1778])).
% 1.27/1.09 tff(1781,plain,(hskp3 | hskp29), inference(lemma,lemma(discharge,[]))).
% 1.27/1.09 tff(1782,plain,
% 1.27/1.09 (hskp3),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1781, 53])).
% 1.27/1.09 tff(1783,plain,
% 1.27/1.09 (~c1_1(a294)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[784, 1782])).
% 1.27/1.09 tff(1784,plain,
% 1.27/1.09 (c2_1(a294)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[795, 1782])).
% 1.27/1.09 tff(1785,plain,
% 1.27/1.09 (c0_1(a294)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[806, 1782])).
% 1.27/1.09 tff(1786,plain,
% 1.27/1.09 (((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp24 | hskp16 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1787,plain,
% 1.27/1.09 ((hskp24 | hskp16 | (~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294))) <=> (hskp24 | hskp16 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1788,plain,
% 1.27/1.09 (((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294))))),
% 1.27/1.09 inference(monotonicity,[status(thm)],[1787])).
% 1.27/1.09 tff(1789,plain,
% 1.27/1.09 (((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))) <=> ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp24 | hskp16 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294)))),
% 1.27/1.09 inference(transitivity,[status(thm)],[1788, 1786])).
% 1.27/1.09 tff(1790,plain,
% 1.27/1.09 ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c0_1(a294)))),
% 1.27/1.09 inference(quant_inst,[status(thm)],[])).
% 1.27/1.09 tff(1791,plain,
% 1.27/1.09 ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp24 | hskp16 | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c0_1(a294))),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1790, 1789])).
% 1.27/1.09 tff(1792,plain,
% 1.27/1.09 (hskp16),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1791, 135, 1731, 1465, 1464, 1463, 31])).
% 1.27/1.09 tff(1793,plain,
% 1.27/1.09 (~c3_1(a315)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[477, 1792])).
% 1.27/1.09 tff(1794,plain,
% 1.27/1.09 (~c0_1(a315)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[459, 1792])).
% 1.27/1.09 tff(1795,plain,
% 1.27/1.09 (c2_1(a315)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[453, 1792])).
% 1.27/1.09 tff(1796,plain,
% 1.27/1.09 (((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)))) <=> ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp15 | hskp8 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1797,plain,
% 1.27/1.09 ((hskp15 | hskp8 | (~ndr1_0) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (hskp15 | hskp8 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1798,plain,
% 1.27/1.09 (((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | (~ndr1_0) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315))))),
% 1.27/1.09 inference(monotonicity,[status(thm)],[1797])).
% 1.27/1.09 tff(1799,plain,
% 1.27/1.09 (((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | (~ndr1_0) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp15 | hskp8 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)))),
% 1.27/1.09 inference(transitivity,[status(thm)],[1798, 1796])).
% 1.27/1.09 tff(1800,plain,
% 1.27/1.09 ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp15 | hskp8 | (~ndr1_0) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 1.27/1.09 inference(quant_inst,[status(thm)],[])).
% 1.27/1.09 tff(1801,plain,
% 1.27/1.09 ((~![U: $i] : (hskp15 | hskp8 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp15 | hskp8 | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315))),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.27/1.09 tff(1802,plain,
% 1.27/1.09 (hskp15 | hskp8),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1801, 135, 1795, 1794, 1793, 1121])).
% 1.27/1.09 tff(1803,plain,
% 1.27/1.09 (hskp15),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1802, 637])).
% 1.27/1.09 tff(1804,plain,
% 1.27/1.09 (~c3_1(a311)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[866, 1803])).
% 1.27/1.09 tff(1805,plain,
% 1.27/1.09 (c1_1(a311)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[842, 1803])).
% 1.27/1.09 tff(1806,plain,
% 1.27/1.09 (c0_1(a311)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[853, 1803])).
% 1.27/1.09 tff(1807,plain,
% 1.27/1.09 (hskp7),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[873, 135, 1806, 1805, 1465, 1464, 1804, 1463, 52])).
% 1.27/1.09 tff(1808,plain,
% 1.27/1.09 (~c2_1(a299)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[775, 1807])).
% 1.27/1.09 tff(1809,plain,
% 1.27/1.09 (c3_1(a299)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[758, 1807])).
% 1.27/1.09 tff(1810,plain,
% 1.27/1.09 (c0_1(a299)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[747, 1807])).
% 1.27/1.09 tff(1811,assumption,(~hskp13), introduced(assumption)).
% 1.27/1.09 tff(1812,plain,
% 1.27/1.09 ($false),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1042, 135, 32, 1811, 1036, 943, 942, 1035])).
% 1.27/1.09 tff(1813,plain,(hskp16 | hskp13 | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.27/1.09 tff(1814,plain,
% 1.27/1.09 (hskp16),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1813, 1811, 940])).
% 1.27/1.09 tff(1815,plain,
% 1.27/1.09 (c2_1(a315)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[453, 1814])).
% 1.27/1.09 tff(1816,plain,
% 1.27/1.09 (~c3_1(a315)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[477, 1814])).
% 1.27/1.09 tff(1817,plain,
% 1.27/1.09 ((hskp18 | hskp13 | hskp8) <=> (hskp18 | hskp13 | hskp8)),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1818,plain,
% 1.27/1.09 (((hskp13 | hskp8) | hskp18) <=> (hskp18 | hskp13 | hskp8)),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1819,plain,
% 1.27/1.09 ((hskp8 | hskp13) <=> (hskp13 | hskp8)),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1820,plain,
% 1.27/1.09 (((hskp8 | hskp13) | hskp18) <=> ((hskp13 | hskp8) | hskp18)),
% 1.27/1.09 inference(monotonicity,[status(thm)],[1819])).
% 1.27/1.09 tff(1821,plain,
% 1.27/1.09 (((hskp8 | hskp13) | hskp18) <=> (hskp18 | hskp13 | hskp8)),
% 1.27/1.09 inference(transitivity,[status(thm)],[1820, 1818])).
% 1.27/1.09 tff(1822,axiom,((hskp8 | hskp13) | hskp18), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause36')).
% 1.27/1.09 tff(1823,plain,
% 1.27/1.09 (hskp18 | hskp13 | hskp8),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1822, 1821])).
% 1.27/1.09 tff(1824,plain,
% 1.27/1.09 (hskp18 | hskp13 | hskp8),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1823, 1817])).
% 1.27/1.09 tff(1825,plain,
% 1.27/1.09 (hskp18 | hskp13 | hskp8),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1824, 1817])).
% 1.27/1.09 tff(1826,plain,
% 1.27/1.09 (hskp18 | hskp13 | hskp8),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1825, 1817])).
% 1.27/1.09 tff(1827,plain,
% 1.27/1.09 (hskp18 | hskp13 | hskp8),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1826, 1817])).
% 1.27/1.09 tff(1828,plain,
% 1.27/1.09 (hskp18 | hskp13 | hskp8),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1827, 1817])).
% 1.27/1.09 tff(1829,plain,
% 1.27/1.09 (hskp18 | hskp13 | hskp8),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1828, 1817])).
% 1.27/1.09 tff(1830,plain,
% 1.27/1.09 (hskp18 | hskp13 | hskp8),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1829, 1817])).
% 1.27/1.09 tff(1831,plain,
% 1.27/1.09 (hskp18),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1830, 1811, 637])).
% 1.27/1.09 tff(1832,plain,
% 1.27/1.09 (((~hskp18) | (~c3_1(a325))) <=> ((~hskp18) | (~c3_1(a325)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1833,plain,
% 1.27/1.09 (((~c3_1(a325)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a325)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1834,axiom,((~c3_1(a325)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.27/1.09 tff(1835,plain,
% 1.27/1.09 ((~hskp18) | (~c3_1(a325))),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1834, 1833])).
% 1.27/1.09 tff(1836,plain,
% 1.27/1.09 ((~hskp18) | (~c3_1(a325))),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1835, 1832])).
% 1.27/1.09 tff(1837,plain,
% 1.27/1.09 (~c3_1(a325)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1836, 1831])).
% 1.27/1.09 tff(1838,plain,
% 1.27/1.09 (((~hskp18) | (~c1_1(a325))) <=> ((~hskp18) | (~c1_1(a325)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1839,plain,
% 1.27/1.09 (((~c1_1(a325)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a325)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1840,axiom,((~c1_1(a325)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.27/1.09 tff(1841,plain,
% 1.27/1.09 ((~hskp18) | (~c1_1(a325))),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 1.27/1.09 tff(1842,plain,
% 1.27/1.09 ((~hskp18) | (~c1_1(a325))),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1841, 1838])).
% 1.27/1.09 tff(1843,plain,
% 1.27/1.09 (~c1_1(a325)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1842, 1831])).
% 1.27/1.09 tff(1844,plain,
% 1.27/1.09 (((~hskp18) | c0_1(a325)) <=> ((~hskp18) | c0_1(a325))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1845,axiom,((~hskp18) | c0_1(a325)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.27/1.09 tff(1846,plain,
% 1.27/1.09 ((~hskp18) | c0_1(a325)),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1845, 1844])).
% 1.27/1.09 tff(1847,plain,
% 1.27/1.09 ((~hskp18) | c0_1(a325)),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1846, 1844])).
% 1.27/1.09 tff(1848,plain,
% 1.27/1.09 ((~hskp18) | c0_1(a325)),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1847, 1844])).
% 1.27/1.09 tff(1849,plain,
% 1.27/1.09 ((~hskp18) | c0_1(a325)),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1848, 1844])).
% 1.27/1.09 tff(1850,plain,
% 1.27/1.09 ((~hskp18) | c0_1(a325)),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1849, 1844])).
% 1.27/1.09 tff(1851,plain,
% 1.27/1.09 ((~hskp18) | c0_1(a325)),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1850, 1844])).
% 1.27/1.09 tff(1852,plain,
% 1.27/1.09 ((~hskp18) | c0_1(a325)),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1851, 1844])).
% 1.27/1.09 tff(1853,plain,
% 1.27/1.09 ((~hskp18) | c0_1(a325)),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1852, 1844])).
% 1.27/1.09 tff(1854,plain,
% 1.27/1.09 (c0_1(a325)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1853, 1831])).
% 1.27/1.09 tff(1855,plain,
% 1.27/1.09 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | c1_1(a325) | c3_1(a325) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c0_1(a325)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a325) | c3_1(a325) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c0_1(a325)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1856,plain,
% 1.27/1.09 ((hskp13 | (~ndr1_0) | c3_1(a325) | c1_1(a325) | (~c0_1(a325)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315))) <=> (hskp13 | c1_1(a325) | c3_1(a325) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c0_1(a325)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1857,plain,
% 1.27/1.09 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a325) | c1_1(a325) | (~c0_1(a325)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | c1_1(a325) | c3_1(a325) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c0_1(a325))))),
% 1.27/1.09 inference(monotonicity,[status(thm)],[1856])).
% 1.27/1.09 tff(1858,plain,
% 1.27/1.09 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a325) | c1_1(a325) | (~c0_1(a325)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a325) | c3_1(a325) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c0_1(a325)))),
% 1.27/1.09 inference(transitivity,[status(thm)],[1857, 1855])).
% 1.27/1.09 tff(1859,plain,
% 1.27/1.09 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a325) | c1_1(a325) | (~c0_1(a325)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)))),
% 1.27/1.09 inference(quant_inst,[status(thm)],[])).
% 1.27/1.09 tff(1860,plain,
% 1.27/1.09 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a325) | c3_1(a325) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c2_1(a315)) | (~c0_1(a325))),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1859, 1858])).
% 1.27/1.09 tff(1861,plain,
% 1.27/1.09 (c3_1(a315) | (~c2_1(a315))),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1860, 135, 1811, 1854, 1843, 1837, 462, 1396])).
% 1.27/1.09 tff(1862,plain,
% 1.27/1.09 ($false),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1861, 1816, 1815])).
% 1.27/1.09 tff(1863,plain,(hskp13 | c0_1(a315) | hskp22 | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.27/1.09 tff(1864,plain,
% 1.27/1.09 (hskp13),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1863, 940, 637, 462])).
% 1.27/1.09 tff(1865,plain,
% 1.27/1.09 (c0_1(a308)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1070, 1864])).
% 1.27/1.09 tff(1866,plain,
% 1.27/1.09 (~c2_1(a308)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1048, 1864])).
% 1.27/1.09 tff(1867,plain,
% 1.27/1.09 (hskp15 | hskp8),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1801, 135, 463, 462, 1475, 1121])).
% 1.27/1.09 tff(1868,plain,
% 1.27/1.09 (hskp15),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1867, 637])).
% 1.27/1.09 tff(1869,plain,
% 1.27/1.09 (~c3_1(a311)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[866, 1868])).
% 1.27/1.09 tff(1870,plain,
% 1.27/1.09 (c0_1(a311)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[853, 1868])).
% 1.27/1.09 tff(1871,plain,
% 1.27/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1872,plain,
% 1.27/1.09 (((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1873,plain,
% 1.27/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315))))),
% 1.27/1.09 inference(monotonicity,[status(thm)],[1872])).
% 1.27/1.09 tff(1874,plain,
% 1.27/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315)))),
% 1.27/1.09 inference(transitivity,[status(thm)],[1873, 1871])).
% 1.27/1.09 tff(1875,plain,
% 1.27/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a308) | c3_1(a308) | (~c0_1(a308)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 1.27/1.09 inference(quant_inst,[status(thm)],[])).
% 1.27/1.09 tff(1876,plain,
% 1.27/1.09 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a308) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | c3_1(a308) | (~c0_1(a308)) | (~c2_1(a315))),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1875, 1874])).
% 1.27/1.09 tff(1877,plain,
% 1.27/1.09 (c3_1(a308)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1876, 135, 463, 1865, 1543, 1542, 462, 1475, 1866, 760, 591])).
% 1.27/1.09 tff(1878,plain,
% 1.27/1.09 (~c1_1(a308)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1300, 1864])).
% 1.27/1.09 tff(1879,plain,
% 1.27/1.09 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1880,plain,
% 1.27/1.09 ((hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308))) <=> (hskp22 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1881,plain,
% 1.27/1.09 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311))))),
% 1.27/1.09 inference(monotonicity,[status(thm)],[1880])).
% 1.27/1.09 tff(1882,plain,
% 1.27/1.09 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 1.27/1.09 inference(transitivity,[status(thm)],[1881, 1879])).
% 1.27/1.09 tff(1883,plain,
% 1.27/1.09 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308)))),
% 1.27/1.09 inference(quant_inst,[status(thm)],[])).
% 1.27/1.09 tff(1884,plain,
% 1.27/1.09 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp22 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311))),
% 1.27/1.09 inference(modus_ponens,[status(thm)],[1883, 1882])).
% 1.27/1.09 tff(1885,plain,
% 1.27/1.09 (~c2_1(a311)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1884, 135, 940, 1870, 1869, 1878, 1866, 1344, 1877])).
% 1.27/1.09 tff(1886,plain,
% 1.27/1.09 ($false),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1484, 1885, 1877, 463, 1475, 462, 1870, 1869, 1866, 1865])).
% 1.27/1.09 tff(1887,plain,(hskp22 | (~c2_1(a315)) | c3_1(a315) | c0_1(a315) | (~c0_1(a299)) | (~c3_1(a299)) | c2_1(a299) | hskp8), inference(lemma,lemma(discharge,[]))).
% 1.27/1.09 tff(1888,plain,
% 1.27/1.09 (hskp22),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[1887, 1810, 1793, 1794, 1795, 1809, 1808, 637])).
% 1.27/1.09 tff(1889,plain,
% 1.27/1.09 (~c3_1(a331)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[82, 1888])).
% 1.27/1.09 tff(1890,plain,
% 1.27/1.09 (~c2_1(a331)),
% 1.27/1.09 inference(unit_resolution,[status(thm)],[70, 1888])).
% 1.27/1.09 tff(1891,plain,
% 1.27/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a331) | c3_1(a331) | c0_1(a315) | c3_1(a315) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)) | (~c0_1(a331)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a331) | c3_1(a331) | c0_1(a315) | c3_1(a315) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)) | (~c0_1(a331)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1892,plain,
% 1.27/1.09 (((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a331) | c3_1(a331) | (~c0_1(a331)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c2_1(a331) | c3_1(a331) | c0_1(a315) | c3_1(a315) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)) | (~c0_1(a331)))),
% 1.27/1.09 inference(rewrite,[status(thm)],[])).
% 1.27/1.09 tff(1893,plain,
% 1.27/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a331) | c3_1(a331) | (~c0_1(a331)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c2_1(a331) | c3_1(a331) | c0_1(a315) | c3_1(a315) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)) | (~c0_1(a331))))),
% 1.27/1.09 inference(monotonicity,[status(thm)],[1892])).
% 1.27/1.09 tff(1894,plain,
% 1.27/1.09 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a331) | c3_1(a331) | (~c0_1(a331)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a331) | c3_1(a331) | c0_1(a315) | c3_1(a315) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)) | (~c0_1(a331)))),
% 1.27/1.10 inference(transitivity,[status(thm)],[1893, 1891])).
% 1.27/1.10 tff(1895,plain,
% 1.27/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)) | c2_1(a331) | c3_1(a331) | (~c0_1(a331)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 1.27/1.10 inference(quant_inst,[status(thm)],[])).
% 1.27/1.10 tff(1896,plain,
% 1.27/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c2_1(a331) | c3_1(a331) | c0_1(a315) | c3_1(a315) | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c2_1(a315)) | (~c0_1(a331))),
% 1.27/1.10 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 1.27/1.10 tff(1897,plain,
% 1.27/1.10 (~c0_1(a331)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1896, 135, 1795, 1810, 1809, 1890, 1889, 1794, 1793, 1808, 591])).
% 1.27/1.10 tff(1898,plain,
% 1.27/1.10 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a311) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a311) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(1899,plain,
% 1.27/1.10 ((hskp13 | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311))) <=> (hskp13 | c3_1(a311) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(1900,plain,
% 1.27/1.10 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a311) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311))))),
% 1.27/1.10 inference(monotonicity,[status(thm)],[1899])).
% 1.27/1.10 tff(1901,plain,
% 1.27/1.10 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a311) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311)))),
% 1.27/1.10 inference(transitivity,[status(thm)],[1900, 1898])).
% 1.27/1.10 tff(1902,plain,
% 1.27/1.10 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | c3_1(a311) | (~c1_1(a311)) | (~c0_1(a311)))),
% 1.27/1.10 inference(quant_inst,[status(thm)],[])).
% 1.27/1.10 tff(1903,plain,
% 1.27/1.10 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a311) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | (~c0_1(a294)) | (~c1_1(a311)) | (~c0_1(a311))),
% 1.27/1.10 inference(modus_ponens,[status(thm)],[1902, 1901])).
% 1.27/1.10 tff(1904,plain,
% 1.27/1.10 (hskp13 | (~c3_1(a294))),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1903, 135, 1476, 1499, 1465, 1464, 1474, 304])).
% 1.27/1.10 tff(1905,plain,
% 1.27/1.10 (~c3_1(a294)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1904, 1811])).
% 1.27/1.10 tff(1906,plain,
% 1.27/1.10 ($false),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1402, 135, 1811, 1795, 1465, 1794, 1793, 1463, 1396, 1905])).
% 1.27/1.10 tff(1907,plain,(hskp13 | (~c0_1(a294)) | c1_1(a294) | (~c0_1(a311)) | (~c1_1(a311)) | (~c2_1(a294)) | c3_1(a311)), inference(lemma,lemma(discharge,[]))).
% 1.27/1.10 tff(1908,plain,
% 1.27/1.10 (hskp13),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1907, 1806, 1463, 1465, 1805, 1464, 1804])).
% 1.27/1.10 tff(1909,plain,
% 1.27/1.10 (c0_1(a308)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1070, 1908])).
% 1.27/1.10 tff(1910,plain,
% 1.27/1.10 (~c2_1(a308)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1048, 1908])).
% 1.27/1.10 tff(1911,plain,
% 1.27/1.10 (c3_1(a308)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1876, 135, 1795, 1909, 1810, 1809, 1794, 1793, 1910, 1808, 591])).
% 1.27/1.10 tff(1912,plain,
% 1.27/1.10 (c2_1(a311)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1484, 1911, 1795, 1793, 1794, 1806, 1804, 1910, 1909])).
% 1.27/1.10 tff(1913,plain,
% 1.27/1.10 (hskp23 | (~c2_1(a311))),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[860, 135, 1806, 1805, 325])).
% 1.27/1.10 tff(1914,plain,
% 1.27/1.10 (hskp23),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1913, 1912])).
% 1.27/1.10 tff(1915,plain,
% 1.27/1.10 (~c2_1(a337)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[901, 1914])).
% 1.27/1.10 tff(1916,plain,
% 1.27/1.10 (c3_1(a337)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[912, 1914])).
% 1.27/1.10 tff(1917,plain,
% 1.27/1.10 (c1_1(a337)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[923, 1914])).
% 1.27/1.10 tff(1918,plain,
% 1.27/1.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a337) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331) | (~c1_1(a337)) | (~c3_1(a337)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a337) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331) | (~c1_1(a337)) | (~c3_1(a337)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(1919,plain,
% 1.27/1.10 ((hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a331) | c0_1(a331) | c3_1(a331)) <=> (hskp8 | c2_1(a337) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331) | (~c1_1(a337)) | (~c3_1(a337)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(1920,plain,
% 1.27/1.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a331) | c0_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | c2_1(a337) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331) | (~c1_1(a337)) | (~c3_1(a337))))),
% 1.27/1.10 inference(monotonicity,[status(thm)],[1919])).
% 1.27/1.10 tff(1921,plain,
% 1.27/1.10 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a331) | c0_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a337) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331) | (~c1_1(a337)) | (~c3_1(a337)))),
% 1.27/1.10 inference(transitivity,[status(thm)],[1920, 1918])).
% 1.27/1.10 tff(1922,plain,
% 1.27/1.10 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp8 | (~ndr1_0) | c2_1(a337) | (~c1_1(a337)) | (~c3_1(a337)) | c2_1(a331) | c0_1(a331) | c3_1(a331))),
% 1.27/1.10 inference(quant_inst,[status(thm)],[])).
% 1.27/1.10 tff(1923,plain,
% 1.27/1.10 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp8 | c2_1(a337) | c2_1(a331) | c3_1(a331) | (~ndr1_0) | c0_1(a331) | (~c1_1(a337)) | (~c3_1(a337))),
% 1.27/1.10 inference(modus_ponens,[status(thm)],[1922, 1921])).
% 1.27/1.10 tff(1924,plain,
% 1.27/1.10 ($false),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1923, 135, 637, 1917, 1916, 1915, 1890, 1889, 315, 1897])).
% 1.27/1.10 tff(1925,plain,(hskp8 | c1_1(a294) | (~c0_1(a294)) | (~c2_1(a294))), inference(lemma,lemma(discharge,[]))).
% 1.27/1.10 tff(1926,plain,
% 1.27/1.10 (hskp8),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1925, 1783, 1785, 1784])).
% 1.27/1.10 tff(1927,plain,
% 1.27/1.10 (~c1_1(a300)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[549, 1926])).
% 1.27/1.10 tff(1928,plain,
% 1.27/1.10 (c3_1(a300)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[560, 1926])).
% 1.27/1.10 tff(1929,plain,
% 1.27/1.10 (c0_1(a300)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[571, 1926])).
% 1.27/1.10 tff(1930,plain,
% 1.27/1.10 (hskp15),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[831, 135, 53, 1929, 1928, 1927, 335])).
% 1.27/1.10 tff(1931,plain,
% 1.27/1.10 (~c3_1(a311)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[866, 1930])).
% 1.27/1.10 tff(1932,plain,
% 1.27/1.10 (c1_1(a311)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[842, 1930])).
% 1.27/1.10 tff(1933,plain,
% 1.27/1.10 (c0_1(a311)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[853, 1930])).
% 1.27/1.10 tff(1934,plain,
% 1.27/1.10 (hskp7),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[873, 135, 1933, 1932, 1785, 1784, 1931, 1783, 52])).
% 1.27/1.10 tff(1935,plain,
% 1.27/1.10 (c3_1(a299)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[758, 1934])).
% 1.27/1.10 tff(1936,plain,
% 1.27/1.10 (~c2_1(a299)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[775, 1934])).
% 1.27/1.10 tff(1937,plain,
% 1.27/1.10 (c0_1(a299)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[747, 1934])).
% 1.27/1.10 tff(1938,plain,
% 1.27/1.10 (hskp16),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1791, 135, 1731, 1785, 1784, 1783, 31])).
% 1.27/1.10 tff(1939,assumption,(hskp4), introduced(assumption)).
% 1.27/1.10 tff(1940,plain,
% 1.27/1.10 (~c3_1(a295)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1018, 1939])).
% 1.27/1.10 tff(1941,plain,
% 1.27/1.10 (c0_1(a295)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1059, 1939])).
% 1.27/1.10 tff(1942,plain,
% 1.27/1.10 (~c2_1(a295)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1024, 1939])).
% 1.27/1.10 tff(1943,plain,
% 1.27/1.10 ($false),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1552, 1942, 1941, 1538, 1543, 760, 1542, 1940])).
% 1.27/1.10 tff(1944,plain,((~hskp4) | (~hskp16) | (~c0_1(a299)) | c2_1(a299) | (~c3_1(a299))), inference(lemma,lemma(discharge,[]))).
% 1.27/1.10 tff(1945,plain,
% 1.27/1.10 (~hskp4),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1944, 1938, 1937, 1936, 1935])).
% 1.27/1.10 tff(1946,plain,
% 1.27/1.10 (hskp13),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1907, 1933, 1783, 1785, 1932, 1784, 1931])).
% 1.27/1.10 tff(1947,plain,
% 1.27/1.10 (c0_1(a308)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1070, 1946])).
% 1.27/1.10 tff(1948,plain,
% 1.27/1.10 (~c2_1(a308)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1048, 1946])).
% 1.27/1.10 tff(1949,plain,
% 1.27/1.10 (~c0_1(a315)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[459, 1938])).
% 1.27/1.10 tff(1950,plain,
% 1.27/1.10 (~c3_1(a315)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[477, 1938])).
% 1.27/1.10 tff(1951,plain,
% 1.27/1.10 (c2_1(a315)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[453, 1938])).
% 1.27/1.10 tff(1952,plain,
% 1.27/1.10 (c3_1(a308)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1876, 135, 1951, 1947, 1937, 1935, 1949, 1950, 1948, 1936, 591])).
% 1.27/1.10 tff(1953,plain,
% 1.27/1.10 (c2_1(a311)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1484, 1952, 1951, 1950, 1949, 1933, 1931, 1948, 1947])).
% 1.27/1.10 tff(1954,plain,
% 1.27/1.10 (~c1_1(a308)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1300, 1946])).
% 1.27/1.10 tff(1955,plain,
% 1.27/1.10 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(1956,plain,
% 1.27/1.10 ((hskp21 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308))) <=> (hskp21 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(1957,plain,
% 1.27/1.10 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311))))),
% 1.27/1.10 inference(monotonicity,[status(thm)],[1956])).
% 1.27/1.10 tff(1958,plain,
% 1.27/1.10 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311)))),
% 1.27/1.10 inference(transitivity,[status(thm)],[1957, 1955])).
% 1.27/1.10 tff(1959,plain,
% 1.27/1.10 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp21 | (~ndr1_0) | c3_1(a311) | (~c2_1(a311)) | (~c0_1(a311)) | c2_1(a308) | c1_1(a308) | (~c3_1(a308)))),
% 1.27/1.10 inference(quant_inst,[status(thm)],[])).
% 1.27/1.10 tff(1960,plain,
% 1.27/1.10 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp21 | c3_1(a311) | c1_1(a308) | c2_1(a308) | (~ndr1_0) | (~c3_1(a308)) | (~c2_1(a311)) | (~c0_1(a311))),
% 1.27/1.10 inference(modus_ponens,[status(thm)],[1959, 1958])).
% 1.27/1.10 tff(1961,plain,
% 1.27/1.10 (hskp21 | (~c3_1(a308)) | (~c2_1(a311))),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1960, 135, 1933, 1931, 1954, 1948, 1422])).
% 1.27/1.10 tff(1962,plain,
% 1.27/1.10 (hskp21),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1961, 1952, 1953])).
% 1.27/1.10 tff(1963,plain,
% 1.27/1.10 (c3_1(a330)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1461, 1962])).
% 1.27/1.10 tff(1964,plain,
% 1.27/1.10 (~c2_1(a330)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1450, 1962])).
% 1.27/1.10 tff(1965,plain,
% 1.27/1.10 (~c0_1(a330)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1434, 1962])).
% 1.27/1.10 tff(1966,plain,
% 1.27/1.10 (hskp22 | (~c3_1(a308)) | (~c2_1(a311))),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1884, 135, 1933, 1931, 1954, 1948, 1344])).
% 1.27/1.10 tff(1967,plain,
% 1.27/1.10 (hskp22),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1966, 1952, 1953])).
% 1.27/1.10 tff(1968,plain,
% 1.27/1.10 (~c3_1(a331)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[82, 1967])).
% 1.27/1.10 tff(1969,plain,
% 1.27/1.10 (~c2_1(a331)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[70, 1967])).
% 1.27/1.10 tff(1970,plain,
% 1.27/1.10 (~c1_1(a331)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[76, 1967])).
% 1.27/1.10 tff(1971,plain,
% 1.27/1.10 (c1_1(a315)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1529, 1945, 1950, 1932, 1931, 1953, 1970, 1969, 1968, 1965, 1964, 1949, 1963])).
% 1.27/1.10 tff(1972,plain,
% 1.27/1.10 (^[U: $i] : refl((hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.27/1.10 inference(bind,[status(th)],[])).
% 1.27/1.10 tff(1973,plain,
% 1.27/1.10 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.27/1.10 inference(quant_intro,[status(thm)],[1972])).
% 1.27/1.10 tff(1974,plain,
% 1.27/1.10 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(1975,plain,
% 1.27/1.10 (^[U: $i] : 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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) | hskp11) <=> ((hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp11))), rewrite(((hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp11) <=> (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) | hskp11) <=> (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.27/1.10 inference(bind,[status(th)],[])).
% 1.27/1.10 tff(1976,plain,
% 1.27/1.10 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) | hskp11) <=> ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.27/1.10 inference(quant_intro,[status(thm)],[1975])).
% 1.27/1.10 tff(1977,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp4) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 1.27/1.10 tff(1978,plain,
% 1.27/1.10 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.27/1.10 inference(modus_ponens,[status(thm)],[1977, 1976])).
% 1.27/1.10 tff(1979,plain,
% 1.27/1.10 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.27/1.10 inference(modus_ponens,[status(thm)],[1978, 1974])).
% 1.27/1.10 tff(1980,plain,(
% 1.27/1.10 ![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.27/1.10 inference(skolemize,[status(sab)],[1979])).
% 1.27/1.10 tff(1981,plain,
% 1.27/1.10 (![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.27/1.10 inference(modus_ponens,[status(thm)],[1980, 1973])).
% 1.27/1.10 tff(1982,plain,
% 1.27/1.10 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp11 | hskp4 | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp11 | hskp4 | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(1983,plain,
% 1.27/1.10 ((hskp11 | hskp4 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315))) <=> (hskp11 | hskp4 | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(1984,plain,
% 1.27/1.10 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp11 | hskp4 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp11 | hskp4 | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315))))),
% 1.27/1.10 inference(monotonicity,[status(thm)],[1983])).
% 1.27/1.10 tff(1985,plain,
% 1.27/1.10 (((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp11 | hskp4 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)))) <=> ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp11 | hskp4 | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315)))),
% 1.27/1.10 inference(transitivity,[status(thm)],[1984, 1982])).
% 1.27/1.10 tff(1986,plain,
% 1.27/1.10 ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp11 | hskp4 | (~ndr1_0) | c0_1(a315) | (~c2_1(a315)) | (~c1_1(a315)))),
% 1.27/1.10 inference(quant_inst,[status(thm)],[])).
% 1.27/1.10 tff(1987,plain,
% 1.27/1.10 ((~![U: $i] : (hskp11 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp11 | hskp4 | c0_1(a315) | (~ndr1_0) | (~c1_1(a315)) | (~c2_1(a315))),
% 1.27/1.10 inference(modus_ponens,[status(thm)],[1986, 1985])).
% 1.27/1.10 tff(1988,plain,
% 1.27/1.10 (hskp11 | hskp4 | (~c1_1(a315))),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1987, 135, 1951, 1949, 1981])).
% 1.27/1.10 tff(1989,plain,
% 1.27/1.10 (hskp11),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1988, 1971, 1945])).
% 1.27/1.10 tff(1990,plain,
% 1.27/1.10 (~c0_1(a306)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[669, 1989])).
% 1.27/1.10 tff(1991,plain,
% 1.27/1.10 (c3_1(a306)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[680, 1989])).
% 1.27/1.10 tff(1992,plain,
% 1.27/1.10 (c1_1(a306)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[691, 1989])).
% 1.27/1.10 tff(1993,plain,
% 1.27/1.10 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(1994,plain,
% 1.27/1.10 ((hskp4 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a331) | c1_1(a331) | c3_1(a331)) <=> (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(1995,plain,
% 1.27/1.10 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306))))),
% 1.27/1.10 inference(monotonicity,[status(thm)],[1994])).
% 1.27/1.10 tff(1996,plain,
% 1.27/1.10 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306)))),
% 1.27/1.10 inference(transitivity,[status(thm)],[1995, 1993])).
% 1.27/1.10 tff(1997,plain,
% 1.27/1.10 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a306) | (~c1_1(a306)) | (~c3_1(a306)) | c2_1(a331) | c1_1(a331) | c3_1(a331))),
% 1.27/1.10 inference(quant_inst,[status(thm)],[])).
% 1.27/1.10 tff(1998,plain,
% 1.27/1.10 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a306) | (~ndr1_0) | (~c3_1(a306)) | (~c1_1(a306))),
% 1.27/1.10 inference(modus_ponens,[status(thm)],[1997, 1996])).
% 1.27/1.10 tff(1999,plain,
% 1.27/1.10 ($false),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1998, 135, 1945, 1992, 1991, 1970, 1969, 1968, 1990, 42])).
% 1.27/1.10 tff(2000,plain,(hskp29), inference(lemma,lemma(discharge,[]))).
% 1.27/1.10 tff(2001,plain,
% 1.27/1.10 (c2_1(a301)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[347, 2000])).
% 1.27/1.10 tff(2002,plain,
% 1.27/1.10 (c0_1(a301)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[358, 2000])).
% 1.27/1.10 tff(2003,plain,
% 1.27/1.10 (((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(2004,plain,
% 1.27/1.10 ((hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c0_1(a301))) <=> (hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(2005,plain,
% 1.27/1.10 (((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c0_1(a301)))) <=> ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c0_1(a301)) | (~c2_1(a301))))),
% 1.27/1.10 inference(monotonicity,[status(thm)],[2004])).
% 1.27/1.10 tff(2006,plain,
% 1.27/1.10 (((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c0_1(a301)))) <=> ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.27/1.10 inference(transitivity,[status(thm)],[2005, 2003])).
% 1.27/1.10 tff(2007,plain,
% 1.27/1.10 ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c0_1(a301)))),
% 1.27/1.10 inference(quant_inst,[status(thm)],[])).
% 1.27/1.10 tff(2008,plain,
% 1.27/1.10 ((~![U: $i] : (hskp24 | hskp16 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp24 | hskp16 | (~ndr1_0) | c1_1(a301) | (~c0_1(a301)) | (~c2_1(a301))),
% 1.27/1.10 inference(modus_ponens,[status(thm)],[2007, 2006])).
% 1.27/1.10 tff(2009,plain,
% 1.27/1.10 (hskp16 | c1_1(a301)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[2008, 135, 1731, 2002, 2001, 31])).
% 1.27/1.10 tff(2010,plain,
% 1.27/1.10 (c1_1(a301)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[2009, 32])).
% 1.27/1.10 tff(2011,assumption,(c1_1(a301)), introduced(assumption)).
% 1.27/1.10 tff(2012,plain,
% 1.27/1.10 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(2013,plain,
% 1.27/1.10 ((hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301))) <=> (hskp26 | hskp3 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(2014,plain,
% 1.27/1.10 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 1.27/1.10 inference(monotonicity,[status(thm)],[2013])).
% 1.27/1.10 tff(2015,plain,
% 1.27/1.10 (((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301)))) <=> ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.27/1.10 inference(transitivity,[status(thm)],[2014, 2012])).
% 1.27/1.10 tff(2016,plain,
% 1.27/1.10 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c0_1(a301)))),
% 1.27/1.10 inference(quant_inst,[status(thm)],[])).
% 1.27/1.10 tff(2017,plain,
% 1.27/1.10 ((~![U: $i] : (hskp26 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp26 | hskp3 | (~ndr1_0) | (~c1_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 1.27/1.10 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 1.27/1.10 tff(2018,plain,
% 1.27/1.10 (hskp26 | hskp3 | (~c1_1(a301))),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[2017, 135, 2002, 2001, 176])).
% 1.27/1.10 tff(2019,plain,
% 1.27/1.10 ($false),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[2018, 238, 64, 2011])).
% 1.27/1.10 tff(2020,plain,(hskp3 | (~c1_1(a301))), inference(lemma,lemma(discharge,[]))).
% 1.27/1.10 tff(2021,plain,
% 1.27/1.10 (hskp3),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[2020, 2010])).
% 1.27/1.10 tff(2022,plain,
% 1.27/1.10 (~c1_1(a294)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[784, 2021])).
% 1.27/1.10 tff(2023,plain,
% 1.27/1.10 (c2_1(a294)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[795, 2021])).
% 1.27/1.10 tff(2024,plain,
% 1.27/1.10 (c0_1(a294)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[806, 2021])).
% 1.27/1.10 tff(2025,plain,
% 1.27/1.10 ($false),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1791, 135, 1731, 32, 2024, 2023, 2022, 31])).
% 1.27/1.10 tff(2026,plain,(hskp16), inference(lemma,lemma(discharge,[]))).
% 1.27/1.10 tff(2027,plain,
% 1.27/1.10 (~c3_1(a315)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[477, 2026])).
% 1.27/1.10 tff(2028,plain,
% 1.27/1.10 (~c0_1(a315)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[459, 2026])).
% 1.27/1.10 tff(2029,plain,
% 1.27/1.10 (c2_1(a315)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[453, 2026])).
% 1.27/1.10 tff(2030,plain,
% 1.27/1.10 (c3_1(a301)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[376, 2000])).
% 1.27/1.10 tff(2031,plain,
% 1.27/1.10 (hskp5),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1564, 135, 2002, 2001, 2030, 2029, 2028, 2027, 21])).
% 1.27/1.10 tff(2032,plain,
% 1.27/1.10 (~c0_1(a297)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[392, 2031])).
% 1.27/1.10 tff(2033,plain,
% 1.27/1.10 (~c1_1(a301)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[2020, 64])).
% 1.27/1.10 tff(2034,plain,
% 1.27/1.10 (hskp3 | c1_1(a315)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[484, 135, 2028, 2027, 93])).
% 1.27/1.10 tff(2035,plain,
% 1.27/1.10 (c1_1(a315)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[2034, 64])).
% 1.27/1.10 tff(2036,plain,
% 1.27/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c1_1(a315)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c1_1(a315)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(2037,plain,
% 1.27/1.10 (((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315))) <=> (c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c1_1(a315)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.27/1.10 inference(rewrite,[status(thm)],[])).
% 1.27/1.10 tff(2038,plain,
% 1.27/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c1_1(a315)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 1.27/1.10 inference(monotonicity,[status(thm)],[2037])).
% 1.27/1.10 tff(2039,plain,
% 1.27/1.10 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c1_1(a315)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.27/1.10 inference(transitivity,[status(thm)],[2038, 2036])).
% 1.27/1.10 tff(2040,plain,
% 1.27/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315)))),
% 1.27/1.10 inference(quant_inst,[status(thm)],[])).
% 1.27/1.10 tff(2041,plain,
% 1.27/1.10 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a315) | c3_1(a315) | (~ndr1_0) | (~c1_1(a315)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 1.27/1.10 inference(modus_ponens,[status(thm)],[2040, 2039])).
% 1.27/1.10 tff(2042,plain,
% 1.27/1.10 ($false),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[2041, 135, 2002, 2001, 2030, 2028, 2027, 11, 2035, 2033])).
% 1.27/1.10 tff(2043,plain,(hskp3), inference(lemma,lemma(discharge,[]))).
% 1.27/1.10 tff(2044,plain,
% 1.27/1.10 (c2_1(a294)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[795, 2043])).
% 1.27/1.10 tff(2045,plain,
% 1.27/1.10 (c0_1(a294)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[806, 2043])).
% 1.27/1.10 tff(2046,plain,
% 1.27/1.10 (~c1_1(a294)),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[784, 2043])).
% 1.27/1.10 tff(2047,plain,
% 1.27/1.10 (hskp8),
% 1.27/1.10 inference(unit_resolution,[status(thm)],[1925, 2046, 2045, 2044])).
% 1.27/1.11 tff(2048,plain,
% 1.27/1.11 (~c1_1(a300)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[549, 2047])).
% 1.27/1.11 tff(2049,plain,
% 1.27/1.11 (c1_1(a297)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[403, 2031])).
% 1.27/1.11 tff(2050,plain,
% 1.27/1.11 (c3_1(a300)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[560, 2047])).
% 1.27/1.11 tff(2051,plain,
% 1.27/1.11 (c0_1(a300)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[571, 2047])).
% 1.27/1.11 tff(2052,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a300) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c1_1(a297)) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a300) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c1_1(a297)) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2053,plain,
% 1.27/1.11 (((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297))) <=> (c1_1(a300) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c1_1(a297)) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2054,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a300) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c1_1(a297)) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300))))),
% 1.27/1.11 inference(monotonicity,[status(thm)],[2053])).
% 1.27/1.11 tff(2055,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a300) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c1_1(a297)) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 1.27/1.11 inference(transitivity,[status(thm)],[2054, 2052])).
% 1.27/1.11 tff(2056,plain,
% 1.27/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297)))),
% 1.27/1.11 inference(quant_inst,[status(thm)],[])).
% 1.27/1.11 tff(2057,plain,
% 1.27/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a300) | c0_1(a297) | (~ndr1_0) | c3_1(a297) | (~c1_1(a297)) | (~c2_1(a300)) | (~c3_1(a300)) | (~c0_1(a300))),
% 1.27/1.11 inference(modus_ponens,[status(thm)],[2056, 2055])).
% 1.27/1.11 tff(2058,plain,
% 1.27/1.11 (~c2_1(a300)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2057, 135, 2051, 2050, 2049, 2048, 2032, 11, 1])).
% 1.27/1.11 tff(2059,plain,
% 1.27/1.11 (c2_1(a297)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[414, 2031])).
% 1.27/1.11 tff(2060,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a300) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a300) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2061,plain,
% 1.27/1.11 (((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300)) <=> (c1_1(a300) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2062,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | (c1_1(a300) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301))))),
% 1.27/1.11 inference(monotonicity,[status(thm)],[2061])).
% 1.27/1.11 tff(2063,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a300) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301)))),
% 1.27/1.11 inference(transitivity,[status(thm)],[2062, 2060])).
% 1.27/1.11 tff(2064,plain,
% 1.27/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a301)) | (~c1_1(a301)) | (~c3_1(a301)) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | c1_1(a300))),
% 1.27/1.11 inference(quant_inst,[status(thm)],[])).
% 1.27/1.11 tff(2065,plain,
% 1.27/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | (~c2_1(V)) | (~c1_1(V)) | c2_1(W) | (~c3_1(W)) | c1_1(W))) | c1_1(a300) | (~ndr1_0) | c3_1(a297) | (~c2_1(a297)) | (~c1_1(a297)) | c2_1(a300) | (~c3_1(a300)) | (~c3_1(a301)) | (~c1_1(a301)) | (~c2_1(a301))),
% 1.27/1.11 inference(modus_ponens,[status(thm)],[2064, 2063])).
% 1.27/1.11 tff(2066,plain,
% 1.27/1.11 (~c1_1(a301)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2065, 135, 2001, 2030, 2050, 2049, 2059, 2048, 1100, 1, 2058])).
% 1.27/1.11 tff(2067,assumption,(c3_1(a294)), introduced(assumption)).
% 1.27/1.11 tff(2068,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a300) | c0_1(a297) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c3_1(a297) | (~c1_1(a297)) | (~c3_1(a300)) | (~c0_1(a300)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a300) | c0_1(a297) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c3_1(a297) | (~c1_1(a297)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2069,plain,
% 1.27/1.11 (((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297))) <=> (c1_1(a300) | c0_1(a297) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c3_1(a297) | (~c1_1(a297)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2070,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a300) | c0_1(a297) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c3_1(a297) | (~c1_1(a297)) | (~c3_1(a300)) | (~c0_1(a300))))),
% 1.27/1.11 inference(monotonicity,[status(thm)],[2069])).
% 1.27/1.11 tff(2071,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a300) | c0_1(a297) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c3_1(a297) | (~c1_1(a297)) | (~c3_1(a300)) | (~c0_1(a300)))),
% 1.27/1.11 inference(transitivity,[status(thm)],[2070, 2068])).
% 1.27/1.11 tff(2072,plain,
% 1.27/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c3_1(a297) | c0_1(a297) | (~c1_1(a297)))),
% 1.27/1.11 inference(quant_inst,[status(thm)],[])).
% 1.27/1.11 tff(2073,plain,
% 1.27/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a300) | c0_1(a297) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c3_1(a297) | (~c1_1(a297)) | (~c3_1(a300)) | (~c0_1(a300))),
% 1.27/1.11 inference(modus_ponens,[status(thm)],[2072, 2071])).
% 1.27/1.11 tff(2074,plain,
% 1.27/1.11 ($false),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2073, 135, 2051, 2050, 2049, 2044, 2048, 2032, 2046, 11, 1, 2067])).
% 1.27/1.11 tff(2075,plain,(c3_1(a297) | (~c3_1(a294))), inference(lemma,lemma(discharge,[]))).
% 1.27/1.11 tff(2076,plain,
% 1.27/1.11 (~c3_1(a294)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2075, 1])).
% 1.27/1.11 tff(2077,plain,
% 1.27/1.11 (hskp20 | c3_1(a294)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[1638, 135, 2045, 2044, 1632])).
% 1.27/1.11 tff(2078,plain,
% 1.27/1.11 (hskp20),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2077, 2076])).
% 1.27/1.11 tff(2079,plain,
% 1.27/1.11 (~c2_1(a329)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[1645, 2078])).
% 1.27/1.11 tff(2080,plain,
% 1.27/1.11 (~c1_1(a329)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[1651, 2078])).
% 1.27/1.11 tff(2081,plain,
% 1.27/1.11 (~c0_1(a329)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[1657, 2078])).
% 1.27/1.11 tff(2082,plain,
% 1.27/1.11 (hskp0),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[1664, 135, 2045, 2081, 2080, 2079, 2046, 1622, 2076])).
% 1.27/1.11 tff(2083,plain,
% 1.27/1.11 (~c3_1(a291)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[542, 2082])).
% 1.27/1.11 tff(2084,plain,
% 1.27/1.11 (~c2_1(a291)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[517, 2082])).
% 1.27/1.11 tff(2085,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a315)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2086,plain,
% 1.27/1.11 (((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a315)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2087,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a315) | c3_1(a315) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a315))))),
% 1.27/1.11 inference(monotonicity,[status(thm)],[2086])).
% 1.27/1.11 tff(2088,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a315)))),
% 1.27/1.11 inference(transitivity,[status(thm)],[2087, 2085])).
% 1.27/1.11 tff(2089,plain,
% 1.27/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | c2_1(a291) | c3_1(a291) | (~c0_1(a291)) | c3_1(a315) | c0_1(a315) | (~c2_1(a315)))),
% 1.27/1.11 inference(quant_inst,[status(thm)],[])).
% 1.27/1.11 tff(2090,plain,
% 1.27/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a315) | c3_1(a315) | c2_1(a291) | c3_1(a291) | (~ndr1_0) | (~c0_1(a291)) | c2_1(a300) | (~c3_1(a300)) | (~c0_1(a300)) | (~c2_1(a315))),
% 1.27/1.11 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 1.27/1.11 tff(2091,plain,
% 1.27/1.11 (~c0_1(a291)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2090, 135, 2029, 2051, 2050, 2028, 2027, 2084, 2083, 591, 2058])).
% 1.27/1.11 tff(2092,plain,
% 1.27/1.11 (c1_1(a291)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[528, 2082])).
% 1.27/1.11 tff(2093,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2094,plain,
% 1.27/1.11 (((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a291) | c0_1(a291) | (~c1_1(a291))) <=> (c3_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2095,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a291) | c0_1(a291) | (~c1_1(a291)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 1.27/1.11 inference(monotonicity,[status(thm)],[2094])).
% 1.27/1.11 tff(2096,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a291) | c0_1(a291) | (~c1_1(a291)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.27/1.11 inference(transitivity,[status(thm)],[2095, 2093])).
% 1.27/1.11 tff(2097,plain,
% 1.27/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c1_1(a301) | (~c2_1(a301)) | (~c3_1(a301)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | c3_1(a291) | c0_1(a291) | (~c1_1(a291)))),
% 1.27/1.11 inference(quant_inst,[status(thm)],[])).
% 1.27/1.11 tff(2098,plain,
% 1.27/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a291) | (~ndr1_0) | c0_1(a291) | (~c1_1(a291)) | c1_1(a301) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 1.27/1.11 inference(modus_ponens,[status(thm)],[2097, 2096])).
% 1.27/1.11 tff(2099,plain,
% 1.27/1.11 ($false),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2098, 135, 2002, 2001, 2030, 2092, 2083, 11, 2091, 2066])).
% 1.27/1.11 tff(2100,plain,(c3_1(a297)), inference(lemma,lemma(discharge,[]))).
% 1.27/1.11 tff(2101,plain,
% 1.27/1.11 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a297)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a297)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2102,plain,
% 1.27/1.11 ((hskp7 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297))) <=> (hskp7 | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a297)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2103,plain,
% 1.27/1.11 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a297))))),
% 1.27/1.11 inference(monotonicity,[status(thm)],[2102])).
% 1.27/1.11 tff(2104,plain,
% 1.27/1.11 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a297)))),
% 1.27/1.11 inference(transitivity,[status(thm)],[2103, 2101])).
% 1.27/1.11 tff(2105,plain,
% 1.27/1.11 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp7 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c0_1(a297) | (~c2_1(a297)) | (~c1_1(a297)))),
% 1.27/1.11 inference(quant_inst,[status(thm)],[])).
% 1.27/1.11 tff(2106,plain,
% 1.27/1.11 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp7 | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a297))),
% 1.27/1.11 inference(modus_ponens,[status(thm)],[2105, 2104])).
% 1.27/1.11 tff(2107,plain,
% 1.27/1.11 (hskp7 | (~c3_1(a297))),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2106, 135, 2049, 2059, 2032, 497])).
% 1.27/1.11 tff(2108,plain,
% 1.27/1.11 (hskp7),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2107, 2100])).
% 1.27/1.11 tff(2109,assumption,(c3_1(a297)), introduced(assumption)).
% 1.27/1.11 tff(2110,plain,
% 1.27/1.11 (hskp7),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2107, 2109])).
% 1.27/1.11 tff(2111,plain,
% 1.27/1.11 (c3_1(a299)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[758, 2110])).
% 1.27/1.11 tff(2112,plain,
% 1.27/1.11 (~c3_1(a294)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2073, 135, 2051, 2050, 2049, 2044, 2048, 2032, 2046, 11, 1])).
% 1.27/1.11 tff(2113,plain,
% 1.27/1.11 ($false),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[1441, 135, 940, 2050, 2045, 2044, 2048, 1344, 2112, 2058])).
% 1.27/1.11 tff(2114,plain,(c3_1(a297) | hskp22), inference(lemma,lemma(discharge,[]))).
% 1.27/1.11 tff(2115,plain,
% 1.27/1.11 (c3_1(a297)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2114, 940])).
% 1.27/1.11 tff(2116,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a315)) | (~c2_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a315)) | (~c2_1(a315)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2117,plain,
% 1.27/1.11 (((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315))) <=> (c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a315)) | (~c2_1(a315)))),
% 1.27/1.11 inference(rewrite,[status(thm)],[])).
% 1.27/1.11 tff(2118,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a315)) | (~c2_1(a315))))),
% 1.27/1.11 inference(monotonicity,[status(thm)],[2117])).
% 1.27/1.11 tff(2119,plain,
% 1.27/1.11 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a315)) | (~c2_1(a315)))),
% 1.27/1.11 inference(transitivity,[status(thm)],[2118, 2116])).
% 1.27/1.11 tff(2120,plain,
% 1.27/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c0_1(a297) | (~c2_1(a297)) | (~c3_1(a297)) | c0_1(a315) | c3_1(a315) | (~c2_1(a315)) | c3_1(a315) | c0_1(a315) | (~c1_1(a315)))),
% 1.27/1.11 inference(quant_inst,[status(thm)],[])).
% 1.27/1.11 tff(2121,plain,
% 1.27/1.11 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a315) | c3_1(a315) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c2_1(a297)) | (~c1_1(a315)) | (~c2_1(a315))),
% 1.27/1.11 inference(modus_ponens,[status(thm)],[2120, 2119])).
% 1.27/1.11 tff(2122,plain,
% 1.27/1.11 ((~c3_1(a297)) | (~c1_1(a315))),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2121, 135, 2029, 2059, 2028, 2027, 2032, 281])).
% 1.27/1.11 tff(2123,plain,
% 1.27/1.11 (~c1_1(a315)),
% 1.27/1.11 inference(unit_resolution,[status(thm)],[2122, 2115])).
% 1.27/1.11 tff(2124,plain,
% 1.27/1.11 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 1.27/1.11 inference(bind,[status(th)],[])).
% 1.27/1.11 tff(2125,plain,
% 1.27/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.27/1.11 inference(quant_intro,[status(thm)],[2124])).
% 1.27/1.11 tff(2126,plain,
% 1.27/1.11 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.27/1.12 inference(rewrite,[status(thm)],[])).
% 1.27/1.12 tff(2127,plain,
% 1.27/1.12 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 1.27/1.12 inference(bind,[status(th)],[])).
% 1.27/1.12 tff(2128,plain,
% 1.27/1.12 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.27/1.12 inference(quant_intro,[status(thm)],[2127])).
% 1.27/1.12 tff(2129,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause191')).
% 1.27/1.12 tff(2130,plain,
% 1.27/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.27/1.12 inference(modus_ponens,[status(thm)],[2129, 2128])).
% 1.27/1.12 tff(2131,plain,
% 1.27/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.27/1.12 inference(modus_ponens,[status(thm)],[2130, 2126])).
% 1.27/1.12 tff(2132,plain,(
% 1.27/1.12 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.27/1.12 inference(skolemize,[status(sab)],[2131])).
% 1.27/1.12 tff(2133,plain,
% 1.27/1.12 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 1.27/1.12 inference(modus_ponens,[status(thm)],[2132, 2125])).
% 1.27/1.12 tff(2134,plain,
% 1.27/1.12 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 1.27/1.12 inference(bind,[status(th)],[])).
% 1.27/1.12 tff(2135,plain,
% 1.27/1.12 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.27/1.12 inference(quant_intro,[status(thm)],[2134])).
% 1.27/1.12 tff(2136,plain,
% 1.27/1.12 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.27/1.12 inference(rewrite,[status(thm)],[])).
% 1.27/1.12 tff(2137,plain,
% 1.27/1.12 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp21) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp21))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 1.31/1.12 inference(bind,[status(th)],[])).
% 1.31/1.12 tff(2138,plain,
% 1.31/1.12 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.31/1.12 inference(quant_intro,[status(thm)],[2137])).
% 1.31/1.12 tff(2139,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 1.31/1.12 tff(2140,plain,
% 1.31/1.12 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[2139, 2138])).
% 1.31/1.12 tff(2141,plain,
% 1.31/1.12 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[2140, 2136])).
% 1.31/1.12 tff(2142,plain,(
% 1.31/1.12 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.31/1.12 inference(skolemize,[status(sab)],[2141])).
% 1.31/1.12 tff(2143,plain,
% 1.31/1.12 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[2142, 2135])).
% 1.31/1.12 tff(2144,plain,
% 1.31/1.12 (hskp7),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[2107, 2115])).
% 1.31/1.12 tff(2145,plain,
% 1.31/1.12 (~c2_1(a299)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[775, 2144])).
% 1.31/1.12 tff(2146,plain,
% 1.31/1.12 (c3_1(a299)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[758, 2144])).
% 1.31/1.12 tff(2147,plain,
% 1.31/1.12 (c0_1(a299)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[747, 2144])).
% 1.31/1.12 tff(2148,plain,
% 1.31/1.12 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(2149,plain,
% 1.31/1.12 ((hskp21 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299))) <=> (hskp21 | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(2150,plain,
% 1.31/1.12 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))))),
% 1.31/1.12 inference(monotonicity,[status(thm)],[2149])).
% 1.31/1.12 tff(2151,plain,
% 1.31/1.12 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301)))),
% 1.31/1.12 inference(transitivity,[status(thm)],[2150, 2148])).
% 1.31/1.12 tff(2152,plain,
% 1.31/1.12 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp21 | (~ndr1_0) | (~c2_1(a301)) | (~c3_1(a301)) | (~c0_1(a301)) | c2_1(a299) | (~c3_1(a299)) | (~c0_1(a299)))),
% 1.31/1.12 inference(quant_inst,[status(thm)],[])).
% 1.31/1.12 tff(2153,plain,
% 1.31/1.12 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp21 | c2_1(a299) | (~ndr1_0) | (~c3_1(a299)) | (~c0_1(a299)) | (~c3_1(a301)) | (~c0_1(a301)) | (~c2_1(a301))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[2152, 2151])).
% 1.31/1.12 tff(2154,plain,
% 1.31/1.12 (hskp21),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[2153, 135, 2002, 2001, 2030, 2147, 2146, 2145, 2143])).
% 1.31/1.12 tff(2155,plain,
% 1.31/1.12 (~c2_1(a330)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1450, 2154])).
% 1.31/1.12 tff(2156,plain,
% 1.31/1.12 (~c0_1(a330)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1434, 2154])).
% 1.31/1.12 tff(2157,plain,
% 1.31/1.12 (c3_1(a330)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1461, 2154])).
% 1.31/1.12 tff(2158,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(2159,plain,
% 1.31/1.12 (((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330))) <=> (c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(2160,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330))))),
% 1.31/1.12 inference(monotonicity,[status(thm)],[2159])).
% 1.31/1.12 tff(2161,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))),
% 1.31/1.12 inference(transitivity,[status(thm)],[2160, 2158])).
% 1.31/1.12 tff(2162,plain,
% 1.31/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a300) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))),
% 1.31/1.12 inference(quant_inst,[status(thm)],[])).
% 1.31/1.12 tff(2163,plain,
% 1.31/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a300) | (~ndr1_0) | (~c2_1(a300)) | (~c3_1(a300)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 1.31/1.12 tff(2164,plain,
% 1.31/1.12 (~c2_1(a300)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[2163, 135, 2157, 2029, 2050, 2156, 2155, 2027, 2048, 2133, 2123])).
% 1.31/1.12 tff(2165,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(2166,plain,
% 1.31/1.12 (((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330))) <=> (c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))),
% 1.31/1.12 inference(rewrite,[status(thm)],[])).
% 1.31/1.12 tff(2167,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330))))),
% 1.31/1.12 inference(monotonicity,[status(thm)],[2166])).
% 1.31/1.12 tff(2168,plain,
% 1.31/1.12 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330)))),
% 1.31/1.12 inference(transitivity,[status(thm)],[2167, 2165])).
% 1.31/1.12 tff(2169,plain,
% 1.31/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a294) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | c3_1(a315) | (~c2_1(a315)) | c2_1(a330) | c0_1(a330) | (~c3_1(a330)))),
% 1.31/1.12 inference(quant_inst,[status(thm)],[])).
% 1.31/1.12 tff(2170,plain,
% 1.31/1.12 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a330) | c2_1(a330) | c3_1(a315) | c1_1(a294) | (~ndr1_0) | (~c2_1(a294)) | (~c3_1(a294)) | c1_1(a315) | (~c2_1(a315)) | (~c3_1(a330))),
% 1.31/1.12 inference(modus_ponens,[status(thm)],[2169, 2168])).
% 1.31/1.12 tff(2171,plain,
% 1.31/1.12 (~c3_1(a294)),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[2170, 135, 2157, 2029, 2044, 2156, 2155, 2027, 2046, 2133, 2123])).
% 1.31/1.12 tff(2172,plain,
% 1.31/1.12 ($false),
% 1.31/1.12 inference(unit_resolution,[status(thm)],[1441, 135, 940, 2050, 2045, 2044, 2048, 1344, 2171, 2164])).
% 1.31/1.13 tff(2173,plain,(hskp22), inference(lemma,lemma(discharge,[]))).
% 1.31/1.13 tff(2174,plain,
% 1.31/1.13 (~c3_1(a331)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[82, 2173])).
% 1.31/1.13 tff(2175,plain,
% 1.31/1.13 (~c2_1(a331)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[70, 2173])).
% 1.31/1.13 tff(2176,plain,
% 1.31/1.13 (~c1_1(a331)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[76, 2173])).
% 1.31/1.13 tff(2177,plain,
% 1.31/1.13 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c1_1(a297)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c1_1(a297)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(2178,plain,
% 1.31/1.13 ((hskp4 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c2_1(a331) | c1_1(a331) | c3_1(a331)) <=> (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c1_1(a297)))),
% 1.31/1.13 inference(rewrite,[status(thm)],[])).
% 1.31/1.13 tff(2179,plain,
% 1.31/1.13 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c1_1(a297))))),
% 1.31/1.13 inference(monotonicity,[status(thm)],[2178])).
% 1.31/1.13 tff(2180,plain,
% 1.31/1.13 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c2_1(a331) | c1_1(a331) | c3_1(a331))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c1_1(a297)))),
% 1.31/1.13 inference(transitivity,[status(thm)],[2179, 2177])).
% 1.31/1.13 tff(2181,plain,
% 1.31/1.13 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp4 | (~ndr1_0) | c0_1(a297) | (~c1_1(a297)) | (~c3_1(a297)) | c2_1(a331) | c1_1(a331) | c3_1(a331))),
% 1.31/1.13 inference(quant_inst,[status(thm)],[])).
% 1.31/1.13 tff(2182,plain,
% 1.31/1.13 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp4 | c1_1(a331) | c2_1(a331) | c3_1(a331) | c0_1(a297) | (~ndr1_0) | (~c3_1(a297)) | (~c1_1(a297))),
% 1.31/1.13 inference(modus_ponens,[status(thm)],[2181, 2180])).
% 1.31/1.13 tff(2183,plain,
% 1.31/1.13 (hskp4 | (~c3_1(a297))),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[2182, 135, 2049, 2176, 2175, 2174, 2032, 42])).
% 1.31/1.13 tff(2184,plain,
% 1.31/1.13 (hskp4),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[2183, 2109])).
% 1.31/1.13 tff(2185,plain,
% 1.31/1.13 (c0_1(a299)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[747, 2110])).
% 1.31/1.13 tff(2186,plain,
% 1.31/1.13 ($false),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[1944, 2185, 2184, 2026, 760, 2111])).
% 1.31/1.13 tff(2187,plain,((~c3_1(a297)) | c2_1(a299)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.13 tff(2188,plain,
% 1.31/1.13 (c2_1(a299)),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[2187, 2100])).
% 1.31/1.13 tff(2189,plain,
% 1.31/1.13 ($false),
% 1.31/1.13 inference(unit_resolution,[status(thm)],[775, 2188, 2108])).
% 1.31/1.13 % SZS output end Proof
%------------------------------------------------------------------------------