TSTP Solution File: SYN452-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN452-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 23:55:31 EDT 2022
% Result : Unsatisfiable 0.62s 0.65s
% Output : Proof 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN452-1 : TPTP v8.1.0. Released v2.1.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 03:47:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.62/0.65 % SZS status Unsatisfiable
% 0.62/0.65 % SZS output start Proof
% 0.62/0.65 tff(c0_1_type, type, (
% 0.62/0.65 c0_1: $i > $o)).
% 0.62/0.65 tff(a865_type, type, (
% 0.62/0.65 a865: $i)).
% 0.62/0.65 tff(c3_1_type, type, (
% 0.62/0.65 c3_1: $i > $o)).
% 0.62/0.65 tff(a828_type, type, (
% 0.62/0.65 a828: $i)).
% 0.62/0.65 tff(c1_1_type, type, (
% 0.62/0.65 c1_1: $i > $o)).
% 0.62/0.65 tff(a826_type, type, (
% 0.62/0.65 a826: $i)).
% 0.62/0.65 tff(c2_1_type, type, (
% 0.62/0.65 c2_1: $i > $o)).
% 0.62/0.65 tff(ndr1_0_type, type, (
% 0.62/0.65 ndr1_0: $o)).
% 0.62/0.65 tff(hskp7_type, type, (
% 0.62/0.65 hskp7: $o)).
% 0.62/0.65 tff(a860_type, type, (
% 0.62/0.65 a860: $i)).
% 0.62/0.65 tff(hskp22_type, type, (
% 0.62/0.65 hskp22: $o)).
% 0.62/0.65 tff(a821_type, type, (
% 0.62/0.65 a821: $i)).
% 0.62/0.65 tff(a816_type, type, (
% 0.62/0.65 a816: $i)).
% 0.62/0.65 tff(a830_type, type, (
% 0.62/0.65 a830: $i)).
% 0.62/0.65 tff(hskp8_type, type, (
% 0.62/0.65 hskp8: $o)).
% 0.62/0.65 tff(hskp1_type, type, (
% 0.62/0.65 hskp1: $o)).
% 0.62/0.65 tff(a842_type, type, (
% 0.62/0.65 a842: $i)).
% 0.62/0.65 tff(hskp14_type, type, (
% 0.62/0.65 hskp14: $o)).
% 0.62/0.65 tff(a878_type, type, (
% 0.62/0.65 a878: $i)).
% 0.62/0.65 tff(hskp24_type, type, (
% 0.62/0.65 hskp24: $o)).
% 0.62/0.65 tff(a815_type, type, (
% 0.62/0.65 a815: $i)).
% 0.62/0.65 tff(hskp0_type, type, (
% 0.62/0.65 hskp0: $o)).
% 0.62/0.65 tff(a833_type, type, (
% 0.62/0.65 a833: $i)).
% 0.62/0.65 tff(hskp28_type, type, (
% 0.62/0.65 hskp28: $o)).
% 0.62/0.65 tff(hskp20_type, type, (
% 0.62/0.65 hskp20: $o)).
% 0.62/0.65 tff(a817_type, type, (
% 0.62/0.65 a817: $i)).
% 0.62/0.65 tff(hskp2_type, type, (
% 0.62/0.65 hskp2: $o)).
% 0.62/0.65 tff(a831_type, type, (
% 0.62/0.65 a831: $i)).
% 0.62/0.65 tff(hskp9_type, type, (
% 0.62/0.65 hskp9: $o)).
% 0.62/0.65 tff(a856_type, type, (
% 0.62/0.65 a856: $i)).
% 0.62/0.65 tff(hskp29_type, type, (
% 0.62/0.65 hskp29: $o)).
% 0.62/0.65 tff(hskp4_type, type, (
% 0.62/0.65 hskp4: $o)).
% 0.62/0.65 tff(a825_type, type, (
% 0.62/0.65 a825: $i)).
% 0.62/0.65 tff(hskp5_type, type, (
% 0.62/0.65 hskp5: $o)).
% 0.62/0.65 tff(a855_type, type, (
% 0.62/0.65 a855: $i)).
% 0.62/0.65 tff(hskp19_type, type, (
% 0.62/0.65 hskp19: $o)).
% 0.62/0.65 tff(hskp27_type, type, (
% 0.62/0.65 hskp27: $o)).
% 0.62/0.65 tff(a839_type, type, (
% 0.62/0.65 a839: $i)).
% 0.62/0.65 tff(hskp13_type, type, (
% 0.62/0.65 hskp13: $o)).
% 0.62/0.65 tff(hskp16_type, type, (
% 0.62/0.65 hskp16: $o)).
% 0.62/0.65 tff(a848_type, type, (
% 0.62/0.65 a848: $i)).
% 0.62/0.65 tff(a857_type, type, (
% 0.62/0.65 a857: $i)).
% 0.62/0.65 tff(hskp21_type, type, (
% 0.62/0.65 hskp21: $o)).
% 0.62/0.65 tff(a827_type, type, (
% 0.62/0.65 a827: $i)).
% 0.62/0.65 tff(hskp6_type, type, (
% 0.62/0.65 hskp6: $o)).
% 0.62/0.65 tff(a844_type, type, (
% 0.62/0.65 a844: $i)).
% 0.62/0.65 tff(hskp15_type, type, (
% 0.62/0.65 hskp15: $o)).
% 0.62/0.65 tff(1,assumption,(~c3_1(a828)), introduced(assumption)).
% 0.62/0.65 tff(2,plain,
% 0.62/0.65 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))),
% 0.62/0.65 inference(bind,[status(th)],[])).
% 0.62/0.65 tff(3,plain,
% 0.62/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.65 inference(quant_intro,[status(thm)],[2])).
% 0.62/0.65 tff(4,plain,
% 0.62/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.65 inference(rewrite,[status(thm)],[])).
% 0.62/0.65 tff(5,plain,
% 0.62/0.65 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))))),
% 0.62/0.65 inference(bind,[status(th)],[])).
% 0.62/0.65 tff(6,plain,
% 0.62/0.65 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.65 inference(quant_intro,[status(thm)],[5])).
% 0.62/0.65 tff(7,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.62/0.65 tff(8,plain,
% 0.62/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.62/0.65 tff(9,plain,
% 0.62/0.65 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.65 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.62/0.66 tff(10,plain,(
% 0.62/0.66 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.66 inference(skolemize,[status(sab)],[9])).
% 0.62/0.66 tff(11,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.62/0.66 tff(12,assumption,(~hskp7), introduced(assumption)).
% 0.62/0.66 tff(13,assumption,(~hskp22), introduced(assumption)).
% 0.62/0.66 tff(14,plain,
% 0.62/0.66 (^[U: $i] : refl((hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(15,plain,
% 0.62/0.66 (![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[14])).
% 0.62/0.66 tff(16,plain,
% 0.62/0.66 (![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(17,plain,
% 0.62/0.66 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp22) <=> ((hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp22))), rewrite(((hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp22) <=> (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp22) <=> (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(18,plain,
% 0.62/0.66 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp22) <=> ![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[17])).
% 0.62/0.66 tff(19,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.62/0.66 tff(20,plain,
% 0.62/0.66 (![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.62/0.66 tff(21,plain,
% 0.62/0.66 (![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.62/0.66 tff(22,plain,(
% 0.62/0.66 ![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.62/0.66 inference(skolemize,[status(sab)],[21])).
% 0.62/0.66 tff(23,plain,
% 0.62/0.66 (![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.62/0.66 tff(24,assumption,(~hskp1), introduced(assumption)).
% 0.62/0.66 tff(25,plain,
% 0.62/0.66 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(26,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[25])).
% 0.62/0.66 tff(27,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(28,plain,
% 0.62/0.66 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(29,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[28])).
% 0.62/0.66 tff(30,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.62/0.66 tff(31,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.62/0.66 tff(32,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.62/0.66 tff(33,plain,(
% 0.62/0.66 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.66 inference(skolemize,[status(sab)],[32])).
% 0.62/0.66 tff(34,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.62/0.66 tff(35,plain,
% 0.62/0.66 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(36,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[35])).
% 0.62/0.66 tff(37,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(38,plain,
% 0.62/0.66 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c1_1(W) | (~c0_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(39,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[38])).
% 0.62/0.66 tff(40,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(W))) | c1_1(V)) | c2_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 0.62/0.66 tff(41,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.62/0.66 tff(42,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.62/0.66 tff(43,plain,(
% 0.62/0.66 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.62/0.66 inference(skolemize,[status(sab)],[42])).
% 0.62/0.66 tff(44,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.62/0.66 tff(45,assumption,(~hskp24), introduced(assumption)).
% 0.62/0.66 tff(46,plain,
% 0.62/0.66 ((hskp14 | hskp24) <=> (hskp14 | hskp24)),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(47,axiom,(hskp14 | hskp24), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.62/0.66 tff(48,plain,
% 0.62/0.66 (hskp14 | hskp24),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.62/0.66 tff(49,plain,
% 0.62/0.66 (hskp14),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.62/0.66 tff(50,plain,
% 0.62/0.66 (((~hskp14) | (~c2_1(a842))) <=> ((~hskp14) | (~c2_1(a842)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(51,plain,
% 0.62/0.66 (((~c2_1(a842)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a842)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(52,axiom,((~c2_1(a842)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.62/0.66 tff(53,plain,
% 0.62/0.66 ((~hskp14) | (~c2_1(a842))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.62/0.66 tff(54,plain,
% 0.62/0.66 ((~hskp14) | (~c2_1(a842))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[53, 50])).
% 0.62/0.66 tff(55,plain,
% 0.62/0.66 (~c2_1(a842)),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[54, 49])).
% 0.62/0.66 tff(56,plain,
% 0.62/0.66 (((~hskp14) | c1_1(a842)) <=> ((~hskp14) | c1_1(a842))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(57,axiom,((~hskp14) | c1_1(a842)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.62/0.66 tff(58,plain,
% 0.62/0.66 ((~hskp14) | c1_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.62/0.66 tff(59,plain,
% 0.62/0.66 ((~hskp14) | c1_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[58, 56])).
% 0.62/0.66 tff(60,plain,
% 0.62/0.66 ((~hskp14) | c1_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[59, 56])).
% 0.62/0.66 tff(61,plain,
% 0.62/0.66 ((~hskp14) | c1_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.62/0.66 tff(62,plain,
% 0.62/0.66 ((~hskp14) | c1_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[61, 56])).
% 0.62/0.66 tff(63,plain,
% 0.62/0.66 ((~hskp14) | c1_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[62, 56])).
% 0.62/0.66 tff(64,plain,
% 0.62/0.66 ((~hskp14) | c1_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.62/0.66 tff(65,plain,
% 0.62/0.66 ((~hskp14) | c1_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[64, 56])).
% 0.62/0.66 tff(66,plain,
% 0.62/0.66 (c1_1(a842)),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[65, 49])).
% 0.62/0.66 tff(67,plain,
% 0.62/0.66 (((~hskp14) | c0_1(a842)) <=> ((~hskp14) | c0_1(a842))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(68,axiom,((~hskp14) | c0_1(a842)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.62/0.66 tff(69,plain,
% 0.62/0.66 ((~hskp14) | c0_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.62/0.66 tff(70,plain,
% 0.62/0.66 ((~hskp14) | c0_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[69, 67])).
% 0.62/0.66 tff(71,plain,
% 0.62/0.66 ((~hskp14) | c0_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[70, 67])).
% 0.62/0.66 tff(72,plain,
% 0.62/0.66 ((~hskp14) | c0_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.62/0.66 tff(73,plain,
% 0.62/0.66 ((~hskp14) | c0_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[72, 67])).
% 0.62/0.66 tff(74,plain,
% 0.62/0.66 ((~hskp14) | c0_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[73, 67])).
% 0.62/0.66 tff(75,plain,
% 0.62/0.66 ((~hskp14) | c0_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.62/0.66 tff(76,plain,
% 0.62/0.66 ((~hskp14) | c0_1(a842)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[75, 67])).
% 0.62/0.66 tff(77,plain,
% 0.62/0.66 (c0_1(a842)),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[76, 49])).
% 0.62/0.66 tff(78,plain,
% 0.62/0.66 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(79,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[78])).
% 0.62/0.66 tff(80,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(81,plain,
% 0.62/0.66 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(82,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[81])).
% 0.62/0.66 tff(83,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 0.62/0.66 tff(84,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.62/0.66 tff(85,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.62/0.66 tff(86,plain,(
% 0.62/0.66 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.62/0.66 inference(skolemize,[status(sab)],[85])).
% 0.62/0.66 tff(87,plain,
% 0.62/0.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.62/0.66 tff(88,plain,
% 0.62/0.66 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(89,plain,
% 0.62/0.66 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[88])).
% 0.62/0.66 tff(90,plain,
% 0.62/0.66 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(91,plain,
% 0.62/0.66 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(92,plain,
% 0.62/0.67 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[91])).
% 0.62/0.67 tff(93,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.62/0.67 tff(94,plain,
% 0.62/0.67 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.62/0.67 tff(95,plain,
% 0.62/0.67 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.62/0.67 tff(96,plain,(
% 0.62/0.67 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.67 inference(skolemize,[status(sab)],[95])).
% 0.62/0.67 tff(97,plain,
% 0.62/0.67 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.62/0.67 tff(98,assumption,(~c2_1(a842)), introduced(assumption)).
% 0.62/0.67 tff(99,assumption,(hskp20), introduced(assumption)).
% 0.62/0.67 tff(100,plain,
% 0.62/0.67 (((~hskp20) | (~c2_1(a856))) <=> ((~hskp20) | (~c2_1(a856)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(101,plain,
% 0.62/0.67 (((~c2_1(a856)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a856)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(102,axiom,((~c2_1(a856)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 0.62/0.67 tff(103,plain,
% 0.62/0.67 ((~hskp20) | (~c2_1(a856))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.62/0.67 tff(104,plain,
% 0.62/0.67 ((~hskp20) | (~c2_1(a856))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[103, 100])).
% 0.62/0.67 tff(105,plain,
% 0.62/0.67 (~c2_1(a856)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[104, 99])).
% 0.62/0.67 tff(106,assumption,(c1_1(a842)), introduced(assumption)).
% 0.62/0.67 tff(107,assumption,(c0_1(a842)), introduced(assumption)).
% 0.62/0.67 tff(108,plain,
% 0.62/0.67 (((~hskp20) | (~c1_1(a856))) <=> ((~hskp20) | (~c1_1(a856)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(109,plain,
% 0.62/0.67 (((~c1_1(a856)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a856)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(110,axiom,((~c1_1(a856)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.62/0.67 tff(111,plain,
% 0.62/0.67 ((~hskp20) | (~c1_1(a856))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.62/0.67 tff(112,plain,
% 0.62/0.67 ((~hskp20) | (~c1_1(a856))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[111, 108])).
% 0.62/0.67 tff(113,plain,
% 0.62/0.67 (~c1_1(a856)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[112, 99])).
% 0.62/0.67 tff(114,plain,
% 0.62/0.67 (((~hskp20) | c3_1(a856)) <=> ((~hskp20) | c3_1(a856))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(115,axiom,((~hskp20) | c3_1(a856)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 0.62/0.67 tff(116,plain,
% 0.62/0.67 ((~hskp20) | c3_1(a856)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.62/0.67 tff(117,plain,
% 0.62/0.67 ((~hskp20) | c3_1(a856)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[116, 114])).
% 0.62/0.67 tff(118,plain,
% 0.62/0.67 ((~hskp20) | c3_1(a856)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[117, 114])).
% 0.62/0.67 tff(119,plain,
% 0.62/0.67 ((~hskp20) | c3_1(a856)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.62/0.67 tff(120,plain,
% 0.62/0.67 ((~hskp20) | c3_1(a856)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[119, 114])).
% 0.62/0.67 tff(121,plain,
% 0.62/0.67 ((~hskp20) | c3_1(a856)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[120, 114])).
% 0.62/0.67 tff(122,plain,
% 0.62/0.67 ((~hskp20) | c3_1(a856)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.62/0.67 tff(123,plain,
% 0.62/0.67 ((~hskp20) | c3_1(a856)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[122, 114])).
% 0.62/0.67 tff(124,plain,
% 0.62/0.67 (c3_1(a856)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[123, 99])).
% 0.62/0.67 tff(125,assumption,(~c0_1(a856)), introduced(assumption)).
% 0.62/0.67 tff(126,assumption,(~c2_1(a856)), introduced(assumption)).
% 0.62/0.67 tff(127,assumption,(~c1_1(a856)), introduced(assumption)).
% 0.62/0.67 tff(128,assumption,(c3_1(a856)), introduced(assumption)).
% 0.62/0.67 tff(129,assumption,(~ndr1_0), introduced(assumption)).
% 0.62/0.67 tff(130,plain,
% 0.62/0.67 ((ndr1_0 | (~hskp20)) <=> (ndr1_0 | (~hskp20))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(131,plain,
% 0.62/0.67 (((~hskp20) | ndr1_0) <=> (ndr1_0 | (~hskp20))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(132,axiom,((~hskp20) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause11')).
% 0.62/0.67 tff(133,plain,
% 0.62/0.67 (ndr1_0 | (~hskp20)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.62/0.67 tff(134,plain,
% 0.62/0.67 (ndr1_0 | (~hskp20)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[133, 130])).
% 0.62/0.67 tff(135,plain,
% 0.62/0.67 (~hskp20),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[134, 129])).
% 0.62/0.67 tff(136,plain,
% 0.62/0.67 ((ndr1_0 | (~hskp28)) <=> (ndr1_0 | (~hskp28))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(137,plain,
% 0.62/0.67 (((~hskp28) | ndr1_0) <=> (ndr1_0 | (~hskp28))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(138,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 0.62/0.67 tff(139,plain,
% 0.62/0.67 (ndr1_0 | (~hskp28)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.62/0.67 tff(140,plain,
% 0.62/0.67 (ndr1_0 | (~hskp28)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[139, 136])).
% 0.62/0.67 tff(141,plain,
% 0.62/0.67 (~hskp28),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[140, 129])).
% 0.62/0.67 tff(142,plain,
% 0.62/0.67 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(143,plain,
% 0.62/0.67 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(144,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause7')).
% 0.62/0.67 tff(145,plain,
% 0.62/0.67 (ndr1_0 | (~hskp24)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.62/0.67 tff(146,plain,
% 0.62/0.67 (ndr1_0 | (~hskp24)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[145, 142])).
% 0.62/0.67 tff(147,plain,
% 0.62/0.67 (~hskp24),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[146, 129])).
% 0.62/0.67 tff(148,plain,
% 0.62/0.67 ((hskp24 | hskp28 | hskp20) <=> (hskp24 | hskp28 | hskp20)),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(149,plain,
% 0.62/0.67 (((hskp24 | hskp28) | hskp20) <=> (hskp24 | hskp28 | hskp20)),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(150,plain,
% 0.62/0.67 ((hskp28 | hskp24) <=> (hskp24 | hskp28)),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(151,plain,
% 0.62/0.67 (((hskp28 | hskp24) | hskp20) <=> ((hskp24 | hskp28) | hskp20)),
% 0.62/0.67 inference(monotonicity,[status(thm)],[150])).
% 0.62/0.67 tff(152,plain,
% 0.62/0.67 (((hskp28 | hskp24) | hskp20) <=> (hskp24 | hskp28 | hskp20)),
% 0.62/0.67 inference(transitivity,[status(thm)],[151, 149])).
% 0.62/0.67 tff(153,axiom,((hskp28 | hskp24) | hskp20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 0.62/0.67 tff(154,plain,
% 0.62/0.67 (hskp24 | hskp28 | hskp20),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.62/0.67 tff(155,plain,
% 0.62/0.67 (hskp24 | hskp28 | hskp20),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[154, 148])).
% 0.62/0.67 tff(156,plain,
% 0.62/0.67 (hskp24 | hskp28 | hskp20),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.62/0.67 tff(157,plain,
% 0.62/0.67 (hskp24 | hskp28 | hskp20),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[156, 148])).
% 0.62/0.67 tff(158,plain,
% 0.62/0.67 (hskp24 | hskp28 | hskp20),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[157, 148])).
% 0.62/0.67 tff(159,plain,
% 0.62/0.67 (hskp24 | hskp28 | hskp20),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[158, 148])).
% 0.62/0.67 tff(160,plain,
% 0.62/0.67 (hskp24 | hskp28 | hskp20),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[159, 148])).
% 0.62/0.67 tff(161,plain,
% 0.62/0.67 (hskp24 | hskp28 | hskp20),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[160, 148])).
% 0.62/0.67 tff(162,plain,
% 0.62/0.67 ($false),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[161, 147, 141, 135])).
% 0.62/0.67 tff(163,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.62/0.67 tff(164,plain,
% 0.62/0.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | c0_1(a856) | (~c3_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | c0_1(a856) | (~c3_1(a856)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(165,plain,
% 0.62/0.67 ((hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a856) | c0_1(a856) | (~c3_1(a856))) <=> (hskp2 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | c0_1(a856) | (~c3_1(a856)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(166,plain,
% 0.62/0.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | c0_1(a856) | (~c3_1(a856))))),
% 0.62/0.67 inference(monotonicity,[status(thm)],[165])).
% 0.62/0.67 tff(167,plain,
% 0.62/0.67 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | c0_1(a856) | (~c3_1(a856)))),
% 0.62/0.67 inference(transitivity,[status(thm)],[166, 164])).
% 0.62/0.67 tff(168,plain,
% 0.62/0.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(169,plain,
% 0.62/0.67 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | c0_1(a856) | (~c3_1(a856))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.62/0.67 tff(170,plain,
% 0.62/0.67 (hskp2 | c0_1(a856)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[169, 163, 128, 127, 126, 97])).
% 0.62/0.67 tff(171,plain,
% 0.62/0.67 (hskp2),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[170, 125])).
% 0.62/0.67 tff(172,plain,
% 0.62/0.67 (((~hskp2) | (~c0_1(a817))) <=> ((~hskp2) | (~c0_1(a817)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(173,plain,
% 0.62/0.67 (((~c0_1(a817)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a817)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(174,axiom,((~c0_1(a817)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.62/0.67 tff(175,plain,
% 0.62/0.67 ((~hskp2) | (~c0_1(a817))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.62/0.67 tff(176,plain,
% 0.62/0.67 ((~hskp2) | (~c0_1(a817))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[175, 172])).
% 0.62/0.67 tff(177,plain,
% 0.62/0.67 (~c0_1(a817)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[176, 171])).
% 0.62/0.67 tff(178,plain,
% 0.62/0.67 (((~hskp2) | c2_1(a817)) <=> ((~hskp2) | c2_1(a817))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(179,axiom,((~hskp2) | c2_1(a817)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.62/0.67 tff(180,plain,
% 0.62/0.67 ((~hskp2) | c2_1(a817)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.62/0.67 tff(181,plain,
% 0.62/0.67 ((~hskp2) | c2_1(a817)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[180, 178])).
% 0.62/0.67 tff(182,plain,
% 0.62/0.67 ((~hskp2) | c2_1(a817)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[181, 178])).
% 0.62/0.67 tff(183,plain,
% 0.62/0.67 ((~hskp2) | c2_1(a817)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.62/0.67 tff(184,plain,
% 0.62/0.67 ((~hskp2) | c2_1(a817)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[183, 178])).
% 0.62/0.67 tff(185,plain,
% 0.62/0.67 ((~hskp2) | c2_1(a817)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[184, 178])).
% 0.62/0.67 tff(186,plain,
% 0.62/0.67 ((~hskp2) | c2_1(a817)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.62/0.67 tff(187,plain,
% 0.62/0.67 ((~hskp2) | c2_1(a817)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[186, 178])).
% 0.62/0.67 tff(188,plain,
% 0.62/0.67 (c2_1(a817)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[187, 171])).
% 0.62/0.67 tff(189,plain,
% 0.62/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a856) | c2_1(a856) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a856)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a856) | c2_1(a856) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a856)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(190,plain,
% 0.62/0.67 (((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817))) <=> (c1_1(a856) | c2_1(a856) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a856)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(191,plain,
% 0.62/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a856) | c2_1(a856) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a856))))),
% 0.62/0.67 inference(monotonicity,[status(thm)],[190])).
% 0.62/0.67 tff(192,plain,
% 0.62/0.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a856) | c2_1(a856) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a856)))),
% 0.62/0.67 inference(transitivity,[status(thm)],[191, 189])).
% 0.62/0.67 tff(193,plain,
% 0.62/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(194,plain,
% 0.62/0.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a856) | c2_1(a856) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a856))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.62/0.67 tff(195,plain,
% 0.62/0.67 (~c1_1(a817)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[194, 163, 128, 107, 106, 188, 127, 126, 98, 177, 87])).
% 0.62/0.67 tff(196,plain,
% 0.62/0.67 (^[V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(197,plain,
% 0.62/0.67 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[196])).
% 0.62/0.67 tff(198,plain,
% 0.62/0.67 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(199,plain,
% 0.62/0.67 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(200,plain,
% 0.62/0.67 (![V: $i, U: $i] : (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[199])).
% 0.62/0.67 tff(201,axiom,(![V: $i, U: $i] : (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 0.62/0.67 tff(202,plain,
% 0.62/0.67 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.62/0.67 tff(203,plain,
% 0.62/0.67 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.62/0.67 tff(204,plain,(
% 0.62/0.67 ![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.62/0.67 inference(skolemize,[status(sab)],[203])).
% 0.62/0.67 tff(205,plain,
% 0.62/0.67 (![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.62/0.67 tff(206,plain,
% 0.62/0.67 (((~hskp2) | (~c3_1(a817))) <=> ((~hskp2) | (~c3_1(a817)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(207,plain,
% 0.62/0.67 (((~c3_1(a817)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a817)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(208,axiom,((~c3_1(a817)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 0.62/0.67 tff(209,plain,
% 0.62/0.67 ((~hskp2) | (~c3_1(a817))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.62/0.67 tff(210,plain,
% 0.62/0.67 ((~hskp2) | (~c3_1(a817))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[209, 206])).
% 0.62/0.67 tff(211,plain,
% 0.62/0.67 (~c3_1(a817)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[210, 171])).
% 0.62/0.67 tff(212,plain,
% 0.62/0.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c1_1(a856) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | c0_1(a856) | (~c3_1(a856)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c1_1(a856) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | c0_1(a856) | (~c3_1(a856)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(213,plain,
% 0.62/0.67 (((~ndr1_0) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)) | c1_1(a817) | c0_1(a817) | c3_1(a817)) <=> (c1_1(a856) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | c0_1(a856) | (~c3_1(a856)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(214,plain,
% 0.62/0.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)) | c1_1(a817) | c0_1(a817) | c3_1(a817))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c1_1(a856) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | c0_1(a856) | (~c3_1(a856))))),
% 0.62/0.67 inference(monotonicity,[status(thm)],[213])).
% 0.62/0.67 tff(215,plain,
% 0.62/0.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)) | c1_1(a817) | c0_1(a817) | c3_1(a817))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c1_1(a856) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | c0_1(a856) | (~c3_1(a856)))),
% 0.62/0.67 inference(transitivity,[status(thm)],[214, 212])).
% 0.62/0.67 tff(216,plain,
% 0.62/0.67 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a856) | c0_1(a856) | (~c3_1(a856)) | c1_1(a817) | c0_1(a817) | c3_1(a817))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(217,plain,
% 0.62/0.67 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c1_1(a856) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | c0_1(a856) | (~c3_1(a856))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.62/0.67 tff(218,plain,
% 0.62/0.67 ($false),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[217, 163, 128, 127, 177, 211, 205, 125, 195])).
% 0.62/0.67 tff(219,plain,(c0_1(a856) | (~c3_1(a856)) | c1_1(a856) | (~c0_1(a842)) | (~c1_1(a842)) | c2_1(a856) | c2_1(a842)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.67 tff(220,plain,
% 0.62/0.67 (c0_1(a856)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[219, 124, 113, 107, 106, 105, 98])).
% 0.62/0.67 tff(221,plain,
% 0.62/0.67 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(222,plain,
% 0.62/0.67 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[221])).
% 0.62/0.67 tff(223,plain,
% 0.62/0.67 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(224,plain,
% 0.62/0.67 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(225,plain,
% 0.62/0.67 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[224])).
% 0.62/0.67 tff(226,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 0.62/0.67 tff(227,plain,
% 0.62/0.67 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.62/0.68 tff(228,plain,
% 0.62/0.68 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[227, 223])).
% 0.62/0.68 tff(229,plain,(
% 0.62/0.68 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.68 inference(skolemize,[status(sab)],[228])).
% 0.62/0.68 tff(230,plain,
% 0.62/0.68 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[229, 222])).
% 0.62/0.68 tff(231,plain,
% 0.62/0.68 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | (~c0_1(a856)) | (~c3_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | (~c0_1(a856)) | (~c3_1(a856)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(232,plain,
% 0.62/0.68 ((hskp9 | (~ndr1_0) | c2_1(a856) | (~c3_1(a856)) | (~c0_1(a856)) | c2_1(a856) | c1_1(a856) | (~c0_1(a856))) <=> (hskp9 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | (~c0_1(a856)) | (~c3_1(a856)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(233,plain,
% 0.62/0.68 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a856) | (~c3_1(a856)) | (~c0_1(a856)) | c2_1(a856) | c1_1(a856) | (~c0_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | (~c0_1(a856)) | (~c3_1(a856))))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[232])).
% 0.62/0.68 tff(234,plain,
% 0.62/0.68 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a856) | (~c3_1(a856)) | (~c0_1(a856)) | c2_1(a856) | c1_1(a856) | (~c0_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | (~c0_1(a856)) | (~c3_1(a856)))),
% 0.62/0.68 inference(transitivity,[status(thm)],[233, 231])).
% 0.62/0.68 tff(235,plain,
% 0.62/0.68 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a856) | (~c3_1(a856)) | (~c0_1(a856)) | c2_1(a856) | c1_1(a856) | (~c0_1(a856)))),
% 0.62/0.68 inference(quant_inst,[status(thm)],[])).
% 0.62/0.68 tff(236,plain,
% 0.62/0.68 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a856) | c2_1(a856) | (~ndr1_0) | (~c0_1(a856)) | (~c3_1(a856))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.62/0.68 tff(237,plain,
% 0.62/0.68 (hskp9 | (~c0_1(a856))),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[236, 163, 124, 113, 105, 230])).
% 0.62/0.68 tff(238,plain,
% 0.62/0.68 (hskp9),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[237, 220])).
% 0.62/0.68 tff(239,plain,
% 0.62/0.68 (((~hskp9) | (~c1_1(a831))) <=> ((~hskp9) | (~c1_1(a831)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(240,plain,
% 0.62/0.68 (((~c1_1(a831)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a831)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(241,axiom,((~c1_1(a831)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 0.62/0.68 tff(242,plain,
% 0.62/0.68 ((~hskp9) | (~c1_1(a831))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.62/0.68 tff(243,plain,
% 0.62/0.68 ((~hskp9) | (~c1_1(a831))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[242, 239])).
% 0.62/0.68 tff(244,plain,
% 0.62/0.68 (~c1_1(a831)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[243, 238])).
% 0.62/0.68 tff(245,plain,
% 0.62/0.68 (((~hskp9) | (~c0_1(a831))) <=> ((~hskp9) | (~c0_1(a831)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(246,plain,
% 0.62/0.68 (((~c0_1(a831)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a831)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(247,axiom,((~c0_1(a831)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 0.62/0.68 tff(248,plain,
% 0.62/0.68 ((~hskp9) | (~c0_1(a831))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.62/0.68 tff(249,plain,
% 0.62/0.68 ((~hskp9) | (~c0_1(a831))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[248, 245])).
% 0.62/0.68 tff(250,plain,
% 0.62/0.68 (~c0_1(a831)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[249, 238])).
% 0.62/0.68 tff(251,plain,
% 0.62/0.68 (((~hskp9) | c3_1(a831)) <=> ((~hskp9) | c3_1(a831))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(252,axiom,((~hskp9) | c3_1(a831)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.62/0.68 tff(253,plain,
% 0.62/0.68 ((~hskp9) | c3_1(a831)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.62/0.68 tff(254,plain,
% 0.62/0.68 ((~hskp9) | c3_1(a831)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[253, 251])).
% 0.62/0.68 tff(255,plain,
% 0.62/0.68 ((~hskp9) | c3_1(a831)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[254, 251])).
% 0.62/0.68 tff(256,plain,
% 0.62/0.68 ((~hskp9) | c3_1(a831)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[255, 251])).
% 0.62/0.68 tff(257,plain,
% 0.62/0.68 ((~hskp9) | c3_1(a831)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[256, 251])).
% 0.62/0.68 tff(258,plain,
% 0.62/0.68 ((~hskp9) | c3_1(a831)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[257, 251])).
% 0.62/0.68 tff(259,plain,
% 0.62/0.68 ((~hskp9) | c3_1(a831)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[258, 251])).
% 0.62/0.68 tff(260,plain,
% 0.62/0.68 ((~hskp9) | c3_1(a831)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[259, 251])).
% 0.62/0.68 tff(261,plain,
% 0.62/0.68 (c3_1(a831)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[260, 238])).
% 0.62/0.68 tff(262,plain,
% 0.62/0.68 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a856) | c2_1(a856) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a856)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a856) | c2_1(a856) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a856)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(263,plain,
% 0.62/0.68 ((hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831))) <=> (hskp2 | c1_1(a856) | c2_1(a856) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a856)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(264,plain,
% 0.62/0.68 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a856) | c2_1(a856) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a856))))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[263])).
% 0.62/0.68 tff(265,plain,
% 0.62/0.68 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a856) | c2_1(a856) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a856)))),
% 0.62/0.68 inference(transitivity,[status(thm)],[264, 262])).
% 0.62/0.68 tff(266,plain,
% 0.62/0.68 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a856) | c1_1(a856) | (~c3_1(a856)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))),
% 0.62/0.68 inference(quant_inst,[status(thm)],[])).
% 0.62/0.68 tff(267,plain,
% 0.62/0.68 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a856) | c2_1(a856) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a856))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.62/0.68 tff(268,plain,
% 0.62/0.68 (hskp2),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[267, 163, 124, 261, 113, 105, 250, 244, 97])).
% 0.62/0.68 tff(269,plain,
% 0.62/0.68 (~c0_1(a817)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[176, 268])).
% 0.62/0.68 tff(270,plain,
% 0.62/0.68 (c2_1(a817)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[187, 268])).
% 0.62/0.68 tff(271,plain,
% 0.62/0.68 (~c1_1(a817)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[194, 163, 124, 107, 106, 270, 113, 105, 98, 269, 87])).
% 0.62/0.68 tff(272,plain,
% 0.62/0.68 (~c3_1(a817)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[210, 268])).
% 0.62/0.68 tff(273,plain,
% 0.62/0.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a831) | c1_1(a831) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a831) | c1_1(a831) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a831)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(274,plain,
% 0.62/0.68 (((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a817) | c0_1(a817) | c3_1(a817)) <=> (c0_1(a831) | c1_1(a831) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a831)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(275,plain,
% 0.62/0.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a817) | c0_1(a817) | c3_1(a817))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a831) | c1_1(a831) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a831))))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[274])).
% 0.62/0.68 tff(276,plain,
% 0.62/0.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a817) | c0_1(a817) | c3_1(a817))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a831) | c1_1(a831) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a831)))),
% 0.62/0.68 inference(transitivity,[status(thm)],[275, 273])).
% 0.62/0.68 tff(277,plain,
% 0.62/0.68 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a817) | c0_1(a817) | c3_1(a817))),
% 0.62/0.68 inference(quant_inst,[status(thm)],[])).
% 0.62/0.68 tff(278,plain,
% 0.62/0.68 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a831) | c1_1(a831) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a831))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.62/0.68 tff(279,plain,
% 0.62/0.68 ($false),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[278, 163, 261, 250, 244, 269, 272, 205, 271])).
% 0.62/0.68 tff(280,plain,((~hskp20) | (~c0_1(a842)) | (~c1_1(a842)) | c2_1(a842)), inference(lemma,lemma(discharge,[]))).
% 0.62/0.68 tff(281,plain,
% 0.62/0.68 (~hskp20),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[280, 77, 66, 55])).
% 0.62/0.68 tff(282,plain,
% 0.62/0.68 (hskp28),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[161, 281, 45])).
% 0.62/0.68 tff(283,plain,
% 0.62/0.68 (((~hskp28) | c3_1(a833)) <=> ((~hskp28) | c3_1(a833))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(284,axiom,((~hskp28) | c3_1(a833)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.62/0.68 tff(285,plain,
% 0.62/0.68 ((~hskp28) | c3_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.62/0.68 tff(286,plain,
% 0.62/0.68 ((~hskp28) | c3_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[285, 283])).
% 0.62/0.68 tff(287,plain,
% 0.62/0.68 ((~hskp28) | c3_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[286, 283])).
% 0.62/0.68 tff(288,plain,
% 0.62/0.68 ((~hskp28) | c3_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[287, 283])).
% 0.62/0.68 tff(289,plain,
% 0.62/0.68 ((~hskp28) | c3_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[288, 283])).
% 0.62/0.68 tff(290,plain,
% 0.62/0.68 ((~hskp28) | c3_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[289, 283])).
% 0.62/0.68 tff(291,plain,
% 0.62/0.68 ((~hskp28) | c3_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[290, 283])).
% 0.62/0.68 tff(292,plain,
% 0.62/0.68 ((~hskp28) | c3_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[291, 283])).
% 0.62/0.68 tff(293,plain,
% 0.62/0.68 (c3_1(a833)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[292, 282])).
% 0.62/0.68 tff(294,plain,
% 0.62/0.68 (((~hskp28) | c1_1(a833)) <=> ((~hskp28) | c1_1(a833))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(295,axiom,((~hskp28) | c1_1(a833)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.62/0.68 tff(296,plain,
% 0.62/0.68 ((~hskp28) | c1_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.62/0.68 tff(297,plain,
% 0.62/0.68 ((~hskp28) | c1_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[296, 294])).
% 0.62/0.68 tff(298,plain,
% 0.62/0.68 ((~hskp28) | c1_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[297, 294])).
% 0.62/0.68 tff(299,plain,
% 0.62/0.68 ((~hskp28) | c1_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[298, 294])).
% 0.62/0.68 tff(300,plain,
% 0.62/0.68 ((~hskp28) | c1_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[299, 294])).
% 0.62/0.68 tff(301,plain,
% 0.62/0.68 ((~hskp28) | c1_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[300, 294])).
% 0.62/0.68 tff(302,plain,
% 0.62/0.68 ((~hskp28) | c1_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[301, 294])).
% 0.62/0.68 tff(303,plain,
% 0.62/0.68 ((~hskp28) | c1_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[302, 294])).
% 0.62/0.68 tff(304,plain,
% 0.62/0.68 (c1_1(a833)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[303, 282])).
% 0.62/0.68 tff(305,plain,
% 0.62/0.68 (((~hskp28) | c0_1(a833)) <=> ((~hskp28) | c0_1(a833))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(306,axiom,((~hskp28) | c0_1(a833)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 0.62/0.68 tff(307,plain,
% 0.62/0.68 ((~hskp28) | c0_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.62/0.68 tff(308,plain,
% 0.62/0.68 ((~hskp28) | c0_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[307, 305])).
% 0.62/0.68 tff(309,plain,
% 0.62/0.68 ((~hskp28) | c0_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[308, 305])).
% 0.62/0.68 tff(310,plain,
% 0.62/0.68 ((~hskp28) | c0_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[309, 305])).
% 0.62/0.68 tff(311,plain,
% 0.62/0.68 ((~hskp28) | c0_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[310, 305])).
% 0.62/0.68 tff(312,plain,
% 0.62/0.68 ((~hskp28) | c0_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[311, 305])).
% 0.62/0.68 tff(313,plain,
% 0.62/0.68 ((~hskp28) | c0_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[312, 305])).
% 0.62/0.68 tff(314,plain,
% 0.62/0.68 ((~hskp28) | c0_1(a833)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[313, 305])).
% 0.62/0.68 tff(315,plain,
% 0.62/0.68 (c0_1(a833)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[314, 282])).
% 0.62/0.68 tff(316,plain,
% 0.62/0.68 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | c3_1(a842))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | c3_1(a842))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(317,plain,
% 0.62/0.68 ((hskp22 | hskp1 | (~ndr1_0) | c3_1(a842) | c2_1(a842) | (~c1_1(a842))) <=> (hskp22 | hskp1 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | c3_1(a842))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(318,plain,
% 0.62/0.68 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a842) | c2_1(a842) | (~c1_1(a842)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | c3_1(a842)))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[317])).
% 0.62/0.68 tff(319,plain,
% 0.62/0.68 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a842) | c2_1(a842) | (~c1_1(a842)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | c3_1(a842))),
% 0.62/0.68 inference(transitivity,[status(thm)],[318, 316])).
% 0.62/0.68 tff(320,plain,
% 0.62/0.68 ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a842) | c2_1(a842) | (~c1_1(a842)))),
% 0.62/0.68 inference(quant_inst,[status(thm)],[])).
% 0.62/0.68 tff(321,plain,
% 0.62/0.68 ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | c3_1(a842)),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.62/0.68 tff(322,plain,
% 0.62/0.68 (hskp1 | c3_1(a842)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[321, 163, 13, 106, 98, 23])).
% 0.62/0.68 tff(323,plain,
% 0.62/0.68 (c3_1(a842)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[322, 24])).
% 0.62/0.68 tff(324,plain,
% 0.62/0.68 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(325,plain,
% 0.62/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[324])).
% 0.62/0.68 tff(326,plain,
% 0.62/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(327,plain,
% 0.62/0.68 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(328,plain,
% 0.62/0.68 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[327])).
% 0.62/0.68 tff(329,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 0.62/0.68 tff(330,plain,
% 0.62/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.62/0.68 tff(331,plain,
% 0.62/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[330, 326])).
% 0.62/0.68 tff(332,plain,(
% 0.62/0.68 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.62/0.68 inference(skolemize,[status(sab)],[331])).
% 0.62/0.68 tff(333,plain,
% 0.62/0.68 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[332, 325])).
% 0.62/0.68 tff(334,plain,
% 0.62/0.68 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))),
% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(335,plain,
% 0.62/0.68 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[334])).
% 0.62/0.68 tff(336,plain,
% 0.62/0.68 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(337,plain,
% 0.62/0.68 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~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)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(338,plain,
% 0.62/0.69 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[337])).
% 0.62/0.69 tff(339,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(V))) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 0.62/0.69 tff(340,plain,
% 0.62/0.69 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.62/0.69 tff(341,plain,
% 0.62/0.69 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[340, 336])).
% 0.62/0.69 tff(342,plain,(
% 0.62/0.69 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.62/0.69 inference(skolemize,[status(sab)],[341])).
% 0.62/0.69 tff(343,plain,
% 0.62/0.69 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[342, 335])).
% 0.62/0.69 tff(344,plain,
% 0.62/0.69 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(345,plain,
% 0.62/0.69 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[344])).
% 0.62/0.69 tff(346,plain,
% 0.62/0.69 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(347,plain,
% 0.62/0.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp29) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp29))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(348,plain,
% 0.62/0.69 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[347])).
% 0.62/0.69 tff(349,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 0.62/0.69 tff(350,plain,
% 0.62/0.69 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.62/0.69 tff(351,plain,
% 0.62/0.69 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[350, 346])).
% 0.62/0.69 tff(352,plain,(
% 0.62/0.69 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.62/0.69 inference(skolemize,[status(sab)],[351])).
% 0.62/0.69 tff(353,plain,
% 0.62/0.69 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[352, 345])).
% 0.62/0.69 tff(354,assumption,(c3_1(a833)), introduced(assumption)).
% 0.62/0.69 tff(355,assumption,(c1_1(a833)), introduced(assumption)).
% 0.62/0.69 tff(356,assumption,(c0_1(a833)), introduced(assumption)).
% 0.62/0.69 tff(357,plain,
% 0.62/0.69 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a842) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a842)) | (~c3_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a842) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(358,plain,
% 0.62/0.69 ((hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842))) <=> (hskp29 | c2_1(a842) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(359,plain,
% 0.62/0.69 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a842) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a842)) | (~c3_1(a842))))),
% 0.62/0.69 inference(monotonicity,[status(thm)],[358])).
% 0.62/0.69 tff(360,plain,
% 0.62/0.69 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a842) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.62/0.69 inference(transitivity,[status(thm)],[359, 357])).
% 0.62/0.69 tff(361,plain,
% 0.62/0.69 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)))),
% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
% 0.62/0.69 tff(362,plain,
% 0.62/0.69 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a842) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a842)) | (~c3_1(a842))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[361, 360])).
% 0.62/0.69 tff(363,plain,
% 0.62/0.69 (hskp29 | (~c3_1(a842))),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[362, 163, 356, 355, 354, 107, 98, 353])).
% 0.62/0.69 tff(364,plain,
% 0.62/0.69 (hskp29),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[363, 323])).
% 0.62/0.69 tff(365,plain,
% 0.62/0.69 (((~hskp29) | c3_1(a865)) <=> ((~hskp29) | c3_1(a865))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(366,axiom,((~hskp29) | c3_1(a865)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 0.62/0.69 tff(367,plain,
% 0.62/0.69 ((~hskp29) | c3_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.62/0.69 tff(368,plain,
% 0.62/0.69 ((~hskp29) | c3_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[367, 365])).
% 0.62/0.69 tff(369,plain,
% 0.62/0.69 ((~hskp29) | c3_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[368, 365])).
% 0.62/0.69 tff(370,plain,
% 0.62/0.69 ((~hskp29) | c3_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[369, 365])).
% 0.62/0.69 tff(371,plain,
% 0.62/0.69 ((~hskp29) | c3_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[370, 365])).
% 0.62/0.69 tff(372,plain,
% 0.62/0.69 ((~hskp29) | c3_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[371, 365])).
% 0.62/0.69 tff(373,plain,
% 0.62/0.69 ((~hskp29) | c3_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[372, 365])).
% 0.62/0.69 tff(374,plain,
% 0.62/0.69 ((~hskp29) | c3_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[373, 365])).
% 0.62/0.69 tff(375,plain,
% 0.62/0.69 (c3_1(a865)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[374, 364])).
% 0.62/0.69 tff(376,plain,
% 0.62/0.69 (((~hskp29) | c2_1(a865)) <=> ((~hskp29) | c2_1(a865))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(377,axiom,((~hskp29) | c2_1(a865)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.62/0.69 tff(378,plain,
% 0.62/0.69 ((~hskp29) | c2_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.62/0.69 tff(379,plain,
% 0.62/0.69 ((~hskp29) | c2_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[378, 376])).
% 0.62/0.69 tff(380,plain,
% 0.62/0.69 ((~hskp29) | c2_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[379, 376])).
% 0.62/0.69 tff(381,plain,
% 0.62/0.69 ((~hskp29) | c2_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[380, 376])).
% 0.62/0.69 tff(382,plain,
% 0.62/0.69 ((~hskp29) | c2_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[381, 376])).
% 0.62/0.69 tff(383,plain,
% 0.62/0.69 ((~hskp29) | c2_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[382, 376])).
% 0.62/0.69 tff(384,plain,
% 0.62/0.69 ((~hskp29) | c2_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[383, 376])).
% 0.62/0.69 tff(385,plain,
% 0.62/0.69 ((~hskp29) | c2_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[384, 376])).
% 0.62/0.69 tff(386,plain,
% 0.62/0.69 (c2_1(a865)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[385, 364])).
% 0.62/0.69 tff(387,plain,
% 0.62/0.69 (((~hskp29) | c1_1(a865)) <=> ((~hskp29) | c1_1(a865))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(388,axiom,((~hskp29) | c1_1(a865)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 0.62/0.69 tff(389,plain,
% 0.62/0.69 ((~hskp29) | c1_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.62/0.69 tff(390,plain,
% 0.62/0.69 ((~hskp29) | c1_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[389, 387])).
% 0.62/0.69 tff(391,plain,
% 0.62/0.69 ((~hskp29) | c1_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[390, 387])).
% 0.62/0.69 tff(392,plain,
% 0.62/0.69 ((~hskp29) | c1_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[391, 387])).
% 0.62/0.69 tff(393,plain,
% 0.62/0.69 ((~hskp29) | c1_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[392, 387])).
% 0.62/0.69 tff(394,plain,
% 0.62/0.69 ((~hskp29) | c1_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[393, 387])).
% 0.62/0.69 tff(395,plain,
% 0.62/0.69 ((~hskp29) | c1_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[394, 387])).
% 0.62/0.69 tff(396,plain,
% 0.62/0.69 ((~hskp29) | c1_1(a865)),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[395, 387])).
% 0.62/0.69 tff(397,plain,
% 0.62/0.69 (c1_1(a865)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[396, 364])).
% 0.62/0.69 tff(398,plain,
% 0.62/0.69 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(399,plain,
% 0.62/0.69 ((hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842))) <=> (hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(400,plain,
% 0.62/0.69 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842))))),
% 0.62/0.69 inference(monotonicity,[status(thm)],[399])).
% 0.62/0.69 tff(401,plain,
% 0.62/0.69 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.62/0.69 inference(transitivity,[status(thm)],[400, 398])).
% 0.62/0.69 tff(402,plain,
% 0.62/0.69 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
% 0.62/0.69 tff(403,plain,
% 0.62/0.69 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.62/0.69 tff(404,plain,
% 0.62/0.69 (hskp8),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[403, 163, 397, 386, 375, 107, 106, 343, 323])).
% 0.62/0.69 tff(405,plain,
% 0.62/0.69 (((~hskp8) | (~c2_1(a830))) <=> ((~hskp8) | (~c2_1(a830)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(406,plain,
% 0.62/0.69 (((~c2_1(a830)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a830)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(407,axiom,((~c2_1(a830)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.62/0.69 tff(408,plain,
% 0.62/0.69 ((~hskp8) | (~c2_1(a830))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.62/0.69 tff(409,plain,
% 0.62/0.69 ((~hskp8) | (~c2_1(a830))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[408, 405])).
% 0.62/0.69 tff(410,plain,
% 0.62/0.69 (~c2_1(a830)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[409, 404])).
% 0.62/0.69 tff(411,plain,
% 0.62/0.69 (((~hskp8) | (~c0_1(a830))) <=> ((~hskp8) | (~c0_1(a830)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(412,plain,
% 0.62/0.69 (((~c0_1(a830)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a830)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(413,axiom,((~c0_1(a830)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.62/0.69 tff(414,plain,
% 0.62/0.69 ((~hskp8) | (~c0_1(a830))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.62/0.69 tff(415,plain,
% 0.62/0.69 ((~hskp8) | (~c0_1(a830))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[414, 411])).
% 0.62/0.69 tff(416,plain,
% 0.62/0.69 (~c0_1(a830)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[415, 404])).
% 0.62/0.69 tff(417,plain,
% 0.62/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a842) | c0_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a830)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a842) | c0_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a830)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(418,plain,
% 0.62/0.69 (((~ndr1_0) | c2_1(a842) | (~c3_1(a842)) | (~c1_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830))) <=> (c2_1(a842) | c0_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a830)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(419,plain,
% 0.62/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c3_1(a842)) | (~c1_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a842) | c0_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a830)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842))))),
% 0.62/0.69 inference(monotonicity,[status(thm)],[418])).
% 0.62/0.69 tff(420,plain,
% 0.62/0.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c3_1(a842)) | (~c1_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a842) | c0_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a830)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.62/0.69 inference(transitivity,[status(thm)],[419, 417])).
% 0.62/0.69 tff(421,plain,
% 0.62/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c3_1(a842)) | (~c1_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830)))),
% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
% 0.62/0.69 tff(422,plain,
% 0.62/0.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a842) | c0_1(a830) | c2_1(a830) | (~ndr1_0) | (~c1_1(a830)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842))),
% 0.62/0.69 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.62/0.69 tff(423,plain,
% 0.62/0.69 (~c1_1(a830)),
% 0.62/0.69 inference(unit_resolution,[status(thm)],[422, 163, 107, 106, 98, 416, 410, 333, 323])).
% 0.62/0.69 tff(424,plain,
% 0.62/0.69 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(425,plain,
% 0.62/0.69 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[424])).
% 0.62/0.69 tff(426,plain,
% 0.62/0.69 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(427,plain,
% 0.62/0.69 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c0_1(V))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c0_1(V)))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c1_1(V) | c0_1(V))), (((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c1_1(V) | c0_1(V)))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.62/0.70 inference(bind,[status(th)],[])).
% 0.62/0.70 tff(428,plain,
% 0.62/0.70 (![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_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) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.70 inference(quant_intro,[status(thm)],[427])).
% 0.62/0.70 tff(429,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 0.62/0.70 tff(430,plain,
% 0.62/0.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.62/0.70 tff(431,plain,
% 0.62/0.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[430, 426])).
% 0.62/0.70 tff(432,plain,(
% 0.62/0.70 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.70 inference(skolemize,[status(sab)],[431])).
% 0.62/0.70 tff(433,plain,
% 0.62/0.70 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[432, 425])).
% 0.62/0.70 tff(434,plain,
% 0.62/0.70 (((~hskp8) | (~c3_1(a830))) <=> ((~hskp8) | (~c3_1(a830)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(435,plain,
% 0.62/0.70 (((~c3_1(a830)) | (~hskp8)) <=> ((~hskp8) | (~c3_1(a830)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(436,axiom,((~c3_1(a830)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 0.62/0.70 tff(437,plain,
% 0.62/0.70 ((~hskp8) | (~c3_1(a830))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.62/0.70 tff(438,plain,
% 0.62/0.70 ((~hskp8) | (~c3_1(a830))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[437, 434])).
% 0.62/0.70 tff(439,plain,
% 0.62/0.70 (~c3_1(a830)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[438, 404])).
% 0.62/0.70 tff(440,plain,
% 0.62/0.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(441,plain,
% 0.62/0.70 ((hskp0 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c1_1(a830) | c2_1(a830) | c1_1(a830) | c0_1(a830)) <=> (hskp0 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(442,plain,
% 0.62/0.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c1_1(a830) | c2_1(a830) | c1_1(a830) | c0_1(a830))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830)))),
% 0.62/0.70 inference(monotonicity,[status(thm)],[441])).
% 0.62/0.70 tff(443,plain,
% 0.62/0.70 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c1_1(a830) | c2_1(a830) | c1_1(a830) | c0_1(a830))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830))),
% 0.62/0.70 inference(transitivity,[status(thm)],[442, 440])).
% 0.62/0.70 tff(444,plain,
% 0.62/0.70 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c1_1(a830) | c2_1(a830) | c1_1(a830) | c0_1(a830))),
% 0.62/0.70 inference(quant_inst,[status(thm)],[])).
% 0.62/0.70 tff(445,plain,
% 0.62/0.70 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.62/0.70 tff(446,plain,
% 0.62/0.70 (hskp0),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[445, 163, 416, 410, 439, 433, 423])).
% 0.62/0.70 tff(447,plain,
% 0.62/0.70 (((~hskp0) | (~c3_1(a815))) <=> ((~hskp0) | (~c3_1(a815)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(448,plain,
% 0.62/0.70 (((~c3_1(a815)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a815)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(449,axiom,((~c3_1(a815)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.62/0.70 tff(450,plain,
% 0.62/0.70 ((~hskp0) | (~c3_1(a815))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.62/0.70 tff(451,plain,
% 0.62/0.70 ((~hskp0) | (~c3_1(a815))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[450, 447])).
% 0.62/0.70 tff(452,plain,
% 0.62/0.70 (~c3_1(a815)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[451, 446])).
% 0.62/0.70 tff(453,plain,
% 0.62/0.70 (((~hskp0) | c1_1(a815)) <=> ((~hskp0) | c1_1(a815))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(454,axiom,((~hskp0) | c1_1(a815)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.62/0.70 tff(455,plain,
% 0.62/0.70 ((~hskp0) | c1_1(a815)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.62/0.70 tff(456,plain,
% 0.62/0.70 ((~hskp0) | c1_1(a815)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[455, 453])).
% 0.62/0.70 tff(457,plain,
% 0.62/0.70 ((~hskp0) | c1_1(a815)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[456, 453])).
% 0.62/0.70 tff(458,plain,
% 0.62/0.70 ((~hskp0) | c1_1(a815)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[457, 453])).
% 0.62/0.70 tff(459,plain,
% 0.62/0.70 ((~hskp0) | c1_1(a815)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[458, 453])).
% 0.62/0.70 tff(460,plain,
% 0.62/0.70 ((~hskp0) | c1_1(a815)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[459, 453])).
% 0.62/0.70 tff(461,plain,
% 0.62/0.70 ((~hskp0) | c1_1(a815)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[460, 453])).
% 0.62/0.70 tff(462,plain,
% 0.62/0.70 ((~hskp0) | c1_1(a815)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[461, 453])).
% 0.62/0.70 tff(463,plain,
% 0.62/0.70 (c1_1(a815)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[462, 446])).
% 0.62/0.70 tff(464,plain,
% 0.62/0.70 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c1_1(a815)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c1_1(a815)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(465,plain,
% 0.62/0.70 ((hskp22 | hskp1 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c1_1(a815))) <=> (hskp22 | hskp1 | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c1_1(a815)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(466,plain,
% 0.62/0.70 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c1_1(a815)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c1_1(a815))))),
% 0.62/0.70 inference(monotonicity,[status(thm)],[465])).
% 0.62/0.70 tff(467,plain,
% 0.62/0.70 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c1_1(a815)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c1_1(a815)))),
% 0.62/0.70 inference(transitivity,[status(thm)],[466, 464])).
% 0.62/0.70 tff(468,plain,
% 0.62/0.70 ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c1_1(a815)))),
% 0.62/0.70 inference(quant_inst,[status(thm)],[])).
% 0.62/0.70 tff(469,plain,
% 0.62/0.70 ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c1_1(a815))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.62/0.70 tff(470,plain,
% 0.62/0.70 (c2_1(a815)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[469, 163, 13, 24, 463, 452, 23])).
% 0.62/0.70 tff(471,plain,
% 0.62/0.70 (^[U: $i] : refl((hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))),
% 0.62/0.70 inference(bind,[status(th)],[])).
% 0.62/0.70 tff(472,plain,
% 0.62/0.70 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.62/0.70 inference(quant_intro,[status(thm)],[471])).
% 0.62/0.70 tff(473,plain,
% 0.62/0.70 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(474,plain,
% 0.62/0.70 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp4) <=> ((hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp4))), rewrite(((hskp7 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U)) | hskp4) <=> (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp4) <=> (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))))),
% 0.62/0.70 inference(bind,[status(th)],[])).
% 0.62/0.70 tff(475,plain,
% 0.62/0.70 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp4) <=> ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.62/0.70 inference(quant_intro,[status(thm)],[474])).
% 0.62/0.70 tff(476,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp7) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.62/0.70 tff(477,plain,
% 0.62/0.70 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.62/0.70 tff(478,plain,
% 0.62/0.70 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[477, 473])).
% 0.62/0.70 tff(479,plain,(
% 0.62/0.70 ![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.62/0.70 inference(skolemize,[status(sab)],[478])).
% 0.62/0.70 tff(480,plain,
% 0.62/0.70 (![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[479, 472])).
% 0.62/0.70 tff(481,plain,
% 0.62/0.70 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(482,plain,
% 0.62/0.70 ((hskp7 | hskp4 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c0_1(a830)) <=> (hskp7 | hskp4 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(483,plain,
% 0.62/0.70 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c0_1(a830))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0)))),
% 0.62/0.70 inference(monotonicity,[status(thm)],[482])).
% 0.62/0.70 tff(484,plain,
% 0.62/0.70 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c0_1(a830))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0))),
% 0.62/0.70 inference(transitivity,[status(thm)],[483, 481])).
% 0.62/0.70 tff(485,plain,
% 0.62/0.70 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a830) | c2_1(a830) | c0_1(a830))),
% 0.62/0.70 inference(quant_inst,[status(thm)],[])).
% 0.62/0.70 tff(486,plain,
% 0.62/0.70 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a830) | c2_1(a830) | c3_1(a830) | (~ndr1_0)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[485, 484])).
% 0.62/0.70 tff(487,plain,
% 0.62/0.70 (hskp4),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[486, 163, 12, 416, 410, 439, 480])).
% 0.62/0.70 tff(488,plain,
% 0.62/0.70 (((~hskp4) | (~c1_1(a821))) <=> ((~hskp4) | (~c1_1(a821)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(489,plain,
% 0.62/0.70 (((~c1_1(a821)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a821)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(490,axiom,((~c1_1(a821)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.62/0.70 tff(491,plain,
% 0.62/0.70 ((~hskp4) | (~c1_1(a821))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.62/0.70 tff(492,plain,
% 0.62/0.70 ((~hskp4) | (~c1_1(a821))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[491, 488])).
% 0.62/0.70 tff(493,plain,
% 0.62/0.70 (~c1_1(a821)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[492, 487])).
% 0.62/0.70 tff(494,plain,
% 0.62/0.70 (((~hskp4) | (~c0_1(a821))) <=> ((~hskp4) | (~c0_1(a821)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(495,plain,
% 0.62/0.70 (((~c0_1(a821)) | (~hskp4)) <=> ((~hskp4) | (~c0_1(a821)))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(496,axiom,((~c0_1(a821)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.62/0.70 tff(497,plain,
% 0.62/0.70 ((~hskp4) | (~c0_1(a821))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.62/0.70 tff(498,plain,
% 0.62/0.70 ((~hskp4) | (~c0_1(a821))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[497, 494])).
% 0.62/0.70 tff(499,plain,
% 0.62/0.70 (~c0_1(a821)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[498, 487])).
% 0.62/0.70 tff(500,plain,
% 0.62/0.70 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a830) | c3_1(a830) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c1_1(a830))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a830) | c3_1(a830) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c1_1(a830))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(501,plain,
% 0.62/0.70 (((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a830) | c0_1(a830) | c3_1(a830)) <=> (c0_1(a830) | c3_1(a830) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c1_1(a830))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(502,plain,
% 0.62/0.70 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a830) | c0_1(a830) | c3_1(a830))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a830) | c3_1(a830) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c1_1(a830)))),
% 0.62/0.70 inference(monotonicity,[status(thm)],[501])).
% 0.62/0.70 tff(503,plain,
% 0.62/0.70 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a830) | c0_1(a830) | c3_1(a830))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a830) | c3_1(a830) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c1_1(a830))),
% 0.62/0.70 inference(transitivity,[status(thm)],[502, 500])).
% 0.62/0.70 tff(504,plain,
% 0.62/0.70 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a830) | c0_1(a830) | c3_1(a830))),
% 0.62/0.70 inference(quant_inst,[status(thm)],[])).
% 0.62/0.70 tff(505,plain,
% 0.62/0.70 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a830) | c3_1(a830) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c1_1(a830)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.62/0.70 tff(506,plain,
% 0.62/0.70 (~c3_1(a821)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[505, 163, 416, 439, 499, 493, 205, 423])).
% 0.62/0.70 tff(507,plain,
% 0.62/0.70 (^[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) | c1_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) | c1_1(W)))),
% 0.62/0.70 inference(bind,[status(th)],[])).
% 0.62/0.70 tff(508,plain,
% 0.62/0.70 (![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) | c1_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) | c1_1(W))),
% 0.62/0.70 inference(quant_intro,[status(thm)],[507])).
% 0.62/0.70 tff(509,plain,
% 0.62/0.70 (![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) | c1_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) | c1_1(W))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(510,plain,
% 0.62/0.70 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W)) | c3_1(V)) <=> ((~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) | c1_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ((~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) | c1_1(W))))),
% 0.62/0.70 inference(bind,[status(th)],[])).
% 0.62/0.70 tff(511,plain,
% 0.62/0.70 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ![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) | c1_1(W))),
% 0.62/0.70 inference(quant_intro,[status(thm)],[510])).
% 0.62/0.70 tff(512,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.62/0.70 tff(513,plain,
% 0.62/0.70 (![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) | c1_1(W))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.62/0.70 tff(514,plain,
% 0.62/0.70 (![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) | c1_1(W))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[513, 509])).
% 0.62/0.70 tff(515,plain,(
% 0.62/0.70 ![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) | c1_1(W))),
% 0.62/0.70 inference(skolemize,[status(sab)],[514])).
% 0.62/0.70 tff(516,plain,
% 0.62/0.70 (![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) | c1_1(W))),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[515, 508])).
% 0.62/0.70 tff(517,plain,
% 0.62/0.70 (((~hskp4) | c2_1(a821)) <=> ((~hskp4) | c2_1(a821))),
% 0.62/0.70 inference(rewrite,[status(thm)],[])).
% 0.62/0.70 tff(518,axiom,((~hskp4) | c2_1(a821)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.62/0.70 tff(519,plain,
% 0.62/0.70 ((~hskp4) | c2_1(a821)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.62/0.70 tff(520,plain,
% 0.62/0.70 ((~hskp4) | c2_1(a821)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[519, 517])).
% 0.62/0.70 tff(521,plain,
% 0.62/0.70 ((~hskp4) | c2_1(a821)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[520, 517])).
% 0.62/0.70 tff(522,plain,
% 0.62/0.70 ((~hskp4) | c2_1(a821)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[521, 517])).
% 0.62/0.70 tff(523,plain,
% 0.62/0.70 ((~hskp4) | c2_1(a821)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[522, 517])).
% 0.62/0.70 tff(524,plain,
% 0.62/0.70 ((~hskp4) | c2_1(a821)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[523, 517])).
% 0.62/0.70 tff(525,plain,
% 0.62/0.70 ((~hskp4) | c2_1(a821)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[524, 517])).
% 0.62/0.70 tff(526,plain,
% 0.62/0.70 ((~hskp4) | c2_1(a821)),
% 0.62/0.70 inference(modus_ponens,[status(thm)],[525, 517])).
% 0.62/0.70 tff(527,plain,
% 0.62/0.70 (c2_1(a821)),
% 0.62/0.70 inference(unit_resolution,[status(thm)],[526, 487])).
% 0.62/0.70 tff(528,plain,
% 0.62/0.70 (((~![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) | c1_1(W))) | (c2_1(a830) | c3_1(a830) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c1_1(a830))) <=> ((~![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) | c1_1(W))) | c2_1(a830) | c3_1(a830) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c1_1(a830))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(529,plain,
% 0.70/0.71 (((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a830) | c2_1(a830) | c1_1(a830)) <=> (c2_1(a830) | c3_1(a830) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c1_1(a830))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(530,plain,
% 0.70/0.71 (((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a830) | c2_1(a830) | c1_1(a830))) <=> ((~![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) | c1_1(W))) | (c2_1(a830) | c3_1(a830) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c1_1(a830)))),
% 0.70/0.71 inference(monotonicity,[status(thm)],[529])).
% 0.70/0.71 tff(531,plain,
% 0.70/0.71 (((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a830) | c2_1(a830) | c1_1(a830))) <=> ((~![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) | c1_1(W))) | c2_1(a830) | c3_1(a830) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c1_1(a830))),
% 0.70/0.71 inference(transitivity,[status(thm)],[530, 528])).
% 0.70/0.71 tff(532,plain,
% 0.70/0.71 ((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a830) | c2_1(a830) | c1_1(a830))),
% 0.70/0.71 inference(quant_inst,[status(thm)],[])).
% 0.70/0.71 tff(533,plain,
% 0.70/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a830) | c3_1(a830) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c1_1(a830)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[532, 531])).
% 0.70/0.71 tff(534,plain,
% 0.70/0.71 ($false),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[533, 163, 527, 463, 410, 439, 499, 452, 516, 423, 506, 470])).
% 0.70/0.71 tff(535,plain,(hskp1 | hskp22 | (~c0_1(a842)) | (~c1_1(a842)) | c2_1(a842) | hskp7 | (~c0_1(a833)) | (~c1_1(a833)) | (~c3_1(a833))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.71 tff(536,plain,
% 0.70/0.71 (hskp1),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[535, 77, 13, 66, 55, 12, 315, 304, 293])).
% 0.70/0.71 tff(537,plain,
% 0.70/0.71 (((~hskp1) | (~c2_1(a816))) <=> ((~hskp1) | (~c2_1(a816)))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(538,plain,
% 0.70/0.71 (((~c2_1(a816)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a816)))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(539,axiom,((~c2_1(a816)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 0.70/0.71 tff(540,plain,
% 0.70/0.71 ((~hskp1) | (~c2_1(a816))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[539, 538])).
% 0.70/0.71 tff(541,plain,
% 0.70/0.71 ((~hskp1) | (~c2_1(a816))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[540, 537])).
% 0.70/0.71 tff(542,plain,
% 0.70/0.71 (~c2_1(a816)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[541, 536])).
% 0.70/0.71 tff(543,plain,
% 0.70/0.71 (((~hskp1) | c3_1(a816)) <=> ((~hskp1) | c3_1(a816))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(544,axiom,((~hskp1) | c3_1(a816)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.70/0.71 tff(545,plain,
% 0.70/0.71 ((~hskp1) | c3_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[544, 543])).
% 0.70/0.71 tff(546,plain,
% 0.70/0.71 ((~hskp1) | c3_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[545, 543])).
% 0.70/0.71 tff(547,plain,
% 0.70/0.71 ((~hskp1) | c3_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[546, 543])).
% 0.70/0.71 tff(548,plain,
% 0.70/0.71 ((~hskp1) | c3_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[547, 543])).
% 0.70/0.71 tff(549,plain,
% 0.70/0.71 ((~hskp1) | c3_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[548, 543])).
% 0.70/0.71 tff(550,plain,
% 0.70/0.71 ((~hskp1) | c3_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[549, 543])).
% 0.70/0.71 tff(551,plain,
% 0.70/0.71 ((~hskp1) | c3_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[550, 543])).
% 0.70/0.71 tff(552,plain,
% 0.70/0.71 ((~hskp1) | c3_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[551, 543])).
% 0.70/0.71 tff(553,plain,
% 0.70/0.71 (c3_1(a816)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[552, 536])).
% 0.70/0.71 tff(554,plain,
% 0.70/0.71 (((~hskp1) | c0_1(a816)) <=> ((~hskp1) | c0_1(a816))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(555,axiom,((~hskp1) | c0_1(a816)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.70/0.71 tff(556,plain,
% 0.70/0.71 ((~hskp1) | c0_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[555, 554])).
% 0.70/0.71 tff(557,plain,
% 0.70/0.71 ((~hskp1) | c0_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[556, 554])).
% 0.70/0.71 tff(558,plain,
% 0.70/0.71 ((~hskp1) | c0_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[557, 554])).
% 0.70/0.71 tff(559,plain,
% 0.70/0.71 ((~hskp1) | c0_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[558, 554])).
% 0.70/0.71 tff(560,plain,
% 0.70/0.71 ((~hskp1) | c0_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[559, 554])).
% 0.70/0.71 tff(561,plain,
% 0.70/0.71 ((~hskp1) | c0_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[560, 554])).
% 0.70/0.71 tff(562,plain,
% 0.70/0.71 ((~hskp1) | c0_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[561, 554])).
% 0.70/0.71 tff(563,plain,
% 0.70/0.71 ((~hskp1) | c0_1(a816)),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[562, 554])).
% 0.70/0.71 tff(564,plain,
% 0.70/0.71 (c0_1(a816)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[563, 536])).
% 0.70/0.71 tff(565,plain,
% 0.70/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(566,plain,
% 0.70/0.71 (((~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816))) <=> (c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(567,plain,
% 0.70/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816))))),
% 0.70/0.71 inference(monotonicity,[status(thm)],[566])).
% 0.70/0.71 tff(568,plain,
% 0.70/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))),
% 0.70/0.71 inference(transitivity,[status(thm)],[567, 565])).
% 0.70/0.71 tff(569,plain,
% 0.70/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816)))),
% 0.70/0.71 inference(quant_inst,[status(thm)],[])).
% 0.70/0.71 tff(570,plain,
% 0.70/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[569, 568])).
% 0.70/0.71 tff(571,plain,
% 0.70/0.71 (c1_1(a816)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[570, 163, 315, 304, 293, 564, 553, 542, 44])).
% 0.70/0.71 tff(572,plain,
% 0.70/0.71 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | (~c0_1(a816)))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(573,plain,
% 0.70/0.71 ((hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816))) <=> (hskp29 | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | (~c0_1(a816)))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(574,plain,
% 0.70/0.71 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | (~c0_1(a816))))),
% 0.70/0.71 inference(monotonicity,[status(thm)],[573])).
% 0.70/0.71 tff(575,plain,
% 0.70/0.71 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | (~c0_1(a816)))),
% 0.70/0.71 inference(transitivity,[status(thm)],[574, 572])).
% 0.70/0.71 tff(576,plain,
% 0.70/0.71 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))),
% 0.70/0.71 inference(quant_inst,[status(thm)],[])).
% 0.70/0.71 tff(577,plain,
% 0.70/0.71 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a816) | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a816)) | (~c0_1(a816))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[576, 575])).
% 0.70/0.71 tff(578,plain,
% 0.70/0.71 (hskp29),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[577, 163, 315, 304, 293, 564, 553, 542, 353])).
% 0.70/0.71 tff(579,plain,
% 0.70/0.71 (c3_1(a865)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[374, 578])).
% 0.70/0.71 tff(580,plain,
% 0.70/0.71 (c2_1(a865)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[385, 578])).
% 0.70/0.71 tff(581,plain,
% 0.70/0.71 (c1_1(a865)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[396, 578])).
% 0.70/0.71 tff(582,plain,
% 0.70/0.71 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(583,plain,
% 0.70/0.71 ((hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833))) <=> (hskp8 | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(584,plain,
% 0.70/0.71 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865))))),
% 0.70/0.71 inference(monotonicity,[status(thm)],[583])).
% 0.70/0.71 tff(585,plain,
% 0.70/0.71 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))),
% 0.70/0.71 inference(transitivity,[status(thm)],[584, 582])).
% 0.70/0.71 tff(586,plain,
% 0.70/0.71 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c0_1(a833)))),
% 0.70/0.71 inference(quant_inst,[status(thm)],[])).
% 0.70/0.71 tff(587,plain,
% 0.70/0.71 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c0_1(a833)) | (~c3_1(a833)) | (~c1_1(a833)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.70/0.71 tff(588,plain,
% 0.70/0.71 (hskp8),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[587, 163, 581, 580, 579, 315, 304, 293, 343])).
% 0.70/0.71 tff(589,plain,
% 0.70/0.71 (~c2_1(a830)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[409, 588])).
% 0.70/0.71 tff(590,plain,
% 0.70/0.71 (~c0_1(a830)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[415, 588])).
% 0.70/0.71 tff(591,plain,
% 0.70/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a830) | c2_1(a830) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c1_1(a830)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a830) | c2_1(a830) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c1_1(a830)))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(592,plain,
% 0.70/0.71 (((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830))) <=> (c0_1(a830) | c2_1(a830) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c1_1(a830)))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(593,plain,
% 0.70/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a830) | c2_1(a830) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c1_1(a830))))),
% 0.70/0.71 inference(monotonicity,[status(thm)],[592])).
% 0.70/0.71 tff(594,plain,
% 0.70/0.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a830) | c2_1(a830) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c1_1(a830)))),
% 0.70/0.71 inference(transitivity,[status(thm)],[593, 591])).
% 0.70/0.71 tff(595,plain,
% 0.70/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a830) | c0_1(a830) | (~c1_1(a830)))),
% 0.70/0.71 inference(quant_inst,[status(thm)],[])).
% 0.70/0.71 tff(596,plain,
% 0.70/0.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a830) | c2_1(a830) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c1_1(a830))),
% 0.70/0.71 inference(modus_ponens,[status(thm)],[595, 594])).
% 0.70/0.71 tff(597,plain,
% 0.70/0.71 (~c1_1(a830)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[596, 163, 564, 553, 590, 589, 542, 333, 571])).
% 0.70/0.71 tff(598,plain,
% 0.70/0.71 (~c3_1(a830)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[438, 588])).
% 0.70/0.71 tff(599,plain,
% 0.70/0.71 (hskp0),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[445, 163, 590, 589, 598, 433, 597])).
% 0.70/0.71 tff(600,plain,
% 0.70/0.71 (~c3_1(a815)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[451, 599])).
% 0.70/0.71 tff(601,plain,
% 0.70/0.71 (hskp4),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[486, 163, 12, 590, 589, 598, 480])).
% 0.70/0.71 tff(602,plain,
% 0.70/0.71 (~c1_1(a821)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[492, 601])).
% 0.70/0.71 tff(603,plain,
% 0.70/0.71 (~c0_1(a821)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[498, 601])).
% 0.70/0.71 tff(604,plain,
% 0.70/0.71 (~c3_1(a821)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[505, 163, 590, 598, 603, 602, 205, 597])).
% 0.70/0.71 tff(605,plain,
% 0.70/0.71 (c1_1(a815)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[462, 599])).
% 0.70/0.71 tff(606,plain,
% 0.70/0.71 (c2_1(a821)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[526, 601])).
% 0.70/0.71 tff(607,plain,
% 0.70/0.71 (~c2_1(a815)),
% 0.70/0.71 inference(unit_resolution,[status(thm)],[533, 163, 606, 605, 589, 598, 603, 600, 516, 597, 604])).
% 0.70/0.71 tff(608,plain,
% 0.70/0.71 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))),
% 0.70/0.71 inference(bind,[status(th)],[])).
% 0.70/0.71 tff(609,plain,
% 0.70/0.71 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.70/0.71 inference(quant_intro,[status(thm)],[608])).
% 0.70/0.71 tff(610,plain,
% 0.70/0.71 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.70/0.71 inference(rewrite,[status(thm)],[])).
% 0.70/0.71 tff(611,plain,
% 0.70/0.71 (^[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(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))))),
% 0.70/0.72 inference(bind,[status(th)],[])).
% 0.70/0.72 tff(612,plain,
% 0.70/0.72 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.70/0.72 inference(quant_intro,[status(thm)],[611])).
% 0.70/0.72 tff(613,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.70/0.72 tff(614,plain,
% 0.70/0.72 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.70/0.72 tff(615,plain,
% 0.70/0.72 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[614, 610])).
% 0.70/0.72 tff(616,plain,(
% 0.70/0.72 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.70/0.72 inference(skolemize,[status(sab)],[615])).
% 0.70/0.72 tff(617,plain,
% 0.70/0.72 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[616, 609])).
% 0.70/0.72 tff(618,plain,
% 0.70/0.72 (((~hskp0) | c0_1(a815)) <=> ((~hskp0) | c0_1(a815))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(619,axiom,((~hskp0) | c0_1(a815)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.70/0.72 tff(620,plain,
% 0.70/0.72 ((~hskp0) | c0_1(a815)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.70/0.72 tff(621,plain,
% 0.70/0.72 ((~hskp0) | c0_1(a815)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[620, 618])).
% 0.70/0.72 tff(622,plain,
% 0.70/0.72 ((~hskp0) | c0_1(a815)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[621, 618])).
% 0.70/0.72 tff(623,plain,
% 0.70/0.72 ((~hskp0) | c0_1(a815)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[622, 618])).
% 0.70/0.72 tff(624,plain,
% 0.70/0.72 ((~hskp0) | c0_1(a815)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[623, 618])).
% 0.70/0.72 tff(625,plain,
% 0.70/0.72 ((~hskp0) | c0_1(a815)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[624, 618])).
% 0.70/0.72 tff(626,plain,
% 0.70/0.72 ((~hskp0) | c0_1(a815)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[625, 618])).
% 0.70/0.72 tff(627,plain,
% 0.70/0.72 ((~hskp0) | c0_1(a815)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[626, 618])).
% 0.70/0.72 tff(628,plain,
% 0.70/0.72 (c0_1(a815)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[627, 599])).
% 0.70/0.72 tff(629,plain,
% 0.70/0.72 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a830) | c2_1(a830) | c3_1(a830) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a830) | c2_1(a830) | c3_1(a830) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(630,plain,
% 0.70/0.72 ((hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a830) | c0_1(a830) | c3_1(a830)) <=> (hskp5 | c0_1(a830) | c2_1(a830) | c3_1(a830) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(631,plain,
% 0.70/0.72 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a830) | c0_1(a830) | c3_1(a830))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a830) | c2_1(a830) | c3_1(a830) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815))))),
% 0.70/0.72 inference(monotonicity,[status(thm)],[630])).
% 0.70/0.72 tff(632,plain,
% 0.70/0.72 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a830) | c0_1(a830) | c3_1(a830))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a830) | c2_1(a830) | c3_1(a830) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)))),
% 0.70/0.72 inference(transitivity,[status(thm)],[631, 629])).
% 0.70/0.72 tff(633,plain,
% 0.70/0.72 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a830) | c0_1(a830) | c3_1(a830))),
% 0.70/0.72 inference(quant_inst,[status(thm)],[])).
% 0.70/0.72 tff(634,plain,
% 0.70/0.72 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a830) | c2_1(a830) | c3_1(a830) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[633, 632])).
% 0.70/0.72 tff(635,plain,
% 0.70/0.72 (hskp5),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[634, 163, 628, 590, 589, 598, 600, 617, 607])).
% 0.70/0.72 tff(636,plain,
% 0.70/0.72 (((~hskp5) | (~c0_1(a825))) <=> ((~hskp5) | (~c0_1(a825)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(637,plain,
% 0.70/0.72 (((~c0_1(a825)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a825)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(638,axiom,((~c0_1(a825)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.70/0.72 tff(639,plain,
% 0.70/0.72 ((~hskp5) | (~c0_1(a825))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[638, 637])).
% 0.70/0.72 tff(640,plain,
% 0.70/0.72 ((~hskp5) | (~c0_1(a825))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[639, 636])).
% 0.70/0.72 tff(641,plain,
% 0.70/0.72 (~c0_1(a825)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[640, 635])).
% 0.70/0.72 tff(642,plain,
% 0.70/0.72 (((~hskp5) | c3_1(a825)) <=> ((~hskp5) | c3_1(a825))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(643,axiom,((~hskp5) | c3_1(a825)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.70/0.72 tff(644,plain,
% 0.70/0.72 ((~hskp5) | c3_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[643, 642])).
% 0.70/0.72 tff(645,plain,
% 0.70/0.72 ((~hskp5) | c3_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[644, 642])).
% 0.70/0.72 tff(646,plain,
% 0.70/0.72 ((~hskp5) | c3_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[645, 642])).
% 0.70/0.72 tff(647,plain,
% 0.70/0.72 ((~hskp5) | c3_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[646, 642])).
% 0.70/0.72 tff(648,plain,
% 0.70/0.72 ((~hskp5) | c3_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[647, 642])).
% 0.70/0.72 tff(649,plain,
% 0.70/0.72 ((~hskp5) | c3_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[648, 642])).
% 0.70/0.72 tff(650,plain,
% 0.70/0.72 ((~hskp5) | c3_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[649, 642])).
% 0.70/0.72 tff(651,plain,
% 0.70/0.72 ((~hskp5) | c3_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[650, 642])).
% 0.70/0.72 tff(652,plain,
% 0.70/0.72 (c3_1(a825)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[651, 635])).
% 0.70/0.72 tff(653,plain,
% 0.70/0.72 (((~hskp5) | c1_1(a825)) <=> ((~hskp5) | c1_1(a825))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(654,axiom,((~hskp5) | c1_1(a825)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.70/0.72 tff(655,plain,
% 0.70/0.72 ((~hskp5) | c1_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.70/0.72 tff(656,plain,
% 0.70/0.72 ((~hskp5) | c1_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[655, 653])).
% 0.70/0.72 tff(657,plain,
% 0.70/0.72 ((~hskp5) | c1_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[656, 653])).
% 0.70/0.72 tff(658,plain,
% 0.70/0.72 ((~hskp5) | c1_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[657, 653])).
% 0.70/0.72 tff(659,plain,
% 0.70/0.72 ((~hskp5) | c1_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[658, 653])).
% 0.70/0.72 tff(660,plain,
% 0.70/0.72 ((~hskp5) | c1_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[659, 653])).
% 0.70/0.72 tff(661,plain,
% 0.70/0.72 ((~hskp5) | c1_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[660, 653])).
% 0.70/0.72 tff(662,plain,
% 0.70/0.72 ((~hskp5) | c1_1(a825)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[661, 653])).
% 0.70/0.72 tff(663,plain,
% 0.70/0.72 (c1_1(a825)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[662, 635])).
% 0.70/0.72 tff(664,plain,
% 0.70/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a825) | c0_1(a821) | c1_1(a821) | c3_1(a815) | (~ndr1_0) | (~c1_1(a815)) | (~c0_1(a815)) | (~c2_1(a821)) | (~c3_1(a825)) | (~c1_1(a825)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a825) | c0_1(a821) | c1_1(a821) | c3_1(a815) | (~ndr1_0) | (~c1_1(a815)) | (~c0_1(a815)) | (~c2_1(a821)) | (~c3_1(a825)) | (~c1_1(a825)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(665,plain,
% 0.70/0.72 (((~ndr1_0) | c3_1(a815) | (~c1_1(a815)) | (~c0_1(a815)) | c0_1(a825) | (~c3_1(a825)) | (~c1_1(a825)) | c1_1(a821) | c0_1(a821) | (~c2_1(a821))) <=> (c0_1(a825) | c0_1(a821) | c1_1(a821) | c3_1(a815) | (~ndr1_0) | (~c1_1(a815)) | (~c0_1(a815)) | (~c2_1(a821)) | (~c3_1(a825)) | (~c1_1(a825)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(666,plain,
% 0.70/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a815) | (~c1_1(a815)) | (~c0_1(a815)) | c0_1(a825) | (~c3_1(a825)) | (~c1_1(a825)) | c1_1(a821) | c0_1(a821) | (~c2_1(a821)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a825) | c0_1(a821) | c1_1(a821) | c3_1(a815) | (~ndr1_0) | (~c1_1(a815)) | (~c0_1(a815)) | (~c2_1(a821)) | (~c3_1(a825)) | (~c1_1(a825))))),
% 0.70/0.72 inference(monotonicity,[status(thm)],[665])).
% 0.70/0.72 tff(667,plain,
% 0.70/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a815) | (~c1_1(a815)) | (~c0_1(a815)) | c0_1(a825) | (~c3_1(a825)) | (~c1_1(a825)) | c1_1(a821) | c0_1(a821) | (~c2_1(a821)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a825) | c0_1(a821) | c1_1(a821) | c3_1(a815) | (~ndr1_0) | (~c1_1(a815)) | (~c0_1(a815)) | (~c2_1(a821)) | (~c3_1(a825)) | (~c1_1(a825)))),
% 0.70/0.72 inference(transitivity,[status(thm)],[666, 664])).
% 0.70/0.72 tff(668,plain,
% 0.70/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c3_1(a815) | (~c1_1(a815)) | (~c0_1(a815)) | c0_1(a825) | (~c3_1(a825)) | (~c1_1(a825)) | c1_1(a821) | c0_1(a821) | (~c2_1(a821)))),
% 0.70/0.72 inference(quant_inst,[status(thm)],[])).
% 0.70/0.72 tff(669,plain,
% 0.70/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a825) | c0_1(a821) | c1_1(a821) | c3_1(a815) | (~ndr1_0) | (~c1_1(a815)) | (~c0_1(a815)) | (~c2_1(a821)) | (~c3_1(a825)) | (~c1_1(a825))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[668, 667])).
% 0.70/0.72 tff(670,plain,
% 0.70/0.72 ($false),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[669, 163, 663, 652, 606, 628, 605, 641, 603, 602, 600, 34])).
% 0.70/0.72 tff(671,plain,(hskp24 | hskp7 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.70/0.72 tff(672,plain,
% 0.70/0.72 (hskp24),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[671, 13, 12])).
% 0.70/0.72 tff(673,plain,
% 0.70/0.72 (((~hskp24) | (~c3_1(a878))) <=> ((~hskp24) | (~c3_1(a878)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(674,plain,
% 0.70/0.72 (((~c3_1(a878)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a878)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(675,axiom,((~c3_1(a878)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.70/0.72 tff(676,plain,
% 0.70/0.72 ((~hskp24) | (~c3_1(a878))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[675, 674])).
% 0.70/0.72 tff(677,plain,
% 0.70/0.72 ((~hskp24) | (~c3_1(a878))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[676, 673])).
% 0.70/0.72 tff(678,plain,
% 0.70/0.72 (~c3_1(a878)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[677, 672])).
% 0.70/0.72 tff(679,plain,
% 0.70/0.72 (((~hskp24) | c1_1(a878)) <=> ((~hskp24) | c1_1(a878))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(680,axiom,((~hskp24) | c1_1(a878)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.70/0.72 tff(681,plain,
% 0.70/0.72 ((~hskp24) | c1_1(a878)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.70/0.72 tff(682,plain,
% 0.70/0.72 ((~hskp24) | c1_1(a878)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[681, 679])).
% 0.70/0.72 tff(683,plain,
% 0.70/0.72 ((~hskp24) | c1_1(a878)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[682, 679])).
% 0.70/0.72 tff(684,plain,
% 0.70/0.72 ((~hskp24) | c1_1(a878)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[683, 679])).
% 0.70/0.72 tff(685,plain,
% 0.70/0.72 ((~hskp24) | c1_1(a878)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[684, 679])).
% 0.70/0.72 tff(686,plain,
% 0.70/0.72 ((~hskp24) | c1_1(a878)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[685, 679])).
% 0.70/0.72 tff(687,plain,
% 0.70/0.72 ((~hskp24) | c1_1(a878)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[686, 679])).
% 0.70/0.72 tff(688,plain,
% 0.70/0.72 ((~hskp24) | c1_1(a878)),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[687, 679])).
% 0.70/0.72 tff(689,plain,
% 0.70/0.72 (c1_1(a878)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[688, 672])).
% 0.70/0.72 tff(690,plain,
% 0.70/0.72 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | c3_1(a878) | (~ndr1_0) | c2_1(a878) | (~c1_1(a878)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c3_1(a878) | (~ndr1_0) | c2_1(a878) | (~c1_1(a878)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(691,plain,
% 0.70/0.72 ((hskp22 | hskp1 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | (~c1_1(a878))) <=> (hskp22 | hskp1 | c3_1(a878) | (~ndr1_0) | c2_1(a878) | (~c1_1(a878)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(692,plain,
% 0.70/0.72 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | (~c1_1(a878)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | c3_1(a878) | (~ndr1_0) | c2_1(a878) | (~c1_1(a878))))),
% 0.70/0.72 inference(monotonicity,[status(thm)],[691])).
% 0.70/0.72 tff(693,plain,
% 0.70/0.72 (((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | (~c1_1(a878)))) <=> ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c3_1(a878) | (~ndr1_0) | c2_1(a878) | (~c1_1(a878)))),
% 0.70/0.72 inference(transitivity,[status(thm)],[692, 690])).
% 0.70/0.72 tff(694,plain,
% 0.70/0.72 ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp22 | hskp1 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | (~c1_1(a878)))),
% 0.70/0.72 inference(quant_inst,[status(thm)],[])).
% 0.70/0.72 tff(695,plain,
% 0.70/0.72 ((~![U: $i] : (hskp22 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp22 | hskp1 | c3_1(a878) | (~ndr1_0) | c2_1(a878) | (~c1_1(a878))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[694, 693])).
% 0.70/0.72 tff(696,plain,
% 0.70/0.72 (hskp1 | c2_1(a878)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[695, 163, 13, 689, 678, 23])).
% 0.70/0.72 tff(697,plain,
% 0.70/0.72 (c2_1(a878)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[696, 24])).
% 0.70/0.72 tff(698,plain,
% 0.70/0.72 (^[U: $i] : refl((hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.70/0.72 inference(bind,[status(th)],[])).
% 0.70/0.72 tff(699,plain,
% 0.70/0.72 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.72 inference(quant_intro,[status(thm)],[698])).
% 0.70/0.72 tff(700,plain,
% 0.70/0.72 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(701,plain,
% 0.70/0.72 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp7) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp7))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp7) <=> (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp7) <=> (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.70/0.72 inference(bind,[status(th)],[])).
% 0.70/0.72 tff(702,plain,
% 0.70/0.72 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp7) <=> ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.72 inference(quant_intro,[status(thm)],[701])).
% 0.70/0.72 tff(703,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 0.70/0.72 tff(704,plain,
% 0.70/0.72 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[703, 702])).
% 0.70/0.72 tff(705,plain,
% 0.70/0.72 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[704, 700])).
% 0.70/0.72 tff(706,plain,(
% 0.70/0.72 ![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.72 inference(skolemize,[status(sab)],[705])).
% 0.70/0.72 tff(707,plain,
% 0.70/0.72 (![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[706, 699])).
% 0.70/0.72 tff(708,plain,
% 0.70/0.72 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c3_1(a878) | (~ndr1_0) | (~c1_1(a878)) | (~c2_1(a878)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c3_1(a878) | (~ndr1_0) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(709,plain,
% 0.70/0.72 ((hskp14 | hskp7 | (~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878))) <=> (hskp14 | hskp7 | c3_1(a878) | (~ndr1_0) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(710,plain,
% 0.70/0.72 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c3_1(a878) | (~ndr1_0) | (~c1_1(a878)) | (~c2_1(a878))))),
% 0.70/0.72 inference(monotonicity,[status(thm)],[709])).
% 0.70/0.72 tff(711,plain,
% 0.70/0.72 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c3_1(a878) | (~ndr1_0) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.70/0.72 inference(transitivity,[status(thm)],[710, 708])).
% 0.70/0.72 tff(712,plain,
% 0.70/0.72 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)))),
% 0.70/0.72 inference(quant_inst,[status(thm)],[])).
% 0.70/0.72 tff(713,plain,
% 0.70/0.72 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c3_1(a878) | (~ndr1_0) | (~c1_1(a878)) | (~c2_1(a878))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[712, 711])).
% 0.70/0.72 tff(714,plain,
% 0.70/0.72 (hskp14 | (~c2_1(a878))),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[713, 163, 12, 689, 678, 707])).
% 0.70/0.72 tff(715,plain,
% 0.70/0.72 (hskp14),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[714, 697])).
% 0.70/0.72 tff(716,plain,
% 0.70/0.72 (~c2_1(a842)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[54, 715])).
% 0.70/0.72 tff(717,plain,
% 0.70/0.72 (c1_1(a842)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[65, 715])).
% 0.70/0.72 tff(718,plain,
% 0.70/0.72 (c3_1(a842)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[321, 163, 13, 24, 717, 716, 23])).
% 0.70/0.72 tff(719,plain,
% 0.70/0.72 (c0_1(a842)),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[76, 715])).
% 0.70/0.72 tff(720,plain,
% 0.70/0.72 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(721,plain,
% 0.70/0.72 ((hskp29 | (~ndr1_0) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842))) <=> (hskp29 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.70/0.72 inference(rewrite,[status(thm)],[])).
% 0.70/0.72 tff(722,plain,
% 0.70/0.72 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842))))),
% 0.70/0.72 inference(monotonicity,[status(thm)],[721])).
% 0.70/0.72 tff(723,plain,
% 0.70/0.72 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842)))),
% 0.70/0.72 inference(transitivity,[status(thm)],[722, 720])).
% 0.70/0.72 tff(724,plain,
% 0.70/0.72 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a842)) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a842) | (~c3_1(a842)) | (~c0_1(a842)))),
% 0.70/0.72 inference(quant_inst,[status(thm)],[])).
% 0.70/0.72 tff(725,plain,
% 0.70/0.72 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a842))),
% 0.70/0.72 inference(modus_ponens,[status(thm)],[724, 723])).
% 0.70/0.72 tff(726,plain,
% 0.70/0.72 (hskp29),
% 0.70/0.72 inference(unit_resolution,[status(thm)],[725, 163, 719, 717, 716, 353, 718])).
% 0.70/0.73 tff(727,plain,
% 0.70/0.73 (c3_1(a865)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[374, 726])).
% 0.70/0.73 tff(728,plain,
% 0.70/0.73 (c2_1(a865)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[385, 726])).
% 0.70/0.73 tff(729,plain,
% 0.70/0.73 (c1_1(a865)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[396, 726])).
% 0.70/0.73 tff(730,plain,
% 0.70/0.73 (hskp8),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[403, 163, 729, 728, 727, 719, 717, 343, 718])).
% 0.70/0.73 tff(731,plain,
% 0.70/0.73 (~c2_1(a830)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[409, 730])).
% 0.70/0.73 tff(732,plain,
% 0.70/0.73 (~c0_1(a830)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[415, 730])).
% 0.70/0.73 tff(733,plain,
% 0.70/0.73 (~c1_1(a830)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[422, 163, 719, 717, 716, 732, 731, 333, 718])).
% 0.70/0.73 tff(734,plain,
% 0.70/0.73 (~c3_1(a830)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[438, 730])).
% 0.70/0.73 tff(735,plain,
% 0.70/0.73 (((~hskp24) | (~c0_1(a878))) <=> ((~hskp24) | (~c0_1(a878)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(736,plain,
% 0.70/0.73 (((~c0_1(a878)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a878)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(737,axiom,((~c0_1(a878)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.70/0.73 tff(738,plain,
% 0.70/0.73 ((~hskp24) | (~c0_1(a878))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[737, 736])).
% 0.70/0.73 tff(739,plain,
% 0.70/0.73 ((~hskp24) | (~c0_1(a878))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[738, 735])).
% 0.70/0.73 tff(740,plain,
% 0.70/0.73 (~c0_1(a878)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[739, 672])).
% 0.70/0.73 tff(741,plain,
% 0.70/0.73 (((~![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) | c1_1(W))) | (c0_1(a878) | c3_1(a878) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830) | (~c1_1(a878)) | (~c2_1(a878)))) <=> ((~![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) | c1_1(W))) | c0_1(a878) | c3_1(a878) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(742,plain,
% 0.70/0.73 (((~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)) | c0_1(a878) | c3_1(a878) | (~c2_1(a878)) | c3_1(a830) | c2_1(a830) | c1_1(a830)) <=> (c0_1(a878) | c3_1(a878) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(743,plain,
% 0.70/0.73 (((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)) | c0_1(a878) | c3_1(a878) | (~c2_1(a878)) | c3_1(a830) | c2_1(a830) | c1_1(a830))) <=> ((~![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) | c1_1(W))) | (c0_1(a878) | c3_1(a878) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830) | (~c1_1(a878)) | (~c2_1(a878))))),
% 0.70/0.73 inference(monotonicity,[status(thm)],[742])).
% 0.70/0.73 tff(744,plain,
% 0.70/0.73 (((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)) | c0_1(a878) | c3_1(a878) | (~c2_1(a878)) | c3_1(a830) | c2_1(a830) | c1_1(a830))) <=> ((~![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) | c1_1(W))) | c0_1(a878) | c3_1(a878) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.70/0.73 inference(transitivity,[status(thm)],[743, 741])).
% 0.70/0.73 tff(745,plain,
% 0.70/0.73 ((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a878) | (~c2_1(a878)) | (~c1_1(a878)) | c0_1(a878) | c3_1(a878) | (~c2_1(a878)) | c3_1(a830) | c2_1(a830) | c1_1(a830))),
% 0.70/0.73 inference(quant_inst,[status(thm)],[])).
% 0.70/0.73 tff(746,plain,
% 0.70/0.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c0_1(a878) | c3_1(a878) | c2_1(a830) | c3_1(a830) | (~ndr1_0) | c1_1(a830) | (~c1_1(a878)) | (~c2_1(a878))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[745, 744])).
% 0.70/0.73 tff(747,plain,
% 0.70/0.73 ($false),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[746, 163, 689, 740, 678, 731, 734, 516, 697, 733])).
% 0.70/0.73 tff(748,plain,(hskp1 | hskp22 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.70/0.73 tff(749,plain,
% 0.70/0.73 (hskp1),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[748, 13, 12])).
% 0.70/0.73 tff(750,plain,
% 0.70/0.73 (c0_1(a816)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[563, 749])).
% 0.70/0.73 tff(751,plain,
% 0.70/0.73 (~c2_1(a816)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[541, 749])).
% 0.70/0.73 tff(752,plain,
% 0.70/0.73 (^[U: $i] : refl((hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(753,plain,
% 0.70/0.73 (![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[752])).
% 0.70/0.73 tff(754,plain,
% 0.70/0.73 (![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(755,plain,
% 0.70/0.73 (^[U: $i] : 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)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp14))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp22) <=> ((hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp22))), rewrite(((hskp14 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp22) <=> (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp22) <=> (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(756,plain,
% 0.70/0.73 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp22) <=> ![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[755])).
% 0.70/0.73 tff(757,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 0.70/0.73 tff(758,plain,
% 0.70/0.73 (![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[757, 756])).
% 0.70/0.73 tff(759,plain,
% 0.70/0.73 (![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[758, 754])).
% 0.70/0.73 tff(760,plain,(
% 0.70/0.73 ![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.70/0.73 inference(skolemize,[status(sab)],[759])).
% 0.70/0.73 tff(761,plain,
% 0.70/0.73 (![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[760, 753])).
% 0.70/0.73 tff(762,assumption,(~hskp14), introduced(assumption)).
% 0.70/0.73 tff(763,plain,
% 0.70/0.73 (~c2_1(a878)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[714, 762])).
% 0.70/0.73 tff(764,plain,
% 0.70/0.73 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | c0_1(a878) | c3_1(a878) | (~ndr1_0) | c2_1(a878))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a878) | c3_1(a878) | (~ndr1_0) | c2_1(a878))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(765,plain,
% 0.70/0.73 ((hskp7 | hskp4 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | c0_1(a878)) <=> (hskp7 | hskp4 | c0_1(a878) | c3_1(a878) | (~ndr1_0) | c2_1(a878))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(766,plain,
% 0.70/0.73 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | c0_1(a878))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | c0_1(a878) | c3_1(a878) | (~ndr1_0) | c2_1(a878)))),
% 0.70/0.73 inference(monotonicity,[status(thm)],[765])).
% 0.70/0.73 tff(767,plain,
% 0.70/0.73 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | c0_1(a878))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a878) | c3_1(a878) | (~ndr1_0) | c2_1(a878))),
% 0.70/0.73 inference(transitivity,[status(thm)],[766, 764])).
% 0.70/0.73 tff(768,plain,
% 0.70/0.73 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a878) | c2_1(a878) | c0_1(a878))),
% 0.70/0.73 inference(quant_inst,[status(thm)],[])).
% 0.70/0.73 tff(769,plain,
% 0.70/0.73 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a878) | c3_1(a878) | (~ndr1_0) | c2_1(a878)),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[768, 767])).
% 0.70/0.73 tff(770,plain,
% 0.70/0.73 (hskp4 | c2_1(a878)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[769, 163, 12, 740, 678, 480])).
% 0.70/0.73 tff(771,plain,
% 0.70/0.73 (hskp4),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[770, 763])).
% 0.70/0.73 tff(772,plain,
% 0.70/0.73 (~c1_1(a821)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[492, 771])).
% 0.70/0.73 tff(773,plain,
% 0.70/0.73 (c2_1(a821)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[526, 771])).
% 0.70/0.73 tff(774,plain,
% 0.70/0.73 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c2_1(a821)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c2_1(a821)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(775,plain,
% 0.70/0.73 ((hskp14 | hskp22 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821))) <=> (hskp14 | hskp22 | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c2_1(a821)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(776,plain,
% 0.70/0.73 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c2_1(a821))))),
% 0.70/0.73 inference(monotonicity,[status(thm)],[775])).
% 0.70/0.73 tff(777,plain,
% 0.70/0.73 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c2_1(a821)))),
% 0.70/0.73 inference(transitivity,[status(thm)],[776, 774])).
% 0.70/0.73 tff(778,plain,
% 0.70/0.73 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)))),
% 0.70/0.73 inference(quant_inst,[status(thm)],[])).
% 0.70/0.73 tff(779,plain,
% 0.70/0.73 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | (~c2_1(a821))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[778, 777])).
% 0.70/0.73 tff(780,plain,
% 0.70/0.73 (~c3_1(a821)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[779, 762, 163, 13, 773, 772, 761])).
% 0.70/0.73 tff(781,plain,
% 0.70/0.73 (~c0_1(a821)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[498, 771])).
% 0.70/0.73 tff(782,plain,
% 0.70/0.73 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(783,plain,
% 0.70/0.73 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[782])).
% 0.70/0.73 tff(784,plain,
% 0.70/0.73 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(785,plain,
% 0.70/0.73 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.70/0.73 inference(bind,[status(th)],[])).
% 0.70/0.73 tff(786,plain,
% 0.70/0.73 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.70/0.73 inference(quant_intro,[status(thm)],[785])).
% 0.70/0.73 tff(787,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 0.70/0.73 tff(788,plain,
% 0.70/0.73 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[787, 786])).
% 0.70/0.73 tff(789,plain,
% 0.70/0.73 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[788, 784])).
% 0.70/0.73 tff(790,plain,(
% 0.70/0.73 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.70/0.73 inference(skolemize,[status(sab)],[789])).
% 0.70/0.73 tff(791,plain,
% 0.70/0.73 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[790, 783])).
% 0.70/0.73 tff(792,plain,
% 0.70/0.73 (c3_1(a816)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[552, 749])).
% 0.70/0.73 tff(793,plain,
% 0.70/0.73 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(794,plain,
% 0.70/0.73 ((hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878))) <=> (hskp9 | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(795,plain,
% 0.70/0.73 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878))))),
% 0.70/0.73 inference(monotonicity,[status(thm)],[794])).
% 0.70/0.73 tff(796,plain,
% 0.70/0.73 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))),
% 0.70/0.73 inference(transitivity,[status(thm)],[795, 793])).
% 0.70/0.73 tff(797,plain,
% 0.70/0.73 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878)))),
% 0.70/0.73 inference(quant_inst,[status(thm)],[])).
% 0.70/0.73 tff(798,plain,
% 0.70/0.73 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp9 | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878))),
% 0.70/0.73 inference(modus_ponens,[status(thm)],[797, 796])).
% 0.70/0.73 tff(799,plain,
% 0.70/0.73 (hskp9),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[798, 163, 689, 750, 792, 740, 751, 791, 763])).
% 0.70/0.73 tff(800,plain,
% 0.70/0.73 (~c1_1(a831)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[243, 799])).
% 0.70/0.73 tff(801,plain,
% 0.70/0.73 (~c0_1(a831)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[249, 799])).
% 0.70/0.73 tff(802,plain,
% 0.70/0.73 (c3_1(a831)),
% 0.70/0.73 inference(unit_resolution,[status(thm)],[260, 799])).
% 0.70/0.73 tff(803,plain,
% 0.70/0.73 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a831) | c1_1(a831) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | c3_1(a821) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a831) | c1_1(a831) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | c3_1(a821) | (~c3_1(a831)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(804,plain,
% 0.70/0.73 (((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a821) | c0_1(a821) | c3_1(a821)) <=> (c0_1(a831) | c1_1(a831) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | c3_1(a821) | (~c3_1(a831)))),
% 0.70/0.73 inference(rewrite,[status(thm)],[])).
% 0.70/0.73 tff(805,plain,
% 0.70/0.73 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a821) | c0_1(a821) | c3_1(a821))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a831) | c1_1(a831) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | c3_1(a821) | (~c3_1(a831))))),
% 0.70/0.74 inference(monotonicity,[status(thm)],[804])).
% 0.70/0.74 tff(806,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a821) | c0_1(a821) | c3_1(a821))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a831) | c1_1(a831) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | c3_1(a821) | (~c3_1(a831)))),
% 0.70/0.74 inference(transitivity,[status(thm)],[805, 803])).
% 0.70/0.74 tff(807,plain,
% 0.70/0.74 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a821) | c0_1(a821) | c3_1(a821))),
% 0.70/0.74 inference(quant_inst,[status(thm)],[])).
% 0.70/0.74 tff(808,plain,
% 0.70/0.74 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a831) | c1_1(a831) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | c3_1(a821) | (~c3_1(a831))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.70/0.74 tff(809,plain,
% 0.70/0.74 ($false),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[808, 163, 802, 801, 800, 781, 772, 205, 780])).
% 0.70/0.74 tff(810,plain,(hskp14 | hskp22 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.70/0.74 tff(811,plain,
% 0.70/0.74 (hskp14),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[810, 13, 12])).
% 0.70/0.74 tff(812,plain,
% 0.70/0.74 (~c2_1(a842)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[54, 811])).
% 0.70/0.74 tff(813,plain,
% 0.70/0.74 (c1_1(a842)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[65, 811])).
% 0.70/0.74 tff(814,plain,
% 0.70/0.74 (c0_1(a842)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[76, 811])).
% 0.70/0.74 tff(815,assumption,(~hskp8), introduced(assumption)).
% 0.70/0.74 tff(816,assumption,(~c2_1(a816)), introduced(assumption)).
% 0.70/0.74 tff(817,assumption,(c3_1(a816)), introduced(assumption)).
% 0.70/0.74 tff(818,assumption,(c0_1(a816)), introduced(assumption)).
% 0.70/0.74 tff(819,assumption,(~hskp29), introduced(assumption)).
% 0.70/0.74 tff(820,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(821,plain,
% 0.70/0.74 ((hskp29 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816))) <=> (hskp29 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(822,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816))))),
% 0.70/0.74 inference(monotonicity,[status(thm)],[821])).
% 0.70/0.74 tff(823,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))),
% 0.70/0.74 inference(transitivity,[status(thm)],[822, 820])).
% 0.70/0.74 tff(824,plain,
% 0.70/0.74 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp29 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))),
% 0.70/0.74 inference(quant_inst,[status(thm)],[])).
% 0.70/0.74 tff(825,plain,
% 0.70/0.74 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp29 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[824, 823])).
% 0.70/0.74 tff(826,plain,
% 0.70/0.74 (hskp29 | (~c1_1(a816))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[825, 163, 818, 817, 816, 353])).
% 0.70/0.74 tff(827,plain,
% 0.70/0.74 (~c1_1(a816)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[826, 819])).
% 0.70/0.74 tff(828,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(829,plain,
% 0.70/0.74 ((hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816))) <=> (hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(830,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816))))),
% 0.70/0.74 inference(monotonicity,[status(thm)],[829])).
% 0.70/0.74 tff(831,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)))),
% 0.70/0.74 inference(transitivity,[status(thm)],[830, 828])).
% 0.70/0.74 tff(832,plain,
% 0.70/0.74 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a816) | c1_1(a816) | (~c0_1(a816)))),
% 0.70/0.74 inference(quant_inst,[status(thm)],[])).
% 0.70/0.74 tff(833,plain,
% 0.70/0.74 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[832, 831])).
% 0.70/0.74 tff(834,plain,
% 0.70/0.74 (hskp9 | c1_1(a816)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[833, 163, 818, 817, 816, 230])).
% 0.70/0.74 tff(835,plain,
% 0.70/0.74 (hskp9),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[834, 827])).
% 0.70/0.74 tff(836,plain,
% 0.70/0.74 (~c1_1(a831)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[243, 835])).
% 0.70/0.74 tff(837,plain,
% 0.70/0.74 (~c0_1(a831)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[249, 835])).
% 0.70/0.74 tff(838,plain,
% 0.70/0.74 (^[U: $i] : refl((hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.70/0.74 inference(bind,[status(th)],[])).
% 0.70/0.74 tff(839,plain,
% 0.70/0.74 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.74 inference(quant_intro,[status(thm)],[838])).
% 0.70/0.74 tff(840,plain,
% 0.70/0.74 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(841,plain,
% 0.70/0.74 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp19) <=> ((hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite(((hskp29 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp19) <=> (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.70/0.74 inference(bind,[status(th)],[])).
% 0.70/0.74 tff(842,plain,
% 0.70/0.74 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp19) <=> ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.74 inference(quant_intro,[status(thm)],[841])).
% 0.70/0.74 tff(843,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp29) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 0.70/0.74 tff(844,plain,
% 0.70/0.74 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[843, 842])).
% 0.70/0.74 tff(845,plain,
% 0.70/0.74 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[844, 840])).
% 0.70/0.74 tff(846,plain,(
% 0.70/0.74 ![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.74 inference(skolemize,[status(sab)],[845])).
% 0.70/0.74 tff(847,plain,
% 0.70/0.74 (![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[846, 839])).
% 0.70/0.74 tff(848,plain,
% 0.70/0.74 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(849,plain,
% 0.70/0.74 ((hskp29 | hskp19 | (~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842))) <=> (hskp29 | hskp19 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(850,plain,
% 0.70/0.74 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842))))),
% 0.70/0.74 inference(monotonicity,[status(thm)],[849])).
% 0.70/0.74 tff(851,plain,
% 0.70/0.74 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.70/0.74 inference(transitivity,[status(thm)],[850, 848])).
% 0.70/0.74 tff(852,plain,
% 0.70/0.74 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.70/0.74 inference(quant_inst,[status(thm)],[])).
% 0.70/0.74 tff(853,plain,
% 0.70/0.74 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a842) | (~ndr1_0) | (~c1_1(a842)) | (~c0_1(a842))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[852, 851])).
% 0.70/0.74 tff(854,plain,
% 0.70/0.74 (hskp29 | hskp19),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[853, 163, 107, 106, 98, 847])).
% 0.70/0.74 tff(855,plain,
% 0.70/0.74 (hskp19),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[854, 819])).
% 0.70/0.74 tff(856,plain,
% 0.70/0.74 (((~hskp19) | (~c3_1(a855))) <=> ((~hskp19) | (~c3_1(a855)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(857,plain,
% 0.70/0.74 (((~c3_1(a855)) | (~hskp19)) <=> ((~hskp19) | (~c3_1(a855)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(858,axiom,((~c3_1(a855)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.70/0.74 tff(859,plain,
% 0.70/0.74 ((~hskp19) | (~c3_1(a855))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[858, 857])).
% 0.70/0.74 tff(860,plain,
% 0.70/0.74 ((~hskp19) | (~c3_1(a855))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[859, 856])).
% 0.70/0.74 tff(861,plain,
% 0.70/0.74 (~c3_1(a855)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[860, 855])).
% 0.70/0.74 tff(862,plain,
% 0.70/0.74 (((~hskp19) | (~c1_1(a855))) <=> ((~hskp19) | (~c1_1(a855)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(863,plain,
% 0.70/0.74 (((~c1_1(a855)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a855)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(864,axiom,((~c1_1(a855)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.70/0.74 tff(865,plain,
% 0.70/0.74 ((~hskp19) | (~c1_1(a855))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[864, 863])).
% 0.70/0.74 tff(866,plain,
% 0.70/0.74 ((~hskp19) | (~c1_1(a855))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[865, 862])).
% 0.70/0.74 tff(867,plain,
% 0.70/0.74 (~c1_1(a855)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[866, 855])).
% 0.70/0.74 tff(868,plain,
% 0.70/0.74 (((~hskp19) | (~c0_1(a855))) <=> ((~hskp19) | (~c0_1(a855)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(869,plain,
% 0.70/0.74 (((~c0_1(a855)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a855)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(870,axiom,((~c0_1(a855)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 0.70/0.74 tff(871,plain,
% 0.70/0.74 ((~hskp19) | (~c0_1(a855))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[870, 869])).
% 0.70/0.74 tff(872,plain,
% 0.70/0.74 ((~hskp19) | (~c0_1(a855))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[871, 868])).
% 0.70/0.74 tff(873,plain,
% 0.70/0.74 (~c0_1(a855)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[872, 855])).
% 0.70/0.74 tff(874,plain,
% 0.70/0.74 (c3_1(a831)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[260, 835])).
% 0.70/0.74 tff(875,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a855) | c1_1(a855) | c3_1(a855) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a855) | c1_1(a855) | c3_1(a855) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(876,plain,
% 0.70/0.74 (((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a855) | c0_1(a855) | c3_1(a855)) <=> (c0_1(a855) | c1_1(a855) | c3_1(a855) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(877,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a855) | c0_1(a855) | c3_1(a855))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a855) | c1_1(a855) | c3_1(a855) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831))))),
% 0.70/0.74 inference(monotonicity,[status(thm)],[876])).
% 0.70/0.74 tff(878,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a855) | c0_1(a855) | c3_1(a855))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a855) | c1_1(a855) | c3_1(a855) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)))),
% 0.70/0.74 inference(transitivity,[status(thm)],[877, 875])).
% 0.70/0.74 tff(879,plain,
% 0.70/0.74 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a855) | c0_1(a855) | c3_1(a855))),
% 0.70/0.74 inference(quant_inst,[status(thm)],[])).
% 0.70/0.74 tff(880,plain,
% 0.70/0.74 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a855) | c1_1(a855) | c3_1(a855) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[879, 878])).
% 0.70/0.74 tff(881,plain,
% 0.70/0.74 ($false),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[880, 163, 874, 873, 867, 861, 837, 836, 205])).
% 0.70/0.74 tff(882,plain,(hskp29 | (~c0_1(a816)) | (~c3_1(a816)) | c2_1(a816) | (~c0_1(a842)) | (~c1_1(a842)) | c2_1(a842)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.74 tff(883,plain,
% 0.70/0.74 (hskp29),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[882, 818, 817, 816, 107, 106, 98])).
% 0.70/0.74 tff(884,plain,
% 0.70/0.74 (c3_1(a865)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[374, 883])).
% 0.70/0.74 tff(885,plain,
% 0.70/0.74 (c2_1(a865)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[385, 883])).
% 0.70/0.74 tff(886,plain,
% 0.70/0.74 (c1_1(a865)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[396, 883])).
% 0.70/0.74 tff(887,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c0_1(a865)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c0_1(a865)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(888,plain,
% 0.70/0.74 ((hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865))) <=> (hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c0_1(a865)))),
% 0.70/0.74 inference(rewrite,[status(thm)],[])).
% 0.70/0.74 tff(889,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c0_1(a865))))),
% 0.70/0.74 inference(monotonicity,[status(thm)],[888])).
% 0.70/0.74 tff(890,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c0_1(a865)))),
% 0.70/0.74 inference(transitivity,[status(thm)],[889, 887])).
% 0.70/0.74 tff(891,plain,
% 0.70/0.74 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)))),
% 0.70/0.74 inference(quant_inst,[status(thm)],[])).
% 0.70/0.74 tff(892,plain,
% 0.70/0.74 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)) | (~c0_1(a865))),
% 0.70/0.74 inference(modus_ponens,[status(thm)],[891, 890])).
% 0.70/0.74 tff(893,plain,
% 0.70/0.74 (hskp8 | (~c0_1(a865))),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[892, 163, 886, 885, 884, 343])).
% 0.70/0.74 tff(894,plain,
% 0.70/0.74 (~c0_1(a865)),
% 0.70/0.74 inference(unit_resolution,[status(thm)],[893, 815])).
% 0.70/0.74 tff(895,plain,
% 0.70/0.74 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(896,plain,
% 0.70/0.75 ((hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816))) <=> (hskp8 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(897,plain,
% 0.70/0.75 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865))))),
% 0.70/0.75 inference(monotonicity,[status(thm)],[896])).
% 0.70/0.75 tff(898,plain,
% 0.70/0.75 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865)))),
% 0.70/0.75 inference(transitivity,[status(thm)],[897, 895])).
% 0.70/0.75 tff(899,plain,
% 0.70/0.75 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a865)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)))),
% 0.70/0.75 inference(quant_inst,[status(thm)],[])).
% 0.70/0.75 tff(900,plain,
% 0.70/0.75 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c0_1(V)))) | hskp8 | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | (~c3_1(a865)) | (~c1_1(a865)) | (~c2_1(a865))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[899, 898])).
% 0.70/0.75 tff(901,plain,
% 0.70/0.75 (hskp8 | (~c1_1(a816))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[900, 163, 886, 885, 884, 818, 817, 343])).
% 0.70/0.75 tff(902,plain,
% 0.70/0.75 (~c1_1(a816)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[901, 815])).
% 0.70/0.75 tff(903,plain,
% 0.70/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(904,plain,
% 0.70/0.75 (((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865))) <=> (c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(905,plain,
% 0.70/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842))))),
% 0.70/0.75 inference(monotonicity,[status(thm)],[904])).
% 0.70/0.75 tff(906,plain,
% 0.70/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.70/0.75 inference(transitivity,[status(thm)],[905, 903])).
% 0.70/0.75 tff(907,plain,
% 0.70/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))),
% 0.70/0.75 inference(quant_inst,[status(thm)],[])).
% 0.70/0.75 tff(908,plain,
% 0.70/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a842)) | (~c0_1(a842))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[907, 906])).
% 0.70/0.75 tff(909,plain,
% 0.70/0.75 ($false),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[908, 163, 886, 885, 107, 106, 817, 98, 816, 87, 902, 894])).
% 0.70/0.75 tff(910,plain,(hskp8 | (~c0_1(a842)) | (~c1_1(a842)) | (~c3_1(a816)) | c2_1(a842) | c2_1(a816) | (~c0_1(a816))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.75 tff(911,plain,
% 0.70/0.75 (hskp8),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[910, 814, 813, 792, 812, 751, 750])).
% 0.70/0.75 tff(912,plain,
% 0.70/0.75 (~c0_1(a830)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[415, 911])).
% 0.70/0.75 tff(913,plain,
% 0.70/0.75 (~c3_1(a830)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[438, 911])).
% 0.70/0.75 tff(914,plain,
% 0.70/0.75 (~c2_1(a830)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[409, 911])).
% 0.70/0.75 tff(915,assumption,(c1_1(a816)), introduced(assumption)).
% 0.70/0.75 tff(916,assumption,(~c2_1(a830)), introduced(assumption)).
% 0.70/0.75 tff(917,assumption,(~c0_1(a830)), introduced(assumption)).
% 0.70/0.75 tff(918,plain,
% 0.70/0.75 ((~c1_1(a816)) | (~c1_1(a830))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[596, 163, 818, 817, 917, 916, 816, 333])).
% 0.70/0.75 tff(919,plain,
% 0.70/0.75 (~c1_1(a830)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[918, 915])).
% 0.70/0.75 tff(920,assumption,(~c3_1(a830)), introduced(assumption)).
% 0.70/0.75 tff(921,assumption,(~c3_1(a878)), introduced(assumption)).
% 0.70/0.75 tff(922,assumption,(~c0_1(a878)), introduced(assumption)).
% 0.70/0.75 tff(923,assumption,(c1_1(a878)), introduced(assumption)).
% 0.70/0.75 tff(924,plain,
% 0.70/0.75 (c1_1(a830) | (~c2_1(a878))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[746, 163, 923, 922, 921, 916, 920, 516])).
% 0.70/0.75 tff(925,plain,
% 0.70/0.75 (~c2_1(a878)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[924, 919])).
% 0.70/0.75 tff(926,plain,
% 0.70/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(927,plain,
% 0.70/0.75 (((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878))) <=> (c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(928,plain,
% 0.70/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878))))),
% 0.70/0.75 inference(monotonicity,[status(thm)],[927])).
% 0.70/0.75 tff(929,plain,
% 0.70/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878)))),
% 0.70/0.75 inference(transitivity,[status(thm)],[928, 926])).
% 0.70/0.75 tff(930,plain,
% 0.70/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c1_1(a816)) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a878) | c0_1(a878) | (~c1_1(a878)))),
% 0.70/0.75 inference(quant_inst,[status(thm)],[])).
% 0.70/0.75 tff(931,plain,
% 0.70/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a878) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c1_1(a816)) | (~c0_1(a816)) | c2_1(a878) | (~c1_1(a878))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[930, 929])).
% 0.70/0.75 tff(932,plain,
% 0.70/0.75 ($false),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[931, 163, 923, 818, 817, 922, 816, 333, 925, 915])).
% 0.70/0.75 tff(933,plain,((~c1_1(a816)) | (~c1_1(a878)) | (~c0_1(a816)) | (~c3_1(a816)) | c0_1(a878) | c2_1(a816) | c3_1(a878) | c2_1(a830) | c3_1(a830) | c0_1(a830)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.75 tff(934,plain,
% 0.70/0.75 (~c1_1(a816)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[933, 689, 750, 792, 740, 751, 678, 914, 913, 912])).
% 0.70/0.75 tff(935,plain,
% 0.70/0.75 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.70/0.75 inference(bind,[status(th)],[])).
% 0.70/0.75 tff(936,plain,
% 0.70/0.75 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.70/0.75 inference(quant_intro,[status(thm)],[935])).
% 0.70/0.75 tff(937,plain,
% 0.70/0.75 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(938,plain,
% 0.70/0.75 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~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(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~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(U)) <=> ((~ndr1_0) | c1_1(U) | (~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(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.70/0.75 inference(bind,[status(th)],[])).
% 0.70/0.75 tff(939,plain,
% 0.70/0.75 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.70/0.75 inference(quant_intro,[status(thm)],[938])).
% 0.70/0.75 tff(940,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 0.70/0.75 tff(941,plain,
% 0.70/0.75 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[940, 939])).
% 0.70/0.75 tff(942,plain,
% 0.70/0.75 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[941, 937])).
% 0.70/0.75 tff(943,plain,(
% 0.70/0.75 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.70/0.75 inference(skolemize,[status(sab)],[942])).
% 0.70/0.75 tff(944,plain,
% 0.70/0.75 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[943, 936])).
% 0.70/0.75 tff(945,assumption,(~hskp4), introduced(assumption)).
% 0.70/0.75 tff(946,plain,
% 0.70/0.75 (hskp4 | c2_1(a878)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[769, 163, 12, 922, 921, 480])).
% 0.70/0.75 tff(947,plain,
% 0.70/0.75 (c2_1(a878)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[946, 945])).
% 0.70/0.75 tff(948,plain,
% 0.70/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a878) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c1_1(a842)) | (~c0_1(a842)) | (~c1_1(a878)) | (~c2_1(a878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a878) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c1_1(a842)) | (~c0_1(a842)) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(949,plain,
% 0.70/0.75 (((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a878) | (~c2_1(a878)) | (~c1_1(a878))) <=> (c0_1(a878) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c1_1(a842)) | (~c0_1(a842)) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(950,plain,
% 0.70/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a878) | (~c2_1(a878)) | (~c1_1(a878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a878) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c1_1(a842)) | (~c0_1(a842)) | (~c1_1(a878)) | (~c2_1(a878))))),
% 0.70/0.75 inference(monotonicity,[status(thm)],[949])).
% 0.70/0.75 tff(951,plain,
% 0.70/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a878) | (~c2_1(a878)) | (~c1_1(a878)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a878) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c1_1(a842)) | (~c0_1(a842)) | (~c1_1(a878)) | (~c2_1(a878)))),
% 0.70/0.75 inference(transitivity,[status(thm)],[950, 948])).
% 0.70/0.75 tff(952,plain,
% 0.70/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a816) | c1_1(a816) | (~c3_1(a816)) | c0_1(a878) | (~c2_1(a878)) | (~c1_1(a878)))),
% 0.70/0.75 inference(quant_inst,[status(thm)],[])).
% 0.70/0.75 tff(953,plain,
% 0.70/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a878) | c2_1(a842) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c1_1(a842)) | (~c0_1(a842)) | (~c1_1(a878)) | (~c2_1(a878))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[952, 951])).
% 0.70/0.75 tff(954,plain,
% 0.70/0.75 (c1_1(a816) | (~c2_1(a878))),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[953, 163, 923, 107, 106, 817, 922, 98, 816, 87])).
% 0.70/0.75 tff(955,plain,
% 0.70/0.75 (c1_1(a816)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[954, 947])).
% 0.70/0.75 tff(956,plain,
% 0.70/0.75 (hskp29),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[826, 955])).
% 0.70/0.75 tff(957,plain,
% 0.70/0.75 (c3_1(a865)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[374, 956])).
% 0.70/0.75 tff(958,plain,
% 0.70/0.75 (c2_1(a865)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[385, 956])).
% 0.70/0.75 tff(959,plain,
% 0.70/0.75 (c1_1(a865)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[396, 956])).
% 0.70/0.75 tff(960,plain,
% 0.70/0.75 (hskp8),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[900, 163, 959, 958, 957, 818, 817, 343, 955])).
% 0.70/0.75 tff(961,plain,
% 0.70/0.75 (~c3_1(a830)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[438, 960])).
% 0.70/0.75 tff(962,plain,
% 0.70/0.75 (~c2_1(a830)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[409, 960])).
% 0.70/0.75 tff(963,plain,
% 0.70/0.75 (~c0_1(a830)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[415, 960])).
% 0.70/0.75 tff(964,plain,
% 0.70/0.75 ($false),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[486, 163, 12, 945, 963, 962, 961, 480])).
% 0.70/0.75 tff(965,plain,(hskp4 | hskp7 | (~c0_1(a816)) | (~c3_1(a816)) | c2_1(a816) | (~c1_1(a878)) | (~c0_1(a842)) | (~c1_1(a842)) | c0_1(a878) | c2_1(a842) | c3_1(a878)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.75 tff(966,plain,
% 0.70/0.75 (hskp4),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[965, 750, 12, 792, 751, 689, 814, 813, 740, 812, 678])).
% 0.70/0.75 tff(967,plain,
% 0.70/0.75 (~c1_1(a821)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[492, 966])).
% 0.70/0.75 tff(968,plain,
% 0.70/0.75 (c2_1(a821)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[526, 966])).
% 0.70/0.75 tff(969,plain,
% 0.70/0.75 (~hskp20),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[280, 814, 813, 812])).
% 0.70/0.75 tff(970,plain,
% 0.70/0.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a821) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)) | (~c3_1(a821)) | (~c2_1(a821)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a821) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)) | (~c3_1(a821)) | (~c2_1(a821)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(971,plain,
% 0.70/0.75 ((hskp20 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816))) <=> (hskp20 | c1_1(a821) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)) | (~c3_1(a821)) | (~c2_1(a821)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(972,plain,
% 0.70/0.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a821) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)) | (~c3_1(a821)) | (~c2_1(a821))))),
% 0.70/0.75 inference(monotonicity,[status(thm)],[971])).
% 0.70/0.75 tff(973,plain,
% 0.70/0.75 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a821) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)) | (~c3_1(a821)) | (~c2_1(a821)))),
% 0.70/0.75 inference(transitivity,[status(thm)],[972, 970])).
% 0.70/0.75 tff(974,plain,
% 0.70/0.75 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a821) | (~c2_1(a821)) | (~c3_1(a821)) | c1_1(a816) | (~c3_1(a816)) | (~c0_1(a816)))),
% 0.70/0.75 inference(quant_inst,[status(thm)],[])).
% 0.70/0.75 tff(975,plain,
% 0.70/0.75 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a821) | (~ndr1_0) | (~c3_1(a816)) | c1_1(a816) | (~c0_1(a816)) | (~c3_1(a821)) | (~c2_1(a821))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[974, 973])).
% 0.70/0.75 tff(976,plain,
% 0.70/0.75 (~c3_1(a821)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[975, 163, 969, 968, 750, 792, 967, 944, 934])).
% 0.70/0.75 tff(977,plain,
% 0.70/0.75 (~c0_1(a821)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[498, 966])).
% 0.70/0.75 tff(978,plain,
% 0.70/0.75 (hskp9 | c1_1(a816)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[833, 163, 750, 792, 751, 230])).
% 0.70/0.75 tff(979,plain,
% 0.70/0.75 (hskp9),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[978, 934])).
% 0.70/0.75 tff(980,plain,
% 0.70/0.75 (~c1_1(a831)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[243, 979])).
% 0.70/0.75 tff(981,plain,
% 0.70/0.75 (~c0_1(a831)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[249, 979])).
% 0.70/0.75 tff(982,plain,
% 0.70/0.75 (c3_1(a831)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[260, 979])).
% 0.70/0.75 tff(983,plain,
% 0.70/0.75 ($false),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[808, 163, 982, 981, 980, 977, 967, 205, 976])).
% 0.70/0.75 tff(984,plain,(hskp22 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.70/0.75 tff(985,plain,
% 0.70/0.75 (hskp22),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[984, 12])).
% 0.70/0.75 tff(986,plain,
% 0.70/0.75 (((~hskp22) | (~c1_1(a860))) <=> ((~hskp22) | (~c1_1(a860)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(987,plain,
% 0.70/0.75 (((~c1_1(a860)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a860)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(988,axiom,((~c1_1(a860)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 0.70/0.75 tff(989,plain,
% 0.70/0.75 ((~hskp22) | (~c1_1(a860))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[988, 987])).
% 0.70/0.75 tff(990,plain,
% 0.70/0.75 ((~hskp22) | (~c1_1(a860))),
% 0.70/0.75 inference(modus_ponens,[status(thm)],[989, 986])).
% 0.70/0.75 tff(991,plain,
% 0.70/0.75 (~c1_1(a860)),
% 0.70/0.75 inference(unit_resolution,[status(thm)],[990, 985])).
% 0.70/0.75 tff(992,plain,
% 0.70/0.75 (((~hskp22) | (~c2_1(a860))) <=> ((~hskp22) | (~c2_1(a860)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(993,plain,
% 0.70/0.75 (((~c2_1(a860)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a860)))),
% 0.70/0.75 inference(rewrite,[status(thm)],[])).
% 0.70/0.75 tff(994,axiom,((~c2_1(a860)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.70/0.76 tff(995,plain,
% 0.70/0.76 ((~hskp22) | (~c2_1(a860))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[994, 993])).
% 0.70/0.76 tff(996,plain,
% 0.70/0.76 ((~hskp22) | (~c2_1(a860))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[995, 992])).
% 0.70/0.76 tff(997,plain,
% 0.70/0.76 (~c2_1(a860)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[996, 985])).
% 0.70/0.76 tff(998,plain,
% 0.70/0.76 (((~hskp22) | (~c0_1(a860))) <=> ((~hskp22) | (~c0_1(a860)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(999,plain,
% 0.70/0.76 (((~c0_1(a860)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a860)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1000,axiom,((~c0_1(a860)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 0.70/0.76 tff(1001,plain,
% 0.70/0.76 ((~hskp22) | (~c0_1(a860))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[1000, 999])).
% 0.70/0.76 tff(1002,plain,
% 0.70/0.76 ((~hskp22) | (~c0_1(a860))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[1001, 998])).
% 0.70/0.76 tff(1003,plain,
% 0.70/0.76 (~c0_1(a860)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1002, 985])).
% 0.70/0.76 tff(1004,assumption,(c3_1(a860)), introduced(assumption)).
% 0.70/0.76 tff(1005,plain,
% 0.70/0.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | (~c3_1(a860)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | (~c3_1(a860)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1006,plain,
% 0.70/0.76 ((hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a860) | c0_1(a860) | (~c3_1(a860))) <=> (hskp2 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | (~c3_1(a860)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1007,plain,
% 0.70/0.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | (~c3_1(a860))))),
% 0.70/0.76 inference(monotonicity,[status(thm)],[1006])).
% 0.70/0.76 tff(1008,plain,
% 0.70/0.76 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | (~c3_1(a860)))),
% 0.70/0.76 inference(transitivity,[status(thm)],[1007, 1005])).
% 0.70/0.76 tff(1009,plain,
% 0.70/0.76 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)))),
% 0.70/0.76 inference(quant_inst,[status(thm)],[])).
% 0.70/0.76 tff(1010,plain,
% 0.70/0.76 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | (~c3_1(a860))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 0.70/0.76 tff(1011,plain,
% 0.70/0.76 (hskp2 | (~c3_1(a860))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1010, 163, 1003, 991, 997, 97])).
% 0.70/0.76 tff(1012,plain,
% 0.70/0.76 (hskp2),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1011, 1004])).
% 0.70/0.76 tff(1013,plain,
% 0.70/0.76 (~c3_1(a817)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[210, 1012])).
% 0.70/0.76 tff(1014,plain,
% 0.70/0.76 (~c0_1(a817)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[176, 1012])).
% 0.70/0.76 tff(1015,assumption,(~c1_1(a817)), introduced(assumption)).
% 0.70/0.76 tff(1016,assumption,(~c3_1(a817)), introduced(assumption)).
% 0.70/0.76 tff(1017,assumption,(~c0_1(a817)), introduced(assumption)).
% 0.70/0.76 tff(1018,assumption,(~c1_1(a860)), introduced(assumption)).
% 0.70/0.76 tff(1019,assumption,(~c0_1(a860)), introduced(assumption)).
% 0.70/0.76 tff(1020,plain,
% 0.70/0.76 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a860)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a860)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1021,plain,
% 0.70/0.76 (((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a817) | c0_1(a817) | c3_1(a817)) <=> (c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a860)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1022,plain,
% 0.70/0.76 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a817) | c0_1(a817) | c3_1(a817))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a860))))),
% 0.70/0.76 inference(monotonicity,[status(thm)],[1021])).
% 0.70/0.76 tff(1023,plain,
% 0.70/0.76 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a817) | c0_1(a817) | c3_1(a817))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a860)))),
% 0.70/0.76 inference(transitivity,[status(thm)],[1022, 1020])).
% 0.70/0.76 tff(1024,plain,
% 0.70/0.76 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a817) | c0_1(a817) | c3_1(a817))),
% 0.70/0.76 inference(quant_inst,[status(thm)],[])).
% 0.70/0.76 tff(1025,plain,
% 0.70/0.76 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~ndr1_0) | c1_1(a817) | (~c3_1(a860))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 0.70/0.76 tff(1026,plain,
% 0.70/0.76 ($false),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1025, 163, 1019, 1018, 1017, 1016, 205, 1004, 1015])).
% 0.70/0.76 tff(1027,plain,(c1_1(a817) | c0_1(a860) | c1_1(a860) | c0_1(a817) | c3_1(a817) | (~c3_1(a860))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.76 tff(1028,plain,
% 0.70/0.76 (c1_1(a817)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1027, 1014, 991, 1003, 1013, 1004])).
% 0.70/0.76 tff(1029,plain,
% 0.70/0.76 (c2_1(a817)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[187, 1012])).
% 0.70/0.76 tff(1030,plain,
% 0.70/0.76 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1031,plain,
% 0.70/0.76 ((hskp14 | hskp7 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817))) <=> (hskp14 | hskp7 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1032,plain,
% 0.70/0.76 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817))))),
% 0.70/0.76 inference(monotonicity,[status(thm)],[1031])).
% 0.70/0.76 tff(1033,plain,
% 0.70/0.76 (((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.70/0.76 inference(transitivity,[status(thm)],[1032, 1030])).
% 0.70/0.76 tff(1034,plain,
% 0.70/0.76 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp7 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.70/0.76 inference(quant_inst,[status(thm)],[])).
% 0.70/0.76 tff(1035,plain,
% 0.70/0.76 ((~![U: $i] : (hskp14 | hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp7 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[1034, 1033])).
% 0.70/0.76 tff(1036,plain,
% 0.70/0.76 (hskp14 | (~c1_1(a817))),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1035, 163, 12, 1029, 1013, 707])).
% 0.70/0.76 tff(1037,plain,
% 0.70/0.76 (hskp14),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1036, 1028])).
% 0.70/0.76 tff(1038,plain,
% 0.70/0.76 (~c2_1(a842)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[54, 1037])).
% 0.70/0.76 tff(1039,plain,
% 0.70/0.76 (c1_1(a842)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[65, 1037])).
% 0.70/0.76 tff(1040,plain,
% 0.70/0.76 (c0_1(a842)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[76, 1037])).
% 0.70/0.76 tff(1041,plain,
% 0.70/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a860) | c2_1(a860) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a860)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a860) | c2_1(a860) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a860)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1042,plain,
% 0.70/0.76 (((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817))) <=> (c1_1(a860) | c2_1(a860) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a860)))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1043,plain,
% 0.70/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a860) | c2_1(a860) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a860))))),
% 0.70/0.76 inference(monotonicity,[status(thm)],[1042])).
% 0.70/0.76 tff(1044,plain,
% 0.70/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a860) | c2_1(a860) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a860)))),
% 0.70/0.76 inference(transitivity,[status(thm)],[1043, 1041])).
% 0.70/0.76 tff(1045,plain,
% 0.70/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.70/0.76 inference(quant_inst,[status(thm)],[])).
% 0.70/0.76 tff(1046,plain,
% 0.70/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a860) | c2_1(a860) | c2_1(a842) | c0_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c1_1(a842)) | (~c0_1(a842)) | (~c3_1(a860))),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 0.70/0.76 tff(1047,plain,
% 0.70/0.76 ($false),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1046, 163, 1040, 1039, 1029, 991, 997, 1038, 1014, 87, 1004, 1028])).
% 0.70/0.76 tff(1048,plain,((~c3_1(a860)) | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.70/0.76 tff(1049,plain,
% 0.70/0.76 (~c3_1(a860)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1048, 12])).
% 0.70/0.76 tff(1050,plain,
% 0.70/0.76 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | c0_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1051,plain,
% 0.70/0.76 ((hskp7 | hskp4 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c0_1(a860)) <=> (hskp7 | hskp4 | c0_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1052,plain,
% 0.70/0.76 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c0_1(a860))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | c0_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860)))),
% 0.70/0.76 inference(monotonicity,[status(thm)],[1051])).
% 0.70/0.76 tff(1053,plain,
% 0.70/0.76 (((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c0_1(a860))) <=> ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))),
% 0.70/0.76 inference(transitivity,[status(thm)],[1052, 1050])).
% 0.70/0.76 tff(1054,plain,
% 0.70/0.76 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | (hskp7 | hskp4 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c0_1(a860))),
% 0.70/0.76 inference(quant_inst,[status(thm)],[])).
% 0.70/0.76 tff(1055,plain,
% 0.70/0.76 ((~![U: $i] : (hskp7 | hskp4 | (~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U))) | hskp7 | hskp4 | c0_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860)),
% 0.70/0.76 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 0.70/0.76 tff(1056,plain,
% 0.70/0.76 (hskp4 | c3_1(a860)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1055, 163, 12, 1003, 997, 480])).
% 0.70/0.76 tff(1057,plain,
% 0.70/0.76 (hskp4),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[1056, 1049])).
% 0.70/0.76 tff(1058,plain,
% 0.70/0.76 (~c1_1(a821)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[492, 1057])).
% 0.70/0.76 tff(1059,plain,
% 0.70/0.76 (c2_1(a821)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[526, 1057])).
% 0.70/0.76 tff(1060,plain,
% 0.70/0.76 (~c0_1(a821)),
% 0.70/0.76 inference(unit_resolution,[status(thm)],[498, 1057])).
% 0.70/0.76 tff(1061,assumption,(~c2_1(a860)), introduced(assumption)).
% 0.70/0.76 tff(1062,assumption,(~c3_1(a860)), introduced(assumption)).
% 0.70/0.76 tff(1063,assumption,(~hskp0), introduced(assumption)).
% 0.70/0.76 tff(1064,plain,
% 0.70/0.76 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1065,plain,
% 0.70/0.76 ((hskp0 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a860) | c0_1(a860)) <=> (hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))),
% 0.70/0.76 inference(rewrite,[status(thm)],[])).
% 0.70/0.76 tff(1066,plain,
% 0.70/0.76 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a860) | c0_1(a860))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860)))),
% 0.70/0.76 inference(monotonicity,[status(thm)],[1065])).
% 0.70/0.76 tff(1067,plain,
% 0.70/0.76 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a860) | c0_1(a860))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860))),
% 0.70/0.76 inference(transitivity,[status(thm)],[1066, 1064])).
% 0.70/0.76 tff(1068,plain,
% 0.70/0.76 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c3_1(a860) | c2_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a860) | c0_1(a860))),
% 0.76/0.77 inference(quant_inst,[status(thm)],[])).
% 0.76/0.77 tff(1069,plain,
% 0.76/0.77 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860) | (~ndr1_0) | c3_1(a860)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1068, 1067])).
% 0.76/0.77 tff(1070,plain,
% 0.76/0.77 ($false),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1069, 163, 1063, 1019, 1018, 1061, 433, 1062])).
% 0.76/0.77 tff(1071,plain,(c3_1(a860) | hskp0 | c0_1(a860) | c1_1(a860) | c2_1(a860)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.77 tff(1072,plain,
% 0.76/0.77 (hskp0),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1071, 1062, 1019, 1018, 1061])).
% 0.76/0.77 tff(1073,plain,
% 0.76/0.77 (~c3_1(a815)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[451, 1072])).
% 0.76/0.77 tff(1074,assumption,(~c1_1(a821)), introduced(assumption)).
% 0.76/0.77 tff(1075,assumption,(~c0_1(a821)), introduced(assumption)).
% 0.76/0.77 tff(1076,plain,
% 0.76/0.77 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c3_1(a860))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c3_1(a860))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1077,plain,
% 0.76/0.77 (((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a860) | c0_1(a860) | c3_1(a860)) <=> (c0_1(a860) | c1_1(a860) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c3_1(a860))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1078,plain,
% 0.76/0.77 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a860) | c0_1(a860) | c3_1(a860))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c3_1(a860)))),
% 0.76/0.77 inference(monotonicity,[status(thm)],[1077])).
% 0.76/0.77 tff(1079,plain,
% 0.76/0.77 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a860) | c0_1(a860) | c3_1(a860))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c3_1(a860))),
% 0.76/0.77 inference(transitivity,[status(thm)],[1078, 1076])).
% 0.76/0.77 tff(1080,plain,
% 0.76/0.77 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a821) | c0_1(a821) | (~c3_1(a821)) | c1_1(a860) | c0_1(a860) | c3_1(a860))),
% 0.76/0.77 inference(quant_inst,[status(thm)],[])).
% 0.76/0.77 tff(1081,plain,
% 0.76/0.77 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a821) | c1_1(a821) | (~ndr1_0) | (~c3_1(a821)) | c3_1(a860)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 0.76/0.77 tff(1082,plain,
% 0.76/0.77 ((~c3_1(a821)) | c3_1(a860)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1081, 163, 1019, 1018, 1075, 1074, 205])).
% 0.76/0.77 tff(1083,plain,
% 0.76/0.77 (~c3_1(a821)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1082, 1062])).
% 0.76/0.77 tff(1084,plain,
% 0.76/0.77 (c1_1(a815)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[462, 1072])).
% 0.76/0.77 tff(1085,assumption,(c2_1(a821)), introduced(assumption)).
% 0.76/0.77 tff(1086,plain,
% 0.76/0.77 (((~![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) | c1_1(W))) | (c1_1(a860) | c2_1(a860) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860))) <=> ((~![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) | c1_1(W))) | c1_1(a860) | c2_1(a860) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1087,plain,
% 0.76/0.77 (((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860) | c2_1(a860) | c1_1(a860)) <=> (c1_1(a860) | c2_1(a860) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1088,plain,
% 0.76/0.77 (((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860) | c2_1(a860) | c1_1(a860))) <=> ((~![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) | c1_1(W))) | (c1_1(a860) | c2_1(a860) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860)))),
% 0.76/0.77 inference(monotonicity,[status(thm)],[1087])).
% 0.76/0.77 tff(1089,plain,
% 0.76/0.77 (((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860) | c2_1(a860) | c1_1(a860))) <=> ((~![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) | c1_1(W))) | c1_1(a860) | c2_1(a860) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860))),
% 0.76/0.77 inference(transitivity,[status(thm)],[1088, 1086])).
% 0.76/0.77 tff(1090,plain,
% 0.76/0.77 ((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a815) | (~c2_1(a815)) | (~c1_1(a815)) | c0_1(a821) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860) | c2_1(a860) | c1_1(a860))),
% 0.76/0.77 inference(quant_inst,[status(thm)],[])).
% 0.76/0.77 tff(1091,plain,
% 0.76/0.77 ((~![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) | c1_1(W))) | c1_1(a860) | c2_1(a860) | c0_1(a821) | c3_1(a815) | (~ndr1_0) | (~c2_1(a815)) | (~c1_1(a815)) | c3_1(a821) | (~c2_1(a821)) | c3_1(a860)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 0.76/0.77 tff(1092,plain,
% 0.76/0.77 (~c2_1(a815)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1091, 163, 1085, 1084, 1018, 1061, 1075, 1073, 516, 1062, 1083])).
% 0.76/0.77 tff(1093,plain,
% 0.76/0.77 (c0_1(a815)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[627, 1072])).
% 0.76/0.77 tff(1094,plain,
% 0.76/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a860) | c2_1(a860) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)) | c3_1(a860))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a860) | c2_1(a860) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)) | c3_1(a860))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1095,plain,
% 0.76/0.77 ((hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a860) | c0_1(a860) | c3_1(a860)) <=> (hskp5 | c0_1(a860) | c2_1(a860) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)) | c3_1(a860))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1096,plain,
% 0.76/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a860) | c0_1(a860) | c3_1(a860))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | c0_1(a860) | c2_1(a860) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)) | c3_1(a860)))),
% 0.76/0.77 inference(monotonicity,[status(thm)],[1095])).
% 0.76/0.77 tff(1097,plain,
% 0.76/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a860) | c0_1(a860) | c3_1(a860))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a860) | c2_1(a860) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)) | c3_1(a860))),
% 0.76/0.77 inference(transitivity,[status(thm)],[1096, 1094])).
% 0.76/0.77 tff(1098,plain,
% 0.76/0.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | (hskp5 | (~ndr1_0) | c3_1(a815) | c2_1(a815) | (~c0_1(a815)) | c2_1(a860) | c0_1(a860) | c3_1(a860))),
% 0.76/0.77 inference(quant_inst,[status(thm)],[])).
% 0.76/0.77 tff(1099,plain,
% 0.76/0.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | c3_1(V))) | hskp5 | c0_1(a860) | c2_1(a860) | c3_1(a815) | (~ndr1_0) | c2_1(a815) | (~c0_1(a815)) | c3_1(a860)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 0.76/0.77 tff(1100,plain,
% 0.76/0.77 (hskp5),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1099, 163, 1093, 1019, 1061, 1073, 617, 1062, 1092])).
% 0.76/0.77 tff(1101,plain,
% 0.76/0.77 (~c0_1(a825)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[640, 1100])).
% 0.76/0.77 tff(1102,plain,
% 0.76/0.77 (c3_1(a825)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[651, 1100])).
% 0.76/0.77 tff(1103,plain,
% 0.76/0.77 (c1_1(a825)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[662, 1100])).
% 0.76/0.77 tff(1104,plain,
% 0.76/0.77 ($false),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[669, 163, 1103, 1102, 1085, 1093, 1084, 1101, 1075, 1074, 1073, 34])).
% 0.76/0.77 tff(1105,plain,(c3_1(a860) | (~c2_1(a821)) | c0_1(a821) | c1_1(a821) | c0_1(a860) | c2_1(a860) | c1_1(a860)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.77 tff(1106,plain,
% 0.76/0.77 ($false),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1105, 1060, 1059, 1049, 1058, 1003, 997, 991])).
% 0.76/0.77 tff(1107,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 0.76/0.77 tff(1108,plain,
% 0.76/0.77 (((~hskp7) | (~c2_1(a828))) <=> ((~hskp7) | (~c2_1(a828)))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1109,plain,
% 0.76/0.77 (((~c2_1(a828)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a828)))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1110,axiom,((~c2_1(a828)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.76/0.77 tff(1111,plain,
% 0.76/0.77 ((~hskp7) | (~c2_1(a828))),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 0.76/0.77 tff(1112,plain,
% 0.76/0.77 ((~hskp7) | (~c2_1(a828))),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1111, 1108])).
% 0.76/0.77 tff(1113,plain,
% 0.76/0.77 (~c2_1(a828)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1112, 1107])).
% 0.76/0.77 tff(1114,plain,
% 0.76/0.77 (((~hskp7) | (~c1_1(a828))) <=> ((~hskp7) | (~c1_1(a828)))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1115,plain,
% 0.76/0.77 (((~c1_1(a828)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a828)))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1116,axiom,((~c1_1(a828)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.76/0.77 tff(1117,plain,
% 0.76/0.77 ((~hskp7) | (~c1_1(a828))),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 0.76/0.77 tff(1118,plain,
% 0.76/0.77 ((~hskp7) | (~c1_1(a828))),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1117, 1114])).
% 0.76/0.77 tff(1119,plain,
% 0.76/0.77 (~c1_1(a828)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1118, 1107])).
% 0.76/0.77 tff(1120,plain,
% 0.76/0.77 (((~hskp7) | c0_1(a828)) <=> ((~hskp7) | c0_1(a828))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1121,axiom,((~hskp7) | c0_1(a828)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 0.76/0.77 tff(1122,plain,
% 0.76/0.77 ((~hskp7) | c0_1(a828)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 0.76/0.77 tff(1123,plain,
% 0.76/0.77 ((~hskp7) | c0_1(a828)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1122, 1120])).
% 0.76/0.77 tff(1124,plain,
% 0.76/0.77 ((~hskp7) | c0_1(a828)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1123, 1120])).
% 0.76/0.77 tff(1125,plain,
% 0.76/0.77 ((~hskp7) | c0_1(a828)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1124, 1120])).
% 0.76/0.77 tff(1126,plain,
% 0.76/0.77 ((~hskp7) | c0_1(a828)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1125, 1120])).
% 0.76/0.77 tff(1127,plain,
% 0.76/0.77 ((~hskp7) | c0_1(a828)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1126, 1120])).
% 0.76/0.77 tff(1128,plain,
% 0.76/0.77 ((~hskp7) | c0_1(a828)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1127, 1120])).
% 0.76/0.77 tff(1129,plain,
% 0.76/0.77 ((~hskp7) | c0_1(a828)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1128, 1120])).
% 0.76/0.77 tff(1130,plain,
% 0.76/0.77 (c0_1(a828)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1129, 1107])).
% 0.76/0.77 tff(1131,plain,
% 0.76/0.77 (^[U: $i] : refl((hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 0.76/0.77 inference(bind,[status(th)],[])).
% 0.76/0.77 tff(1132,plain,
% 0.76/0.77 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.76/0.77 inference(quant_intro,[status(thm)],[1131])).
% 0.76/0.77 tff(1133,plain,
% 0.76/0.77 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1134,plain,
% 0.76/0.77 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 0.76/0.77 inference(bind,[status(th)],[])).
% 0.76/0.77 tff(1135,plain,
% 0.76/0.77 (![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27) <=> ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.76/0.77 inference(quant_intro,[status(thm)],[1134])).
% 0.76/0.77 tff(1136,axiom,(![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.76/0.77 tff(1137,plain,
% 0.76/0.77 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1136, 1135])).
% 0.76/0.77 tff(1138,plain,
% 0.76/0.77 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1137, 1133])).
% 0.76/0.77 tff(1139,plain,(
% 0.76/0.77 ![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.76/0.77 inference(skolemize,[status(sab)],[1138])).
% 0.76/0.77 tff(1140,plain,
% 0.76/0.77 (![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1139, 1132])).
% 0.76/0.77 tff(1141,plain,
% 0.76/0.77 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c3_1(a828))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c3_1(a828))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1142,plain,
% 0.76/0.77 ((hskp27 | (~ndr1_0) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (hskp27 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c3_1(a828))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1143,plain,
% 0.76/0.77 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c3_1(a828)))),
% 0.76/0.77 inference(monotonicity,[status(thm)],[1142])).
% 0.76/0.77 tff(1144,plain,
% 0.76/0.77 (((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c3_1(a828))),
% 0.76/0.77 inference(transitivity,[status(thm)],[1143, 1141])).
% 0.76/0.77 tff(1145,plain,
% 0.76/0.77 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp27 | (~ndr1_0) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 0.76/0.77 inference(quant_inst,[status(thm)],[])).
% 0.76/0.77 tff(1146,plain,
% 0.76/0.77 ((~![U: $i] : (hskp27 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp27 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c3_1(a828)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 0.76/0.77 tff(1147,plain,
% 0.76/0.77 (hskp27 | c3_1(a828)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1146, 163, 1119, 1113, 1140])).
% 0.76/0.77 tff(1148,plain,
% 0.76/0.77 (hskp27),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1147, 1])).
% 0.76/0.77 tff(1149,plain,
% 0.76/0.77 (((~hskp27) | c3_1(a826)) <=> ((~hskp27) | c3_1(a826))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1150,axiom,((~hskp27) | c3_1(a826)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.76/0.77 tff(1151,plain,
% 0.76/0.77 ((~hskp27) | c3_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 0.76/0.77 tff(1152,plain,
% 0.76/0.77 ((~hskp27) | c3_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1151, 1149])).
% 0.76/0.77 tff(1153,plain,
% 0.76/0.77 ((~hskp27) | c3_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1152, 1149])).
% 0.76/0.77 tff(1154,plain,
% 0.76/0.77 ((~hskp27) | c3_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1153, 1149])).
% 0.76/0.77 tff(1155,plain,
% 0.76/0.77 ((~hskp27) | c3_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1154, 1149])).
% 0.76/0.77 tff(1156,plain,
% 0.76/0.77 ((~hskp27) | c3_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1155, 1149])).
% 0.76/0.77 tff(1157,plain,
% 0.76/0.77 ((~hskp27) | c3_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1156, 1149])).
% 0.76/0.77 tff(1158,plain,
% 0.76/0.77 ((~hskp27) | c3_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1157, 1149])).
% 0.76/0.77 tff(1159,plain,
% 0.76/0.77 (c3_1(a826)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1158, 1148])).
% 0.76/0.77 tff(1160,plain,
% 0.76/0.77 (((~hskp27) | c2_1(a826)) <=> ((~hskp27) | c2_1(a826))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1161,axiom,((~hskp27) | c2_1(a826)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 0.76/0.77 tff(1162,plain,
% 0.76/0.77 ((~hskp27) | c2_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 0.76/0.77 tff(1163,plain,
% 0.76/0.77 ((~hskp27) | c2_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1162, 1160])).
% 0.76/0.77 tff(1164,plain,
% 0.76/0.77 ((~hskp27) | c2_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1163, 1160])).
% 0.76/0.77 tff(1165,plain,
% 0.76/0.77 ((~hskp27) | c2_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1164, 1160])).
% 0.76/0.77 tff(1166,plain,
% 0.76/0.77 ((~hskp27) | c2_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1165, 1160])).
% 0.76/0.77 tff(1167,plain,
% 0.76/0.77 ((~hskp27) | c2_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1166, 1160])).
% 0.76/0.77 tff(1168,plain,
% 0.76/0.77 ((~hskp27) | c2_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1167, 1160])).
% 0.76/0.77 tff(1169,plain,
% 0.76/0.77 ((~hskp27) | c2_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1168, 1160])).
% 0.76/0.77 tff(1170,plain,
% 0.76/0.77 (c2_1(a826)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1169, 1148])).
% 0.76/0.77 tff(1171,plain,
% 0.76/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | (~c0_1(a828)) | c3_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | (~c0_1(a828)) | c3_1(a828))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1172,plain,
% 0.76/0.77 (((~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | (~c0_1(a828)) | c3_1(a828))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1173,plain,
% 0.76/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | (~c0_1(a828)) | c3_1(a828)))),
% 0.76/0.77 inference(monotonicity,[status(thm)],[1172])).
% 0.76/0.77 tff(1174,plain,
% 0.76/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | (~c0_1(a828)) | c3_1(a828))),
% 0.76/0.77 inference(transitivity,[status(thm)],[1173, 1171])).
% 0.76/0.77 tff(1175,plain,
% 0.76/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 0.76/0.77 inference(quant_inst,[status(thm)],[])).
% 0.76/0.77 tff(1176,plain,
% 0.76/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c1_1(a826)) | (~c0_1(a828)) | c3_1(a828)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 0.76/0.77 tff(1177,plain,
% 0.76/0.77 (~c1_1(a826)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1176, 163, 1170, 1159, 1130, 1119, 1113, 11, 1])).
% 0.76/0.77 tff(1178,plain,
% 0.76/0.77 (((~hskp27) | c0_1(a826)) <=> ((~hskp27) | c0_1(a826))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1179,axiom,((~hskp27) | c0_1(a826)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.76/0.77 tff(1180,plain,
% 0.76/0.77 ((~hskp27) | c0_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 0.76/0.77 tff(1181,plain,
% 0.76/0.77 ((~hskp27) | c0_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1180, 1178])).
% 0.76/0.77 tff(1182,plain,
% 0.76/0.77 ((~hskp27) | c0_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1181, 1178])).
% 0.76/0.77 tff(1183,plain,
% 0.76/0.77 ((~hskp27) | c0_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1182, 1178])).
% 0.76/0.77 tff(1184,plain,
% 0.76/0.77 ((~hskp27) | c0_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1183, 1178])).
% 0.76/0.77 tff(1185,plain,
% 0.76/0.77 ((~hskp27) | c0_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1184, 1178])).
% 0.76/0.77 tff(1186,plain,
% 0.76/0.77 ((~hskp27) | c0_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1185, 1178])).
% 0.76/0.77 tff(1187,plain,
% 0.76/0.77 ((~hskp27) | c0_1(a826)),
% 0.76/0.77 inference(modus_ponens,[status(thm)],[1186, 1178])).
% 0.76/0.77 tff(1188,plain,
% 0.76/0.77 (c0_1(a826)),
% 0.76/0.77 inference(unit_resolution,[status(thm)],[1187, 1148])).
% 0.76/0.77 tff(1189,plain,
% 0.76/0.77 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1190,plain,
% 0.76/0.77 ((hskp14 | hskp22 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826))) <=> (hskp14 | hskp22 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826))),
% 0.76/0.77 inference(rewrite,[status(thm)],[])).
% 0.76/0.77 tff(1191,plain,
% 0.76/0.77 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826)))),
% 0.76/0.77 inference(monotonicity,[status(thm)],[1190])).
% 0.76/0.77 tff(1192,plain,
% 0.76/0.77 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826))),
% 0.76/0.78 inference(transitivity,[status(thm)],[1191, 1189])).
% 0.76/0.78 tff(1193,plain,
% 0.76/0.78 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)))),
% 0.76/0.78 inference(quant_inst,[status(thm)],[])).
% 0.76/0.78 tff(1194,plain,
% 0.76/0.78 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826)),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 0.76/0.78 tff(1195,plain,
% 0.76/0.78 ($false),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1194, 762, 163, 13, 1170, 1159, 761, 1177])).
% 0.76/0.78 tff(1196,plain,(c3_1(a828) | hskp14 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.76/0.78 tff(1197,plain,
% 0.76/0.78 (c3_1(a828)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1196, 13, 762])).
% 0.76/0.78 tff(1198,plain,
% 0.76/0.78 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1199,plain,
% 0.76/0.78 ((hskp9 | (~ndr1_0) | c2_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828))) <=> (hskp9 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1200,plain,
% 0.76/0.78 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828))))),
% 0.76/0.78 inference(monotonicity,[status(thm)],[1199])).
% 0.76/0.78 tff(1201,plain,
% 0.76/0.78 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.76/0.78 inference(transitivity,[status(thm)],[1200, 1198])).
% 0.76/0.78 tff(1202,plain,
% 0.76/0.78 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))),
% 0.76/0.78 inference(quant_inst,[status(thm)],[])).
% 0.76/0.78 tff(1203,plain,
% 0.76/0.78 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 0.76/0.78 tff(1204,plain,
% 0.76/0.78 (hskp9 | (~c3_1(a828))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1203, 163, 1130, 1119, 1113, 230])).
% 0.76/0.78 tff(1205,plain,
% 0.76/0.78 (hskp9),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1204, 1197])).
% 0.76/0.78 tff(1206,plain,
% 0.76/0.78 (~c1_1(a831)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[243, 1205])).
% 0.76/0.78 tff(1207,plain,
% 0.76/0.78 (c3_1(a831)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[260, 1205])).
% 0.76/0.78 tff(1208,plain,
% 0.76/0.78 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | c1_1(a831) | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a831) | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1209,plain,
% 0.76/0.78 ((hskp14 | hskp22 | (~ndr1_0) | c1_1(a831) | (~c2_1(a831)) | (~c3_1(a831))) <=> (hskp14 | hskp22 | c1_1(a831) | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1210,plain,
% 0.76/0.78 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a831) | (~c2_1(a831)) | (~c3_1(a831)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | c1_1(a831) | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831))))),
% 0.76/0.78 inference(monotonicity,[status(thm)],[1209])).
% 0.76/0.78 tff(1211,plain,
% 0.76/0.78 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a831) | (~c2_1(a831)) | (~c3_1(a831)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a831) | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831)))),
% 0.76/0.78 inference(transitivity,[status(thm)],[1210, 1208])).
% 0.76/0.78 tff(1212,plain,
% 0.76/0.78 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a831) | (~c2_1(a831)) | (~c3_1(a831)))),
% 0.76/0.78 inference(quant_inst,[status(thm)],[])).
% 0.76/0.78 tff(1213,plain,
% 0.76/0.78 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a831) | (~ndr1_0) | (~c2_1(a831)) | (~c3_1(a831))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 0.76/0.78 tff(1214,plain,
% 0.76/0.78 (~c2_1(a831)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1213, 762, 163, 13, 1207, 1206, 761])).
% 0.76/0.78 tff(1215,plain,
% 0.76/0.78 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 0.76/0.78 inference(bind,[status(th)],[])).
% 0.76/0.78 tff(1216,plain,
% 0.76/0.78 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.78 inference(quant_intro,[status(thm)],[1215])).
% 0.76/0.78 tff(1217,plain,
% 0.76/0.78 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1218,plain,
% 0.76/0.78 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_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)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 0.76/0.78 inference(bind,[status(th)],[])).
% 0.76/0.78 tff(1219,plain,
% 0.76/0.78 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.78 inference(quant_intro,[status(thm)],[1218])).
% 0.76/0.78 tff(1220,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 0.76/0.78 tff(1221,plain,
% 0.76/0.78 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 0.76/0.78 tff(1222,plain,
% 0.76/0.78 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1221, 1217])).
% 0.76/0.78 tff(1223,plain,(
% 0.76/0.78 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.78 inference(skolemize,[status(sab)],[1222])).
% 0.76/0.78 tff(1224,plain,
% 0.76/0.78 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1223, 1216])).
% 0.76/0.78 tff(1225,plain,
% 0.76/0.78 (~c0_1(a831)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[249, 1205])).
% 0.76/0.78 tff(1226,plain,
% 0.76/0.78 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a831) | c1_1(a831) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | c2_1(a831))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a831) | c1_1(a831) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | c2_1(a831))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1227,plain,
% 0.76/0.78 ((hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a831) | c1_1(a831) | c0_1(a831)) <=> (hskp1 | c0_1(a831) | c1_1(a831) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | c2_1(a831))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1228,plain,
% 0.76/0.78 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a831) | c1_1(a831) | c0_1(a831))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a831) | c1_1(a831) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | c2_1(a831)))),
% 0.76/0.78 inference(monotonicity,[status(thm)],[1227])).
% 0.76/0.78 tff(1229,plain,
% 0.76/0.78 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a831) | c1_1(a831) | c0_1(a831))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a831) | c1_1(a831) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | c2_1(a831))),
% 0.76/0.78 inference(transitivity,[status(thm)],[1228, 1226])).
% 0.76/0.78 tff(1230,plain,
% 0.76/0.78 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a831) | c1_1(a831) | c0_1(a831))),
% 0.76/0.78 inference(quant_inst,[status(thm)],[])).
% 0.76/0.78 tff(1231,plain,
% 0.76/0.78 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a831) | c1_1(a831) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)) | c2_1(a831)),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1230, 1229])).
% 0.76/0.78 tff(1232,plain,
% 0.76/0.78 ($false),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1231, 163, 24, 1130, 1225, 1206, 1119, 1113, 1224, 1214])).
% 0.76/0.78 tff(1233,plain,(hskp22 | hskp1 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.76/0.78 tff(1234,plain,
% 0.76/0.78 (hskp22),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1233, 24, 762])).
% 0.76/0.78 tff(1235,plain,
% 0.76/0.78 (~c1_1(a860)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[990, 1234])).
% 0.76/0.78 tff(1236,plain,
% 0.76/0.78 (~c0_1(a860)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1002, 1234])).
% 0.76/0.78 tff(1237,plain,
% 0.76/0.78 (~c2_1(a860)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[996, 1234])).
% 0.76/0.78 tff(1238,assumption,(hskp7), introduced(assumption)).
% 0.76/0.78 tff(1239,plain,
% 0.76/0.78 ((ndr1_0 | (~hskp7)) <=> (ndr1_0 | (~hskp7))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1240,plain,
% 0.76/0.78 (((~hskp7) | ndr1_0) <=> (ndr1_0 | (~hskp7))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1241,axiom,((~hskp7) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause24')).
% 0.76/0.78 tff(1242,plain,
% 0.76/0.78 (ndr1_0 | (~hskp7)),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 0.76/0.78 tff(1243,plain,
% 0.76/0.78 (ndr1_0 | (~hskp7)),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1242, 1239])).
% 0.76/0.78 tff(1244,plain,
% 0.76/0.78 (ndr1_0),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1243, 1238])).
% 0.76/0.78 tff(1245,plain,
% 0.76/0.78 (c0_1(a828)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1129, 1238])).
% 0.76/0.78 tff(1246,assumption,(~c2_1(a828)), introduced(assumption)).
% 0.76/0.78 tff(1247,assumption,(~c1_1(a828)), introduced(assumption)).
% 0.76/0.78 tff(1248,plain,
% 0.76/0.78 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1249,plain,
% 0.76/0.78 ((hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a860) | c1_1(a860) | c0_1(a860)) <=> (hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1250,plain,
% 0.76/0.78 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a860) | c1_1(a860) | c0_1(a860))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828))))),
% 0.76/0.78 inference(monotonicity,[status(thm)],[1249])).
% 0.76/0.78 tff(1251,plain,
% 0.76/0.78 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a860) | c1_1(a860) | c0_1(a860))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828)))),
% 0.76/0.78 inference(transitivity,[status(thm)],[1250, 1248])).
% 0.76/0.78 tff(1252,plain,
% 0.76/0.78 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp1 | (~ndr1_0) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c2_1(a860) | c1_1(a860) | c0_1(a860))),
% 0.76/0.78 inference(quant_inst,[status(thm)],[])).
% 0.76/0.78 tff(1253,plain,
% 0.76/0.78 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c0_1(a828))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 0.76/0.78 tff(1254,plain,
% 0.76/0.78 (hskp1 | c0_1(a860) | c1_1(a860) | (~ndr1_0) | (~c0_1(a828))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1253, 1061, 1247, 1246, 1224])).
% 0.76/0.78 tff(1255,plain,
% 0.76/0.78 ($false),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1254, 1245, 1244, 24, 1019, 1018])).
% 0.76/0.78 tff(1256,plain,((~hskp7) | hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.78 tff(1257,plain,
% 0.76/0.78 (hskp1 | c0_1(a860) | c1_1(a860) | c2_1(a860)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1256, 1107, 1119, 1113])).
% 0.76/0.78 tff(1258,plain,
% 0.76/0.78 ($false),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1257, 1237, 1236, 24, 1235])).
% 0.76/0.78 tff(1259,plain,(hskp1 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.76/0.78 tff(1260,plain,
% 0.76/0.78 (hskp1),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1259, 762])).
% 0.76/0.78 tff(1261,plain,
% 0.76/0.78 (~c2_1(a816)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[541, 1260])).
% 0.76/0.78 tff(1262,plain,
% 0.76/0.78 (c3_1(a816)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[552, 1260])).
% 0.76/0.78 tff(1263,plain,
% 0.76/0.78 (c0_1(a816)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[563, 1260])).
% 0.76/0.78 tff(1264,plain,
% 0.76/0.78 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a828) | c2_1(a828) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a828) | c2_1(a828) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c0_1(a828)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1265,plain,
% 0.76/0.78 ((hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828))) <=> (hskp9 | c1_1(a828) | c2_1(a828) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c0_1(a828)))),
% 0.76/0.78 inference(rewrite,[status(thm)],[])).
% 0.76/0.78 tff(1266,plain,
% 0.76/0.78 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | c1_1(a828) | c2_1(a828) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c0_1(a828))))),
% 0.76/0.78 inference(monotonicity,[status(thm)],[1265])).
% 0.76/0.78 tff(1267,plain,
% 0.76/0.78 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a828) | c2_1(a828) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c0_1(a828)))),
% 0.76/0.78 inference(transitivity,[status(thm)],[1266, 1264])).
% 0.76/0.78 tff(1268,plain,
% 0.76/0.78 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp9 | (~ndr1_0) | c2_1(a816) | (~c3_1(a816)) | (~c0_1(a816)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))),
% 0.76/0.78 inference(quant_inst,[status(thm)],[])).
% 0.76/0.78 tff(1269,plain,
% 0.76/0.78 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp9 | c1_1(a828) | c2_1(a828) | c2_1(a816) | (~ndr1_0) | (~c3_1(a816)) | (~c0_1(a816)) | (~c0_1(a828))),
% 0.76/0.78 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 0.76/0.78 tff(1270,plain,
% 0.76/0.78 (hskp9),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1269, 163, 1130, 1263, 1262, 1119, 1113, 1261, 230])).
% 0.76/0.78 tff(1271,plain,
% 0.76/0.78 (~c1_1(a831)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[243, 1270])).
% 0.76/0.78 tff(1272,plain,
% 0.76/0.78 (~c0_1(a831)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[249, 1270])).
% 0.76/0.78 tff(1273,plain,
% 0.76/0.78 (c3_1(a831)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[260, 1270])).
% 0.76/0.78 tff(1274,plain,
% 0.76/0.78 (hskp22 | (~c2_1(a831))),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1213, 762, 163, 1273, 1271, 761])).
% 0.76/0.78 tff(1275,plain,
% 0.76/0.78 (~c2_1(a831)),
% 0.76/0.78 inference(unit_resolution,[status(thm)],[1274, 13])).
% 0.76/0.79 tff(1276,plain,
% 0.76/0.79 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.76/0.79 inference(bind,[status(th)],[])).
% 0.76/0.79 tff(1277,plain,
% 0.76/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.79 inference(quant_intro,[status(thm)],[1276])).
% 0.76/0.79 tff(1278,plain,
% 0.76/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1279,plain,
% 0.76/0.79 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.76/0.79 inference(bind,[status(th)],[])).
% 0.76/0.79 tff(1280,plain,
% 0.76/0.79 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.79 inference(quant_intro,[status(thm)],[1279])).
% 0.76/0.79 tff(1281,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 0.76/0.79 tff(1282,plain,
% 0.76/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 0.76/0.79 tff(1283,plain,
% 0.76/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1282, 1278])).
% 0.76/0.79 tff(1284,plain,(
% 0.76/0.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.79 inference(skolemize,[status(sab)],[1283])).
% 0.76/0.79 tff(1285,plain,
% 0.76/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1284, 1277])).
% 0.76/0.79 tff(1286,assumption,(~c1_1(a831)), introduced(assumption)).
% 0.76/0.79 tff(1287,assumption,(~c0_1(a831)), introduced(assumption)).
% 0.76/0.79 tff(1288,assumption,(hskp19), introduced(assumption)).
% 0.76/0.79 tff(1289,plain,
% 0.76/0.79 (~c3_1(a855)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[860, 1288])).
% 0.76/0.79 tff(1290,plain,
% 0.76/0.79 (~c1_1(a855)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[866, 1288])).
% 0.76/0.79 tff(1291,plain,
% 0.76/0.79 (~c0_1(a855)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[872, 1288])).
% 0.76/0.79 tff(1292,assumption,(c3_1(a831)), introduced(assumption)).
% 0.76/0.79 tff(1293,plain,
% 0.76/0.79 ($false),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[880, 163, 1292, 1291, 1290, 1289, 1287, 1286, 205])).
% 0.76/0.79 tff(1294,plain,((~hskp19) | (~c3_1(a831)) | c0_1(a831) | c1_1(a831)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.79 tff(1295,plain,
% 0.76/0.79 (~hskp19),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1294, 1273, 1272, 1271])).
% 0.76/0.79 tff(1296,assumption,(hskp16), introduced(assumption)).
% 0.76/0.79 tff(1297,plain,
% 0.76/0.79 (((~hskp16) | (~c1_1(a848))) <=> ((~hskp16) | (~c1_1(a848)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1298,plain,
% 0.76/0.79 (((~c1_1(a848)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a848)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1299,axiom,((~c1_1(a848)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 0.76/0.79 tff(1300,plain,
% 0.76/0.79 ((~hskp16) | (~c1_1(a848))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 0.76/0.79 tff(1301,plain,
% 0.76/0.79 ((~hskp16) | (~c1_1(a848))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1300, 1297])).
% 0.76/0.79 tff(1302,plain,
% 0.76/0.79 (~c1_1(a848)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1301, 1296])).
% 0.76/0.79 tff(1303,plain,
% 0.76/0.79 (((~hskp16) | c3_1(a848)) <=> ((~hskp16) | c3_1(a848))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1304,axiom,((~hskp16) | c3_1(a848)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.76/0.79 tff(1305,plain,
% 0.76/0.79 ((~hskp16) | c3_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 0.76/0.79 tff(1306,plain,
% 0.76/0.79 ((~hskp16) | c3_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1305, 1303])).
% 0.76/0.79 tff(1307,plain,
% 0.76/0.79 ((~hskp16) | c3_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1306, 1303])).
% 0.76/0.79 tff(1308,plain,
% 0.76/0.79 ((~hskp16) | c3_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1307, 1303])).
% 0.76/0.79 tff(1309,plain,
% 0.76/0.79 ((~hskp16) | c3_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1308, 1303])).
% 0.76/0.79 tff(1310,plain,
% 0.76/0.79 ((~hskp16) | c3_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1309, 1303])).
% 0.76/0.79 tff(1311,plain,
% 0.76/0.79 ((~hskp16) | c3_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1310, 1303])).
% 0.76/0.79 tff(1312,plain,
% 0.76/0.79 ((~hskp16) | c3_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1311, 1303])).
% 0.76/0.79 tff(1313,plain,
% 0.76/0.79 (c3_1(a848)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1312, 1296])).
% 0.76/0.79 tff(1314,plain,
% 0.76/0.79 (((~hskp16) | c2_1(a848)) <=> ((~hskp16) | c2_1(a848))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1315,axiom,((~hskp16) | c2_1(a848)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 0.76/0.79 tff(1316,plain,
% 0.76/0.79 ((~hskp16) | c2_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 0.76/0.79 tff(1317,plain,
% 0.76/0.79 ((~hskp16) | c2_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1316, 1314])).
% 0.76/0.79 tff(1318,plain,
% 0.76/0.79 ((~hskp16) | c2_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1317, 1314])).
% 0.76/0.79 tff(1319,plain,
% 0.76/0.79 ((~hskp16) | c2_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1318, 1314])).
% 0.76/0.79 tff(1320,plain,
% 0.76/0.79 ((~hskp16) | c2_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1319, 1314])).
% 0.76/0.79 tff(1321,plain,
% 0.76/0.79 ((~hskp16) | c2_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1320, 1314])).
% 0.76/0.79 tff(1322,plain,
% 0.76/0.79 ((~hskp16) | c2_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1321, 1314])).
% 0.76/0.79 tff(1323,plain,
% 0.76/0.79 ((~hskp16) | c2_1(a848)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1322, 1314])).
% 0.76/0.79 tff(1324,plain,
% 0.76/0.79 (c2_1(a848)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1323, 1296])).
% 0.76/0.79 tff(1325,plain,
% 0.76/0.79 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | c1_1(a848) | (~ndr1_0) | (~c2_1(a848)) | (~c3_1(a848)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a848) | (~ndr1_0) | (~c2_1(a848)) | (~c3_1(a848)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1326,plain,
% 0.76/0.79 ((hskp14 | hskp22 | (~ndr1_0) | c1_1(a848) | (~c2_1(a848)) | (~c3_1(a848))) <=> (hskp14 | hskp22 | c1_1(a848) | (~ndr1_0) | (~c2_1(a848)) | (~c3_1(a848)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1327,plain,
% 0.76/0.79 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a848) | (~c2_1(a848)) | (~c3_1(a848)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | c1_1(a848) | (~ndr1_0) | (~c2_1(a848)) | (~c3_1(a848))))),
% 0.76/0.79 inference(monotonicity,[status(thm)],[1326])).
% 0.76/0.79 tff(1328,plain,
% 0.76/0.79 (((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a848) | (~c2_1(a848)) | (~c3_1(a848)))) <=> ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a848) | (~ndr1_0) | (~c2_1(a848)) | (~c3_1(a848)))),
% 0.76/0.79 inference(transitivity,[status(thm)],[1327, 1325])).
% 0.76/0.79 tff(1329,plain,
% 0.76/0.79 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp14 | hskp22 | (~ndr1_0) | c1_1(a848) | (~c2_1(a848)) | (~c3_1(a848)))),
% 0.76/0.79 inference(quant_inst,[status(thm)],[])).
% 0.76/0.79 tff(1330,plain,
% 0.76/0.79 ((~![U: $i] : (hskp14 | hskp22 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp14 | hskp22 | c1_1(a848) | (~ndr1_0) | (~c2_1(a848)) | (~c3_1(a848))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1329, 1328])).
% 0.76/0.79 tff(1331,plain,
% 0.76/0.79 ($false),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1330, 762, 163, 13, 1324, 1313, 1302, 761])).
% 0.76/0.79 tff(1332,plain,((~hskp16) | hskp14 | hskp22), inference(lemma,lemma(discharge,[]))).
% 0.76/0.79 tff(1333,plain,
% 0.76/0.79 (~hskp16),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1332, 13, 762])).
% 0.76/0.79 tff(1334,plain,
% 0.76/0.79 ((hskp19 | hskp16 | hskp13) <=> (hskp19 | hskp16 | hskp13)),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1335,plain,
% 0.76/0.79 (((hskp13 | hskp16) | hskp19) <=> (hskp19 | hskp16 | hskp13)),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1336,axiom,((hskp13 | hskp16) | hskp19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 0.76/0.79 tff(1337,plain,
% 0.76/0.79 (hskp19 | hskp16 | hskp13),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 0.76/0.79 tff(1338,plain,
% 0.76/0.79 (hskp19 | hskp16 | hskp13),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1337, 1334])).
% 0.76/0.79 tff(1339,plain,
% 0.76/0.79 (hskp19 | hskp16 | hskp13),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1338, 1334])).
% 0.76/0.79 tff(1340,plain,
% 0.76/0.79 (hskp19 | hskp16 | hskp13),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1339, 1334])).
% 0.76/0.79 tff(1341,plain,
% 0.76/0.79 (hskp19 | hskp16 | hskp13),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1340, 1334])).
% 0.76/0.79 tff(1342,plain,
% 0.76/0.79 (hskp19 | hskp16 | hskp13),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1341, 1334])).
% 0.76/0.79 tff(1343,plain,
% 0.76/0.79 (hskp19 | hskp16 | hskp13),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1342, 1334])).
% 0.76/0.79 tff(1344,plain,
% 0.76/0.79 (hskp19 | hskp16 | hskp13),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1343, 1334])).
% 0.76/0.79 tff(1345,plain,
% 0.76/0.79 (hskp13),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1344, 1333, 1295])).
% 0.76/0.79 tff(1346,plain,
% 0.76/0.79 (((~hskp13) | (~c2_1(a839))) <=> ((~hskp13) | (~c2_1(a839)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1347,plain,
% 0.76/0.79 (((~c2_1(a839)) | (~hskp13)) <=> ((~hskp13) | (~c2_1(a839)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1348,axiom,((~c2_1(a839)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.76/0.79 tff(1349,plain,
% 0.76/0.79 ((~hskp13) | (~c2_1(a839))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 0.76/0.79 tff(1350,plain,
% 0.76/0.79 ((~hskp13) | (~c2_1(a839))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1349, 1346])).
% 0.76/0.79 tff(1351,plain,
% 0.76/0.79 (~c2_1(a839)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1350, 1345])).
% 0.76/0.79 tff(1352,plain,
% 0.76/0.79 (((~hskp13) | c3_1(a839)) <=> ((~hskp13) | c3_1(a839))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1353,axiom,((~hskp13) | c3_1(a839)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 0.76/0.79 tff(1354,plain,
% 0.76/0.79 ((~hskp13) | c3_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1353, 1352])).
% 0.76/0.79 tff(1355,plain,
% 0.76/0.79 ((~hskp13) | c3_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1354, 1352])).
% 0.76/0.79 tff(1356,plain,
% 0.76/0.79 ((~hskp13) | c3_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1355, 1352])).
% 0.76/0.79 tff(1357,plain,
% 0.76/0.79 ((~hskp13) | c3_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1356, 1352])).
% 0.76/0.79 tff(1358,plain,
% 0.76/0.79 ((~hskp13) | c3_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1357, 1352])).
% 0.76/0.79 tff(1359,plain,
% 0.76/0.79 ((~hskp13) | c3_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1358, 1352])).
% 0.76/0.79 tff(1360,plain,
% 0.76/0.79 ((~hskp13) | c3_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1359, 1352])).
% 0.76/0.79 tff(1361,plain,
% 0.76/0.79 ((~hskp13) | c3_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1360, 1352])).
% 0.76/0.79 tff(1362,plain,
% 0.76/0.79 (c3_1(a839)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1361, 1345])).
% 0.76/0.79 tff(1363,plain,
% 0.76/0.79 (((~hskp13) | c1_1(a839)) <=> ((~hskp13) | c1_1(a839))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1364,axiom,((~hskp13) | c1_1(a839)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 0.76/0.79 tff(1365,plain,
% 0.76/0.79 ((~hskp13) | c1_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 0.76/0.79 tff(1366,plain,
% 0.76/0.79 ((~hskp13) | c1_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1365, 1363])).
% 0.76/0.79 tff(1367,plain,
% 0.76/0.79 ((~hskp13) | c1_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1366, 1363])).
% 0.76/0.79 tff(1368,plain,
% 0.76/0.79 ((~hskp13) | c1_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1367, 1363])).
% 0.76/0.79 tff(1369,plain,
% 0.76/0.79 ((~hskp13) | c1_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1368, 1363])).
% 0.76/0.79 tff(1370,plain,
% 0.76/0.79 ((~hskp13) | c1_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1369, 1363])).
% 0.76/0.79 tff(1371,plain,
% 0.76/0.79 ((~hskp13) | c1_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1370, 1363])).
% 0.76/0.79 tff(1372,plain,
% 0.76/0.79 ((~hskp13) | c1_1(a839)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1371, 1363])).
% 0.76/0.79 tff(1373,plain,
% 0.76/0.79 (c1_1(a839)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1372, 1345])).
% 0.76/0.79 tff(1374,plain,
% 0.76/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a839) | c0_1(a831) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | c2_1(a831) | (~c3_1(a831)) | (~c1_1(a839)) | (~c3_1(a839)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a839) | c0_1(a831) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | c2_1(a831) | (~c3_1(a831)) | (~c1_1(a839)) | (~c3_1(a839)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1375,plain,
% 0.76/0.79 (((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a831) | c0_1(a831) | (~c3_1(a831))) <=> (c2_1(a839) | c0_1(a831) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | c2_1(a831) | (~c3_1(a831)) | (~c1_1(a839)) | (~c3_1(a839)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1376,plain,
% 0.76/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a839) | c0_1(a831) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | c2_1(a831) | (~c3_1(a831)) | (~c1_1(a839)) | (~c3_1(a839))))),
% 0.76/0.79 inference(monotonicity,[status(thm)],[1375])).
% 0.76/0.79 tff(1377,plain,
% 0.76/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a839) | c0_1(a831) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | c2_1(a831) | (~c3_1(a831)) | (~c1_1(a839)) | (~c3_1(a839)))),
% 0.76/0.79 inference(transitivity,[status(thm)],[1376, 1374])).
% 0.76/0.79 tff(1378,plain,
% 0.76/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a831) | c0_1(a831) | (~c3_1(a831)))),
% 0.76/0.79 inference(quant_inst,[status(thm)],[])).
% 0.76/0.79 tff(1379,plain,
% 0.76/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a839) | c0_1(a831) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | c2_1(a831) | (~c3_1(a831)) | (~c1_1(a839)) | (~c3_1(a839))),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 0.76/0.79 tff(1380,plain,
% 0.76/0.79 ($false),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1379, 163, 1373, 1362, 1273, 1130, 1351, 1272, 1119, 1285, 1197, 1275])).
% 0.76/0.79 tff(1381,plain,(hskp22 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.76/0.79 tff(1382,plain,
% 0.76/0.79 (hskp22),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1381, 762])).
% 0.76/0.79 tff(1383,plain,
% 0.76/0.79 (~c1_1(a860)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[990, 1382])).
% 0.76/0.79 tff(1384,plain,
% 0.76/0.79 (~c0_1(a860)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1002, 1382])).
% 0.76/0.79 tff(1385,plain,
% 0.76/0.79 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | c3_1(a860))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | c3_1(a860))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1386,plain,
% 0.76/0.79 (((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a860) | c0_1(a860) | c3_1(a860)) <=> (c0_1(a860) | c1_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | c3_1(a860))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1387,plain,
% 0.76/0.79 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a860) | c0_1(a860) | c3_1(a860))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | c3_1(a860)))),
% 0.76/0.79 inference(monotonicity,[status(thm)],[1386])).
% 0.76/0.79 tff(1388,plain,
% 0.76/0.79 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a860) | c0_1(a860) | c3_1(a860))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | c3_1(a860))),
% 0.76/0.79 inference(transitivity,[status(thm)],[1387, 1385])).
% 0.76/0.79 tff(1389,plain,
% 0.76/0.79 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)) | c1_1(a860) | c0_1(a860) | c3_1(a860))),
% 0.76/0.79 inference(quant_inst,[status(thm)],[])).
% 0.76/0.79 tff(1390,plain,
% 0.76/0.79 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | c3_1(a860)),
% 0.76/0.79 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 0.76/0.79 tff(1391,plain,
% 0.76/0.79 (c3_1(a860)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[1390, 163, 1273, 1384, 1383, 1272, 1271, 205])).
% 0.76/0.79 tff(1392,plain,
% 0.76/0.79 (~c2_1(a860)),
% 0.76/0.79 inference(unit_resolution,[status(thm)],[996, 1382])).
% 0.76/0.79 tff(1393,plain,
% 0.76/0.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a860) | c2_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a860)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a860) | c2_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a860)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1394,plain,
% 0.76/0.79 ((hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831))) <=> (hskp2 | c1_1(a860) | c2_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a860)))),
% 0.76/0.79 inference(rewrite,[status(thm)],[])).
% 0.76/0.79 tff(1395,plain,
% 0.76/0.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c1_1(a860) | c2_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a860))))),
% 0.76/0.79 inference(monotonicity,[status(thm)],[1394])).
% 0.76/0.79 tff(1396,plain,
% 0.76/0.79 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a860) | c2_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a860)))),
% 0.76/0.80 inference(transitivity,[status(thm)],[1395, 1393])).
% 0.76/0.80 tff(1397,plain,
% 0.76/0.80 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c1_1(a831) | c0_1(a831) | (~c3_1(a831)))),
% 0.76/0.80 inference(quant_inst,[status(thm)],[])).
% 0.76/0.80 tff(1398,plain,
% 0.76/0.80 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c1_1(a860) | c2_1(a860) | c0_1(a831) | c1_1(a831) | (~ndr1_0) | (~c3_1(a831)) | (~c3_1(a860))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1397, 1396])).
% 0.76/0.80 tff(1399,plain,
% 0.76/0.80 (hskp2),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1398, 163, 1273, 1383, 1392, 1272, 1271, 97, 1391])).
% 0.76/0.80 tff(1400,plain,
% 0.76/0.80 (~c3_1(a817)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[210, 1399])).
% 0.76/0.80 tff(1401,plain,
% 0.76/0.80 (~c0_1(a817)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[176, 1399])).
% 0.76/0.80 tff(1402,plain,
% 0.76/0.80 (c1_1(a817)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1027, 1401, 1383, 1391, 1400, 1384])).
% 0.76/0.80 tff(1403,plain,
% 0.76/0.80 (^[U: $i] : refl((hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 0.76/0.80 inference(bind,[status(th)],[])).
% 0.76/0.80 tff(1404,plain,
% 0.76/0.80 (![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.80 inference(quant_intro,[status(thm)],[1403])).
% 0.76/0.80 tff(1405,plain,
% 0.76/0.80 (![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1406,plain,
% 0.76/0.80 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp15) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp15) <=> (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 0.76/0.80 inference(bind,[status(th)],[])).
% 0.76/0.80 tff(1407,plain,
% 0.76/0.80 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp15) <=> ![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.80 inference(quant_intro,[status(thm)],[1406])).
% 0.76/0.80 tff(1408,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp14) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 0.76/0.80 tff(1409,plain,
% 0.76/0.80 (![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 0.76/0.80 tff(1410,plain,
% 0.76/0.80 (![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1409, 1405])).
% 0.76/0.80 tff(1411,plain,(
% 0.76/0.80 ![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.80 inference(skolemize,[status(sab)],[1410])).
% 0.76/0.80 tff(1412,plain,
% 0.76/0.80 (![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1411, 1404])).
% 0.76/0.80 tff(1413,plain,
% 0.76/0.80 (c2_1(a817)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[187, 1399])).
% 0.76/0.80 tff(1414,plain,
% 0.76/0.80 (((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp15 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp15 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1415,plain,
% 0.76/0.80 ((hskp14 | hskp15 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817))) <=> (hskp14 | hskp15 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1416,plain,
% 0.76/0.80 (((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp15 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp15 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817))))),
% 0.76/0.80 inference(monotonicity,[status(thm)],[1415])).
% 0.76/0.80 tff(1417,plain,
% 0.76/0.80 (((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp15 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))) <=> ((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp15 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.76/0.80 inference(transitivity,[status(thm)],[1416, 1414])).
% 0.76/0.80 tff(1418,plain,
% 0.76/0.80 ((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp14 | hskp15 | (~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)))),
% 0.76/0.80 inference(quant_inst,[status(thm)],[])).
% 0.76/0.80 tff(1419,plain,
% 0.76/0.80 ((~![U: $i] : (hskp14 | hskp15 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp14 | hskp15 | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1418, 1417])).
% 0.76/0.80 tff(1420,plain,
% 0.76/0.80 (hskp15),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1419, 762, 163, 1413, 1400, 1412, 1402])).
% 0.76/0.80 tff(1421,plain,
% 0.76/0.80 (((~hskp15) | (~c3_1(a844))) <=> ((~hskp15) | (~c3_1(a844)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1422,plain,
% 0.76/0.80 (((~c3_1(a844)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a844)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1423,axiom,((~c3_1(a844)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.76/0.80 tff(1424,plain,
% 0.76/0.80 ((~hskp15) | (~c3_1(a844))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1423, 1422])).
% 0.76/0.80 tff(1425,plain,
% 0.76/0.80 ((~hskp15) | (~c3_1(a844))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1424, 1421])).
% 0.76/0.80 tff(1426,plain,
% 0.76/0.80 (~c3_1(a844)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1425, 1420])).
% 0.76/0.80 tff(1427,plain,
% 0.76/0.80 (((~hskp15) | (~c1_1(a844))) <=> ((~hskp15) | (~c1_1(a844)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1428,plain,
% 0.76/0.80 (((~c1_1(a844)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a844)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1429,axiom,((~c1_1(a844)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.76/0.80 tff(1430,plain,
% 0.76/0.80 ((~hskp15) | (~c1_1(a844))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1429, 1428])).
% 0.76/0.80 tff(1431,plain,
% 0.76/0.80 ((~hskp15) | (~c1_1(a844))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1430, 1427])).
% 0.76/0.80 tff(1432,plain,
% 0.76/0.80 (~c1_1(a844)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1431, 1420])).
% 0.76/0.80 tff(1433,plain,
% 0.76/0.80 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c1_1(a844) | c3_1(a844) | (~ndr1_0) | c0_1(a844) | (~c3_1(a860)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c1_1(a844) | c3_1(a844) | (~ndr1_0) | c0_1(a844) | (~c3_1(a860)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1434,plain,
% 0.76/0.80 (((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a844) | c0_1(a844) | c3_1(a844)) <=> (c0_1(a860) | c1_1(a860) | c1_1(a844) | c3_1(a844) | (~ndr1_0) | c0_1(a844) | (~c3_1(a860)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1435,plain,
% 0.76/0.80 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a844) | c0_1(a844) | c3_1(a844))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (c0_1(a860) | c1_1(a860) | c1_1(a844) | c3_1(a844) | (~ndr1_0) | c0_1(a844) | (~c3_1(a860))))),
% 0.76/0.80 inference(monotonicity,[status(thm)],[1434])).
% 0.76/0.80 tff(1436,plain,
% 0.76/0.80 (((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a844) | c0_1(a844) | c3_1(a844))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c1_1(a844) | c3_1(a844) | (~ndr1_0) | c0_1(a844) | (~c3_1(a860)))),
% 0.76/0.80 inference(transitivity,[status(thm)],[1435, 1433])).
% 0.76/0.80 tff(1437,plain,
% 0.76/0.80 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | ((~ndr1_0) | c1_1(a860) | c0_1(a860) | (~c3_1(a860)) | c1_1(a844) | c0_1(a844) | c3_1(a844))),
% 0.76/0.80 inference(quant_inst,[status(thm)],[])).
% 0.76/0.80 tff(1438,plain,
% 0.76/0.80 ((~![V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | c0_1(a860) | c1_1(a860) | c1_1(a844) | c3_1(a844) | (~ndr1_0) | c0_1(a844) | (~c3_1(a860))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 0.76/0.80 tff(1439,plain,
% 0.76/0.80 (c0_1(a844)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1438, 163, 1384, 1383, 1432, 1426, 205, 1391])).
% 0.76/0.80 tff(1440,plain,
% 0.76/0.80 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 0.76/0.80 inference(bind,[status(th)],[])).
% 0.76/0.80 tff(1441,plain,
% 0.76/0.80 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.80 inference(quant_intro,[status(thm)],[1440])).
% 0.76/0.80 tff(1442,plain,
% 0.76/0.80 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1443,plain,
% 0.76/0.80 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 0.76/0.80 inference(bind,[status(th)],[])).
% 0.76/0.80 tff(1444,plain,
% 0.76/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.80 inference(quant_intro,[status(thm)],[1443])).
% 0.76/0.80 tff(1445,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 0.76/0.80 tff(1446,plain,
% 0.76/0.80 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 0.76/0.80 tff(1447,plain,
% 0.76/0.80 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1446, 1442])).
% 0.76/0.80 tff(1448,plain,(
% 0.76/0.80 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.80 inference(skolemize,[status(sab)],[1447])).
% 0.76/0.80 tff(1449,plain,
% 0.76/0.80 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1448, 1441])).
% 0.76/0.80 tff(1450,plain,
% 0.76/0.80 (hskp24),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[48, 762])).
% 0.76/0.80 tff(1451,plain,
% 0.76/0.80 (~c3_1(a878)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[677, 1450])).
% 0.76/0.80 tff(1452,plain,
% 0.76/0.80 (~c0_1(a878)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[739, 1450])).
% 0.76/0.80 tff(1453,plain,
% 0.76/0.80 (((~hskp15) | c2_1(a844)) <=> ((~hskp15) | c2_1(a844))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1454,axiom,((~hskp15) | c2_1(a844)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 0.76/0.80 tff(1455,plain,
% 0.76/0.80 ((~hskp15) | c2_1(a844)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 0.76/0.80 tff(1456,plain,
% 0.76/0.80 ((~hskp15) | c2_1(a844)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1455, 1453])).
% 0.76/0.80 tff(1457,plain,
% 0.76/0.80 ((~hskp15) | c2_1(a844)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1456, 1453])).
% 0.76/0.80 tff(1458,plain,
% 0.76/0.80 ((~hskp15) | c2_1(a844)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1457, 1453])).
% 0.76/0.80 tff(1459,plain,
% 0.76/0.80 ((~hskp15) | c2_1(a844)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1458, 1453])).
% 0.76/0.80 tff(1460,plain,
% 0.76/0.80 ((~hskp15) | c2_1(a844)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1459, 1453])).
% 0.76/0.80 tff(1461,plain,
% 0.76/0.80 ((~hskp15) | c2_1(a844)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1460, 1453])).
% 0.76/0.80 tff(1462,plain,
% 0.76/0.80 ((~hskp15) | c2_1(a844)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1461, 1453])).
% 0.76/0.80 tff(1463,plain,
% 0.76/0.80 (c2_1(a844)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1462, 1420])).
% 0.76/0.80 tff(1464,plain,
% 0.76/0.80 (c1_1(a878)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[688, 1450])).
% 0.76/0.80 tff(1465,plain,
% 0.76/0.80 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a878) | c3_1(a878) | c3_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c2_1(a844)) | (~c1_1(a878)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a878) | c3_1(a878) | c3_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c2_1(a844)) | (~c1_1(a878)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1466,plain,
% 0.76/0.80 ((hskp6 | (~ndr1_0) | c3_1(a844) | (~c2_1(a844)) | (~c0_1(a844)) | c0_1(a878) | c3_1(a878) | (~c1_1(a878))) <=> (hskp6 | c0_1(a878) | c3_1(a878) | c3_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c2_1(a844)) | (~c1_1(a878)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1467,plain,
% 0.76/0.80 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a844) | (~c2_1(a844)) | (~c0_1(a844)) | c0_1(a878) | c3_1(a878) | (~c1_1(a878)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a878) | c3_1(a878) | c3_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c2_1(a844)) | (~c1_1(a878))))),
% 0.76/0.80 inference(monotonicity,[status(thm)],[1466])).
% 0.76/0.80 tff(1468,plain,
% 0.76/0.80 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a844) | (~c2_1(a844)) | (~c0_1(a844)) | c0_1(a878) | c3_1(a878) | (~c1_1(a878)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a878) | c3_1(a878) | c3_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c2_1(a844)) | (~c1_1(a878)))),
% 0.76/0.80 inference(transitivity,[status(thm)],[1467, 1465])).
% 0.76/0.80 tff(1469,plain,
% 0.76/0.80 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c3_1(a844) | (~c2_1(a844)) | (~c0_1(a844)) | c0_1(a878) | c3_1(a878) | (~c1_1(a878)))),
% 0.76/0.80 inference(quant_inst,[status(thm)],[])).
% 0.76/0.80 tff(1470,plain,
% 0.76/0.80 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a878) | c3_1(a878) | c3_1(a844) | (~ndr1_0) | (~c0_1(a844)) | (~c2_1(a844)) | (~c1_1(a878))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1469, 1468])).
% 0.76/0.80 tff(1471,plain,
% 0.76/0.80 (hskp6),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1470, 163, 1464, 1463, 1452, 1451, 1426, 1449, 1439])).
% 0.76/0.80 tff(1472,plain,
% 0.76/0.80 (((~hskp6) | c1_1(a827)) <=> ((~hskp6) | c1_1(a827))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1473,axiom,((~hskp6) | c1_1(a827)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.76/0.80 tff(1474,plain,
% 0.76/0.80 ((~hskp6) | c1_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1473, 1472])).
% 0.76/0.80 tff(1475,plain,
% 0.76/0.80 ((~hskp6) | c1_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1474, 1472])).
% 0.76/0.80 tff(1476,plain,
% 0.76/0.80 ((~hskp6) | c1_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1475, 1472])).
% 0.76/0.80 tff(1477,plain,
% 0.76/0.80 ((~hskp6) | c1_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1476, 1472])).
% 0.76/0.80 tff(1478,plain,
% 0.76/0.80 ((~hskp6) | c1_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1477, 1472])).
% 0.76/0.80 tff(1479,plain,
% 0.76/0.80 ((~hskp6) | c1_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1478, 1472])).
% 0.76/0.80 tff(1480,plain,
% 0.76/0.80 ((~hskp6) | c1_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1479, 1472])).
% 0.76/0.80 tff(1481,plain,
% 0.76/0.80 ((~hskp6) | c1_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1480, 1472])).
% 0.76/0.80 tff(1482,plain,
% 0.76/0.80 (c1_1(a827)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1481, 1471])).
% 0.76/0.80 tff(1483,plain,
% 0.76/0.80 (((~hskp6) | (~c0_1(a827))) <=> ((~hskp6) | (~c0_1(a827)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1484,plain,
% 0.76/0.80 (((~c0_1(a827)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a827)))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1485,axiom,((~c0_1(a827)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.76/0.80 tff(1486,plain,
% 0.76/0.80 ((~hskp6) | (~c0_1(a827))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 0.76/0.80 tff(1487,plain,
% 0.76/0.80 ((~hskp6) | (~c0_1(a827))),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1486, 1483])).
% 0.76/0.80 tff(1488,plain,
% 0.76/0.80 (~c0_1(a827)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1487, 1471])).
% 0.76/0.80 tff(1489,plain,
% 0.76/0.80 (((~hskp6) | c2_1(a827)) <=> ((~hskp6) | c2_1(a827))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1490,axiom,((~hskp6) | c2_1(a827)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.76/0.80 tff(1491,plain,
% 0.76/0.80 ((~hskp6) | c2_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1490, 1489])).
% 0.76/0.80 tff(1492,plain,
% 0.76/0.80 ((~hskp6) | c2_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1491, 1489])).
% 0.76/0.80 tff(1493,plain,
% 0.76/0.80 ((~hskp6) | c2_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1492, 1489])).
% 0.76/0.80 tff(1494,plain,
% 0.76/0.80 ((~hskp6) | c2_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1493, 1489])).
% 0.76/0.80 tff(1495,plain,
% 0.76/0.80 ((~hskp6) | c2_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1494, 1489])).
% 0.76/0.80 tff(1496,plain,
% 0.76/0.80 ((~hskp6) | c2_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1495, 1489])).
% 0.76/0.80 tff(1497,plain,
% 0.76/0.80 ((~hskp6) | c2_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1496, 1489])).
% 0.76/0.80 tff(1498,plain,
% 0.76/0.80 ((~hskp6) | c2_1(a827)),
% 0.76/0.80 inference(modus_ponens,[status(thm)],[1497, 1489])).
% 0.76/0.80 tff(1499,plain,
% 0.76/0.80 (c2_1(a827)),
% 0.76/0.80 inference(unit_resolution,[status(thm)],[1498, 1471])).
% 0.76/0.80 tff(1500,assumption,(c2_1(a827)), introduced(assumption)).
% 0.76/0.80 tff(1501,assumption,(c1_1(a827)), introduced(assumption)).
% 0.76/0.80 tff(1502,plain,
% 0.76/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | (~c0_1(a828)) | c3_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | (~c0_1(a828)) | c3_1(a828))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1503,plain,
% 0.76/0.80 (((~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | (~c0_1(a828)) | c3_1(a828))),
% 0.76/0.80 inference(rewrite,[status(thm)],[])).
% 0.76/0.80 tff(1504,plain,
% 0.76/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | (~c0_1(a828)) | c3_1(a828)))),
% 0.76/0.80 inference(monotonicity,[status(thm)],[1503])).
% 0.76/0.80 tff(1505,plain,
% 0.76/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | (~c0_1(a828)) | c3_1(a828))),
% 0.76/0.80 inference(transitivity,[status(thm)],[1504, 1502])).
% 0.76/0.80 tff(1506,plain,
% 0.76/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | ((~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 0.76/0.80 inference(quant_inst,[status(thm)],[])).
% 0.76/0.80 tff(1507,plain,
% 0.76/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c2_1(a827)) | (~c3_1(a827)) | (~c1_1(a827)) | (~c0_1(a828)) | c3_1(a828)),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1506, 1505])).
% 0.76/0.81 tff(1508,plain,
% 0.76/0.81 (~c3_1(a827)),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1507, 163, 1130, 1501, 1500, 1119, 1113, 11, 1])).
% 0.76/0.81 tff(1509,assumption,(c1_1(a817)), introduced(assumption)).
% 0.76/0.81 tff(1510,assumption,(~c0_1(a827)), introduced(assumption)).
% 0.76/0.81 tff(1511,assumption,(c2_1(a817)), introduced(assumption)).
% 0.76/0.81 tff(1512,plain,
% 0.76/0.81 (((~![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) | c1_1(W))) | (c1_1(a828) | c2_1(a828) | c0_1(a827) | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c2_1(a827)) | c3_1(a827) | c3_1(a828))) <=> ((~![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) | c1_1(W))) | c1_1(a828) | c2_1(a828) | c0_1(a827) | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c2_1(a827)) | c3_1(a827) | c3_1(a828))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1513,plain,
% 0.76/0.81 (((~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a828) | c2_1(a828) | c1_1(a828)) <=> (c1_1(a828) | c2_1(a828) | c0_1(a827) | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c2_1(a827)) | c3_1(a827) | c3_1(a828))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1514,plain,
% 0.76/0.81 (((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![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) | c1_1(W))) | (c1_1(a828) | c2_1(a828) | c0_1(a827) | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c2_1(a827)) | c3_1(a827) | c3_1(a828)))),
% 0.76/0.81 inference(monotonicity,[status(thm)],[1513])).
% 0.76/0.81 tff(1515,plain,
% 0.76/0.81 (((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a828) | c2_1(a828) | c1_1(a828))) <=> ((~![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) | c1_1(W))) | c1_1(a828) | c2_1(a828) | c0_1(a827) | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c2_1(a827)) | c3_1(a827) | c3_1(a828))),
% 0.76/0.81 inference(transitivity,[status(thm)],[1514, 1512])).
% 0.76/0.81 tff(1516,plain,
% 0.76/0.81 ((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a817) | (~c2_1(a817)) | (~c1_1(a817)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a828) | c2_1(a828) | c1_1(a828))),
% 0.76/0.81 inference(quant_inst,[status(thm)],[])).
% 0.76/0.81 tff(1517,plain,
% 0.76/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c1_1(a828) | c2_1(a828) | c0_1(a827) | c3_1(a817) | (~ndr1_0) | (~c2_1(a817)) | (~c1_1(a817)) | (~c2_1(a827)) | c3_1(a827) | c3_1(a828)),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1516, 1515])).
% 0.76/0.81 tff(1518,plain,
% 0.76/0.81 ($false),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1517, 163, 1500, 1511, 1119, 1113, 1510, 1016, 516, 1509, 1, 1508])).
% 0.76/0.81 tff(1519,plain,(c3_1(a828) | (~c2_1(a827)) | (~c2_1(a817)) | c0_1(a827) | c3_1(a817) | (~c1_1(a817)) | (~c1_1(a827))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.81 tff(1520,plain,
% 0.76/0.81 (c3_1(a828)),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1519, 1499, 1413, 1488, 1400, 1402, 1482])).
% 0.76/0.81 tff(1521,assumption,(~hskp13), introduced(assumption)).
% 0.76/0.81 tff(1522,plain,
% 0.76/0.81 (^[U: $i] : refl((hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.76/0.81 inference(bind,[status(th)],[])).
% 0.76/0.81 tff(1523,plain,
% 0.76/0.81 (![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.81 inference(quant_intro,[status(thm)],[1522])).
% 0.76/0.81 tff(1524,plain,
% 0.76/0.81 (![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1525,plain,
% 0.76/0.81 (^[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)) | hskp21) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp13) <=> ((hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp13))), rewrite(((hskp21 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp13) <=> (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.76/0.81 inference(bind,[status(th)],[])).
% 0.76/0.81 tff(1526,plain,
% 0.76/0.81 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp13) <=> ![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.81 inference(quant_intro,[status(thm)],[1525])).
% 0.76/0.81 tff(1527,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp21) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 0.76/0.81 tff(1528,plain,
% 0.76/0.81 (![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 0.76/0.81 tff(1529,plain,
% 0.76/0.81 (![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1528, 1524])).
% 0.76/0.81 tff(1530,plain,(
% 0.76/0.81 ![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.81 inference(skolemize,[status(sab)],[1529])).
% 0.76/0.81 tff(1531,plain,
% 0.76/0.81 (![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1530, 1523])).
% 0.76/0.81 tff(1532,plain,
% 0.76/0.81 (((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp13 | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))) <=> ((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp13 | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1533,plain,
% 0.76/0.81 ((hskp21 | hskp13 | (~ndr1_0) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828))) <=> (hskp21 | hskp13 | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1534,plain,
% 0.76/0.81 (((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp13 | (~ndr1_0) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)))) <=> ((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp13 | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828))))),
% 0.76/0.81 inference(monotonicity,[status(thm)],[1533])).
% 0.76/0.81 tff(1535,plain,
% 0.76/0.81 (((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp13 | (~ndr1_0) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)))) <=> ((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp13 | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.76/0.81 inference(transitivity,[status(thm)],[1534, 1532])).
% 0.76/0.81 tff(1536,plain,
% 0.76/0.81 ((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp13 | (~ndr1_0) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)))),
% 0.76/0.81 inference(quant_inst,[status(thm)],[])).
% 0.76/0.81 tff(1537,plain,
% 0.76/0.81 ((~![U: $i] : (hskp21 | hskp13 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp13 | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1536, 1535])).
% 0.76/0.81 tff(1538,plain,
% 0.76/0.81 (hskp21 | hskp13 | (~c3_1(a828))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1537, 163, 1130, 1119, 1531])).
% 0.76/0.81 tff(1539,plain,
% 0.76/0.81 (hskp21),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1538, 1521, 1520])).
% 0.76/0.81 tff(1540,plain,
% 0.76/0.81 (((~hskp21) | (~c2_1(a857))) <=> ((~hskp21) | (~c2_1(a857)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1541,plain,
% 0.76/0.81 (((~c2_1(a857)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a857)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1542,axiom,((~c2_1(a857)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 0.76/0.81 tff(1543,plain,
% 0.76/0.81 ((~hskp21) | (~c2_1(a857))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1542, 1541])).
% 0.76/0.81 tff(1544,plain,
% 0.76/0.81 ((~hskp21) | (~c2_1(a857))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1543, 1540])).
% 0.76/0.81 tff(1545,plain,
% 0.76/0.81 (~c2_1(a857)),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1544, 1539])).
% 0.76/0.81 tff(1546,plain,
% 0.76/0.81 (((~hskp21) | c0_1(a857)) <=> ((~hskp21) | c0_1(a857))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1547,axiom,((~hskp21) | c0_1(a857)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.76/0.81 tff(1548,plain,
% 0.76/0.81 ((~hskp21) | c0_1(a857)),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1547, 1546])).
% 0.76/0.81 tff(1549,plain,
% 0.76/0.81 ((~hskp21) | c0_1(a857)),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1548, 1546])).
% 0.76/0.81 tff(1550,plain,
% 0.76/0.81 ((~hskp21) | c0_1(a857)),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1549, 1546])).
% 0.76/0.81 tff(1551,plain,
% 0.76/0.81 ((~hskp21) | c0_1(a857)),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1550, 1546])).
% 0.76/0.81 tff(1552,plain,
% 0.76/0.81 ((~hskp21) | c0_1(a857)),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1551, 1546])).
% 0.76/0.81 tff(1553,plain,
% 0.76/0.81 ((~hskp21) | c0_1(a857)),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1552, 1546])).
% 0.76/0.81 tff(1554,plain,
% 0.76/0.81 ((~hskp21) | c0_1(a857)),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1553, 1546])).
% 0.76/0.81 tff(1555,plain,
% 0.76/0.81 ((~hskp21) | c0_1(a857)),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1554, 1546])).
% 0.76/0.81 tff(1556,plain,
% 0.76/0.81 (c0_1(a857)),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1555, 1539])).
% 0.76/0.81 tff(1557,plain,
% 0.76/0.81 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | c2_1(a857) | (~ndr1_0) | (~c1_1(a857)) | (~c0_1(a857)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a857) | (~ndr1_0) | (~c1_1(a857)) | (~c0_1(a857)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1558,plain,
% 0.76/0.81 ((hskp29 | hskp19 | (~ndr1_0) | c2_1(a857) | (~c1_1(a857)) | (~c0_1(a857))) <=> (hskp29 | hskp19 | c2_1(a857) | (~ndr1_0) | (~c1_1(a857)) | (~c0_1(a857)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1559,plain,
% 0.76/0.81 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a857) | (~c1_1(a857)) | (~c0_1(a857)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | c2_1(a857) | (~ndr1_0) | (~c1_1(a857)) | (~c0_1(a857))))),
% 0.76/0.81 inference(monotonicity,[status(thm)],[1558])).
% 0.76/0.81 tff(1560,plain,
% 0.76/0.81 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a857) | (~c1_1(a857)) | (~c0_1(a857)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a857) | (~ndr1_0) | (~c1_1(a857)) | (~c0_1(a857)))),
% 0.76/0.81 inference(transitivity,[status(thm)],[1559, 1557])).
% 0.76/0.81 tff(1561,plain,
% 0.76/0.81 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a857) | (~c1_1(a857)) | (~c0_1(a857)))),
% 0.76/0.81 inference(quant_inst,[status(thm)],[])).
% 0.76/0.81 tff(1562,plain,
% 0.76/0.81 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a857) | (~ndr1_0) | (~c1_1(a857)) | (~c0_1(a857))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 0.76/0.81 tff(1563,plain,
% 0.76/0.81 (~c1_1(a857)),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1562, 819, 163, 1295, 1556, 1545, 847])).
% 0.76/0.81 tff(1564,plain,
% 0.76/0.81 (^[U: $i] : refl((hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.76/0.81 inference(bind,[status(th)],[])).
% 0.76/0.81 tff(1565,plain,
% 0.76/0.81 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.81 inference(quant_intro,[status(thm)],[1564])).
% 0.76/0.81 tff(1566,plain,
% 0.76/0.81 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1567,plain,
% 0.76/0.81 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp13) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp13) <=> (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.76/0.81 inference(bind,[status(th)],[])).
% 0.76/0.81 tff(1568,plain,
% 0.76/0.81 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp13) <=> ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.81 inference(quant_intro,[status(thm)],[1567])).
% 0.76/0.81 tff(1569,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp14) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 0.76/0.81 tff(1570,plain,
% 0.76/0.81 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1569, 1568])).
% 0.76/0.81 tff(1571,plain,
% 0.76/0.81 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1570, 1566])).
% 0.76/0.81 tff(1572,plain,(
% 0.76/0.81 ![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.81 inference(skolemize,[status(sab)],[1571])).
% 0.76/0.81 tff(1573,plain,
% 0.76/0.81 (![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1572, 1565])).
% 0.76/0.81 tff(1574,plain,
% 0.76/0.81 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | c0_1(a827) | (~ndr1_0) | (~c3_1(a827)) | (~c1_1(a827)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp13 | c0_1(a827) | (~ndr1_0) | (~c3_1(a827)) | (~c1_1(a827)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1575,plain,
% 0.76/0.81 ((hskp14 | hskp13 | (~ndr1_0) | c0_1(a827) | (~c3_1(a827)) | (~c1_1(a827))) <=> (hskp14 | hskp13 | c0_1(a827) | (~ndr1_0) | (~c3_1(a827)) | (~c1_1(a827)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1576,plain,
% 0.76/0.81 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a827) | (~c3_1(a827)) | (~c1_1(a827)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | c0_1(a827) | (~ndr1_0) | (~c3_1(a827)) | (~c1_1(a827))))),
% 0.76/0.81 inference(monotonicity,[status(thm)],[1575])).
% 0.76/0.81 tff(1577,plain,
% 0.76/0.81 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a827) | (~c3_1(a827)) | (~c1_1(a827)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp13 | c0_1(a827) | (~ndr1_0) | (~c3_1(a827)) | (~c1_1(a827)))),
% 0.76/0.81 inference(transitivity,[status(thm)],[1576, 1574])).
% 0.76/0.81 tff(1578,plain,
% 0.76/0.81 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a827) | (~c3_1(a827)) | (~c1_1(a827)))),
% 0.76/0.81 inference(quant_inst,[status(thm)],[])).
% 0.76/0.81 tff(1579,plain,
% 0.76/0.81 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp13 | c0_1(a827) | (~ndr1_0) | (~c3_1(a827)) | (~c1_1(a827))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1578, 1577])).
% 0.76/0.81 tff(1580,plain,
% 0.76/0.81 (hskp13 | (~c3_1(a827))),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1579, 762, 163, 1482, 1488, 1573])).
% 0.76/0.81 tff(1581,plain,
% 0.76/0.81 (~c3_1(a827)),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1580, 1521])).
% 0.76/0.81 tff(1582,plain,
% 0.76/0.81 (((~hskp21) | (~c3_1(a857))) <=> ((~hskp21) | (~c3_1(a857)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1583,plain,
% 0.76/0.81 (((~c3_1(a857)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a857)))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1584,axiom,((~c3_1(a857)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.76/0.81 tff(1585,plain,
% 0.76/0.81 ((~hskp21) | (~c3_1(a857))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 0.76/0.81 tff(1586,plain,
% 0.76/0.81 ((~hskp21) | (~c3_1(a857))),
% 0.76/0.81 inference(modus_ponens,[status(thm)],[1585, 1582])).
% 0.76/0.81 tff(1587,plain,
% 0.76/0.81 (~c3_1(a857)),
% 0.76/0.81 inference(unit_resolution,[status(thm)],[1586, 1539])).
% 0.76/0.81 tff(1588,plain,
% 0.76/0.81 (((~![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) | c1_1(W))) | (c2_1(a857) | c3_1(a857) | c0_1(a827) | (~ndr1_0) | (~c2_1(a827)) | c3_1(a827) | (~c1_1(a827)) | c1_1(a857))) <=> ((~![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) | c1_1(W))) | c2_1(a857) | c3_1(a857) | c0_1(a827) | (~ndr1_0) | (~c2_1(a827)) | c3_1(a827) | (~c1_1(a827)) | c1_1(a857))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1589,plain,
% 0.76/0.81 (((~ndr1_0) | c3_1(a827) | (~c2_1(a827)) | (~c1_1(a827)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a857) | c2_1(a857) | c1_1(a857)) <=> (c2_1(a857) | c3_1(a857) | c0_1(a827) | (~ndr1_0) | (~c2_1(a827)) | c3_1(a827) | (~c1_1(a827)) | c1_1(a857))),
% 0.76/0.81 inference(rewrite,[status(thm)],[])).
% 0.76/0.81 tff(1590,plain,
% 0.76/0.81 (((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a827) | (~c2_1(a827)) | (~c1_1(a827)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a857) | c2_1(a857) | c1_1(a857))) <=> ((~![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) | c1_1(W))) | (c2_1(a857) | c3_1(a857) | c0_1(a827) | (~ndr1_0) | (~c2_1(a827)) | c3_1(a827) | (~c1_1(a827)) | c1_1(a857)))),
% 0.76/0.81 inference(monotonicity,[status(thm)],[1589])).
% 0.76/0.81 tff(1591,plain,
% 0.76/0.81 (((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a827) | (~c2_1(a827)) | (~c1_1(a827)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a857) | c2_1(a857) | c1_1(a857))) <=> ((~![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) | c1_1(W))) | c2_1(a857) | c3_1(a857) | c0_1(a827) | (~ndr1_0) | (~c2_1(a827)) | c3_1(a827) | (~c1_1(a827)) | c1_1(a857))),
% 0.76/0.82 inference(transitivity,[status(thm)],[1590, 1588])).
% 0.76/0.82 tff(1592,plain,
% 0.76/0.82 ((~![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) | c1_1(W))) | ((~ndr1_0) | c3_1(a827) | (~c2_1(a827)) | (~c1_1(a827)) | c0_1(a827) | c3_1(a827) | (~c2_1(a827)) | c3_1(a857) | c2_1(a857) | c1_1(a857))),
% 0.76/0.82 inference(quant_inst,[status(thm)],[])).
% 0.76/0.82 tff(1593,plain,
% 0.76/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | c3_1(V) | (~c2_1(V)) | c3_1(W) | c2_1(W) | c1_1(W))) | c2_1(a857) | c3_1(a857) | c0_1(a827) | (~ndr1_0) | (~c2_1(a827)) | c3_1(a827) | (~c1_1(a827)) | c1_1(a857)),
% 0.76/0.82 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 0.76/0.82 tff(1594,plain,
% 0.76/0.82 ($false),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1593, 163, 1482, 1499, 1545, 1587, 1488, 516, 1581, 1563])).
% 0.76/0.82 tff(1595,plain,(hskp13 | hskp29 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.76/0.82 tff(1596,plain,
% 0.76/0.82 (hskp13),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1595, 819, 762])).
% 0.76/0.82 tff(1597,plain,
% 0.76/0.82 (~c2_1(a839)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1350, 1596])).
% 0.76/0.82 tff(1598,plain,
% 0.76/0.82 (c1_1(a839)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1372, 1596])).
% 0.76/0.82 tff(1599,plain,
% 0.76/0.82 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | c2_1(a839) | (~ndr1_0) | (~c1_1(a839)) | (~c0_1(a839)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a839) | (~ndr1_0) | (~c1_1(a839)) | (~c0_1(a839)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1600,plain,
% 0.76/0.82 ((hskp29 | hskp19 | (~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839))) <=> (hskp29 | hskp19 | c2_1(a839) | (~ndr1_0) | (~c1_1(a839)) | (~c0_1(a839)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1601,plain,
% 0.76/0.82 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | c2_1(a839) | (~ndr1_0) | (~c1_1(a839)) | (~c0_1(a839))))),
% 0.76/0.82 inference(monotonicity,[status(thm)],[1600])).
% 0.76/0.82 tff(1602,plain,
% 0.76/0.82 (((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)))) <=> ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a839) | (~ndr1_0) | (~c1_1(a839)) | (~c0_1(a839)))),
% 0.76/0.82 inference(transitivity,[status(thm)],[1601, 1599])).
% 0.76/0.82 tff(1603,plain,
% 0.76/0.82 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp19 | (~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)))),
% 0.76/0.82 inference(quant_inst,[status(thm)],[])).
% 0.76/0.82 tff(1604,plain,
% 0.76/0.82 ((~![U: $i] : (hskp29 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp19 | c2_1(a839) | (~ndr1_0) | (~c1_1(a839)) | (~c0_1(a839))),
% 0.76/0.82 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 0.76/0.82 tff(1605,plain,
% 0.76/0.82 (~c0_1(a839)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1604, 819, 163, 1295, 1598, 1597, 847])).
% 0.76/0.82 tff(1606,plain,
% 0.76/0.82 (c3_1(a839)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1361, 1596])).
% 0.76/0.82 tff(1607,plain,
% 0.76/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a839) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | (~c1_1(a839)) | c0_1(a839) | (~c3_1(a839)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a839) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | (~c1_1(a839)) | c0_1(a839) | (~c3_1(a839)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1608,plain,
% 0.76/0.82 (((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a839) | c0_1(a839) | (~c3_1(a839))) <=> (c2_1(a839) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | (~c1_1(a839)) | c0_1(a839) | (~c3_1(a839)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1609,plain,
% 0.76/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a839) | c0_1(a839) | (~c3_1(a839)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a839) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | (~c1_1(a839)) | c0_1(a839) | (~c3_1(a839))))),
% 0.76/0.82 inference(monotonicity,[status(thm)],[1608])).
% 0.76/0.82 tff(1610,plain,
% 0.76/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a839) | c0_1(a839) | (~c3_1(a839)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a839) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | (~c1_1(a839)) | c0_1(a839) | (~c3_1(a839)))),
% 0.76/0.82 inference(transitivity,[status(thm)],[1609, 1607])).
% 0.76/0.82 tff(1611,plain,
% 0.76/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c3_1(a839)) | (~c1_1(a839)) | c1_1(a828) | (~c3_1(a828)) | (~c0_1(a828)) | c2_1(a839) | c0_1(a839) | (~c3_1(a839)))),
% 0.76/0.82 inference(quant_inst,[status(thm)],[])).
% 0.76/0.82 tff(1612,plain,
% 0.76/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a839) | c1_1(a828) | (~ndr1_0) | (~c0_1(a828)) | (~c3_1(a828)) | (~c1_1(a839)) | c0_1(a839) | (~c3_1(a839))),
% 0.76/0.82 inference(modus_ponens,[status(thm)],[1611, 1610])).
% 0.76/0.82 tff(1613,plain,
% 0.76/0.82 ($false),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1612, 163, 1598, 1606, 1130, 1597, 1119, 1285, 1520, 1605])).
% 0.76/0.82 tff(1614,plain,(hskp29 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.76/0.82 tff(1615,plain,
% 0.76/0.82 (hskp29),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1614, 762])).
% 0.76/0.82 tff(1616,plain,
% 0.76/0.82 (c3_1(a865)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[374, 1615])).
% 0.76/0.82 tff(1617,plain,
% 0.76/0.82 (c1_1(a865)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[396, 1615])).
% 0.76/0.82 tff(1618,plain,
% 0.76/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a860)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a860)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1619,plain,
% 0.76/0.82 (((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828))) <=> (c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a860)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1620,plain,
% 0.76/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a860))))),
% 0.76/0.82 inference(monotonicity,[status(thm)],[1619])).
% 0.76/0.82 tff(1621,plain,
% 0.76/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a860)))),
% 0.76/0.82 inference(transitivity,[status(thm)],[1620, 1618])).
% 0.76/0.82 tff(1622,plain,
% 0.76/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))),
% 0.76/0.82 inference(quant_inst,[status(thm)],[])).
% 0.76/0.82 tff(1623,plain,
% 0.76/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a860) | c2_1(a860) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a860))),
% 0.76/0.82 inference(modus_ponens,[status(thm)],[1622, 1621])).
% 0.76/0.82 tff(1624,plain,
% 0.76/0.82 (~c0_1(a865)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1623, 163, 1617, 1616, 1130, 1383, 1392, 1119, 1113, 44, 1391])).
% 0.76/0.82 tff(1625,plain,
% 0.76/0.82 (((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a865) | (~c3_1(a865)) | (~c1_1(a865)))) <=> ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp13 | (~ndr1_0) | c0_1(a865) | (~c3_1(a865)) | (~c1_1(a865)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1626,plain,
% 0.76/0.82 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp14 | hskp13 | (~ndr1_0) | c0_1(a865) | (~c3_1(a865)) | (~c1_1(a865)))),
% 0.76/0.82 inference(quant_inst,[status(thm)],[])).
% 0.76/0.82 tff(1627,plain,
% 0.76/0.82 ((~![U: $i] : (hskp14 | hskp13 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp14 | hskp13 | (~ndr1_0) | c0_1(a865) | (~c3_1(a865)) | (~c1_1(a865))),
% 0.76/0.82 inference(modus_ponens,[status(thm)],[1626, 1625])).
% 0.76/0.82 tff(1628,plain,
% 0.76/0.82 (hskp13 | c0_1(a865)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1627, 762, 163, 1617, 1616, 1573])).
% 0.76/0.82 tff(1629,plain,
% 0.76/0.82 (hskp13),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1628, 1624])).
% 0.76/0.82 tff(1630,plain,
% 0.76/0.82 (~c2_1(a839)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1350, 1629])).
% 0.76/0.82 tff(1631,plain,
% 0.76/0.82 (c1_1(a839)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1372, 1629])).
% 0.76/0.82 tff(1632,plain,
% 0.76/0.82 (c2_1(a865)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[385, 1615])).
% 0.76/0.82 tff(1633,plain,
% 0.76/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a860) | c2_1(a860) | c2_1(a839) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a839)) | (~c0_1(a839)) | (~c3_1(a860)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a860) | c2_1(a860) | c2_1(a839) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a839)) | (~c0_1(a839)) | (~c3_1(a860)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1634,plain,
% 0.76/0.82 (((~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865))) <=> (c1_1(a860) | c2_1(a860) | c2_1(a839) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a839)) | (~c0_1(a839)) | (~c3_1(a860)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1635,plain,
% 0.76/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c1_1(a860) | c2_1(a860) | c2_1(a839) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a839)) | (~c0_1(a839)) | (~c3_1(a860))))),
% 0.76/0.82 inference(monotonicity,[status(thm)],[1634])).
% 0.76/0.82 tff(1636,plain,
% 0.76/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a860) | c2_1(a860) | c2_1(a839) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a839)) | (~c0_1(a839)) | (~c3_1(a860)))),
% 0.76/0.82 inference(transitivity,[status(thm)],[1635, 1633])).
% 0.76/0.82 tff(1637,plain,
% 0.76/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a839) | (~c1_1(a839)) | (~c0_1(a839)) | c2_1(a860) | c1_1(a860) | (~c3_1(a860)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))),
% 0.76/0.82 inference(quant_inst,[status(thm)],[])).
% 0.76/0.82 tff(1638,plain,
% 0.76/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c1_1(a860) | c2_1(a860) | c2_1(a839) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c1_1(a839)) | (~c0_1(a839)) | (~c3_1(a860))),
% 0.76/0.82 inference(modus_ponens,[status(thm)],[1637, 1636])).
% 0.76/0.82 tff(1639,plain,
% 0.76/0.82 (~c0_1(a839)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1638, 163, 1617, 1632, 1631, 1383, 1392, 1630, 87, 1391, 1624])).
% 0.76/0.82 tff(1640,plain,
% 0.76/0.82 (c3_1(a839)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1361, 1629])).
% 0.76/0.82 tff(1641,plain,
% 0.76/0.82 ($false),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1612, 163, 1631, 1640, 1130, 1630, 1119, 1285, 1520, 1639])).
% 0.76/0.82 tff(1642,plain,(hskp14), inference(lemma,lemma(discharge,[]))).
% 0.76/0.82 tff(1643,plain,
% 0.76/0.82 (~c2_1(a842)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[54, 1642])).
% 0.76/0.82 tff(1644,plain,
% 0.76/0.82 (c1_1(a842)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[65, 1642])).
% 0.76/0.82 tff(1645,plain,
% 0.76/0.82 (c0_1(a842)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[76, 1642])).
% 0.76/0.82 tff(1646,plain,
% 0.76/0.82 (~hskp20),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[280, 1645, 1644, 1643])).
% 0.76/0.82 tff(1647,plain,
% 0.76/0.82 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c0_1(a826)) | c1_1(a826))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c0_1(a826)) | c1_1(a826))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1648,plain,
% 0.76/0.82 ((hskp20 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826) | (~c3_1(a826)) | (~c0_1(a826))) <=> (hskp20 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c0_1(a826)) | c1_1(a826))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1649,plain,
% 0.76/0.82 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826) | (~c3_1(a826)) | (~c0_1(a826)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c0_1(a826)) | c1_1(a826)))),
% 0.76/0.82 inference(monotonicity,[status(thm)],[1648])).
% 0.76/0.82 tff(1650,plain,
% 0.76/0.82 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826) | (~c3_1(a826)) | (~c0_1(a826)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c0_1(a826)) | c1_1(a826))),
% 0.76/0.82 inference(transitivity,[status(thm)],[1649, 1647])).
% 0.76/0.82 tff(1651,plain,
% 0.76/0.82 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c1_1(a826) | (~c2_1(a826)) | (~c3_1(a826)) | c1_1(a826) | (~c3_1(a826)) | (~c0_1(a826)))),
% 0.76/0.82 inference(quant_inst,[status(thm)],[])).
% 0.76/0.82 tff(1652,plain,
% 0.76/0.82 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp20 | (~ndr1_0) | (~c2_1(a826)) | (~c3_1(a826)) | (~c0_1(a826)) | c1_1(a826)),
% 0.76/0.82 inference(modus_ponens,[status(thm)],[1651, 1650])).
% 0.76/0.82 tff(1653,plain,
% 0.76/0.82 ($false),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1652, 163, 1646, 1188, 1170, 1159, 944, 1177])).
% 0.76/0.82 tff(1654,plain,(c3_1(a828)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.82 tff(1655,plain,
% 0.76/0.82 (hskp9),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1204, 1654])).
% 0.76/0.82 tff(1656,plain,
% 0.76/0.82 (~c1_1(a831)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[243, 1655])).
% 0.76/0.82 tff(1657,plain,
% 0.76/0.82 (~c0_1(a831)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[249, 1655])).
% 0.76/0.82 tff(1658,plain,
% 0.76/0.82 (c3_1(a831)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[260, 1655])).
% 0.76/0.82 tff(1659,plain,
% 0.76/0.82 (~hskp19),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1294, 1658, 1657, 1656])).
% 0.76/0.82 tff(1660,plain,
% 0.76/0.82 (hskp29 | hskp19),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[853, 163, 1645, 1644, 1643, 847])).
% 0.76/0.82 tff(1661,plain,
% 0.76/0.82 (hskp29),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[1660, 1659])).
% 0.76/0.82 tff(1662,plain,
% 0.76/0.82 (c3_1(a865)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[374, 1661])).
% 0.76/0.82 tff(1663,plain,
% 0.76/0.82 (c1_1(a865)),
% 0.76/0.82 inference(unit_resolution,[status(thm)],[396, 1661])).
% 0.76/0.82 tff(1664,plain,
% 0.76/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1665,plain,
% 0.76/0.82 (((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828))) <=> (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.76/0.82 inference(rewrite,[status(thm)],[])).
% 0.76/0.82 tff(1666,plain,
% 0.76/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a828))))),
% 0.76/0.83 inference(monotonicity,[status(thm)],[1665])).
% 0.76/0.83 tff(1667,plain,
% 0.76/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a828)))),
% 0.76/0.83 inference(transitivity,[status(thm)],[1666, 1664])).
% 0.76/0.83 tff(1668,plain,
% 0.76/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c2_1(a828) | c1_1(a828) | (~c0_1(a828)))),
% 0.76/0.83 inference(quant_inst,[status(thm)],[])).
% 0.76/0.83 tff(1669,plain,
% 0.76/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c2_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | (~c3_1(a865)) | (~c1_1(a865)) | (~c0_1(a865)) | (~c0_1(a828)) | (~c3_1(a828))),
% 0.76/0.83 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 0.76/0.83 tff(1670,plain,
% 0.76/0.83 (~c0_1(a865)),
% 0.76/0.83 inference(unit_resolution,[status(thm)],[1669, 163, 1663, 1662, 1130, 1119, 1113, 44, 1654])).
% 0.76/0.83 tff(1671,plain,
% 0.76/0.83 (c2_1(a865)),
% 0.76/0.83 inference(unit_resolution,[status(thm)],[385, 1661])).
% 0.76/0.83 tff(1672,plain,
% 0.76/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a842) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c3_1(a828)) | (~c1_1(a842)) | (~c0_1(a842)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a842) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c3_1(a828)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.76/0.83 inference(rewrite,[status(thm)],[])).
% 0.76/0.83 tff(1673,plain,
% 0.76/0.83 (((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865))) <=> (c2_1(a842) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c3_1(a828)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.76/0.83 inference(rewrite,[status(thm)],[])).
% 0.76/0.83 tff(1674,plain,
% 0.76/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c2_1(a842) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c3_1(a828)) | (~c1_1(a842)) | (~c0_1(a842))))),
% 0.76/0.83 inference(monotonicity,[status(thm)],[1673])).
% 0.76/0.83 tff(1675,plain,
% 0.76/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a842) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c3_1(a828)) | (~c1_1(a842)) | (~c0_1(a842)))),
% 0.76/0.83 inference(transitivity,[status(thm)],[1674, 1672])).
% 0.76/0.83 tff(1676,plain,
% 0.76/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a842) | (~c1_1(a842)) | (~c0_1(a842)) | c2_1(a828) | c1_1(a828) | (~c3_1(a828)) | c0_1(a865) | (~c2_1(a865)) | (~c1_1(a865)))),
% 0.76/0.83 inference(quant_inst,[status(thm)],[])).
% 0.76/0.83 tff(1677,plain,
% 0.76/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c2_1(a842) | c1_1(a828) | c2_1(a828) | (~ndr1_0) | c0_1(a865) | (~c1_1(a865)) | (~c2_1(a865)) | (~c3_1(a828)) | (~c1_1(a842)) | (~c0_1(a842))),
% 0.76/0.83 inference(modus_ponens,[status(thm)],[1676, 1675])).
% 0.76/0.83 tff(1678,plain,
% 0.76/0.83 ($false),
% 0.76/0.83 inference(unit_resolution,[status(thm)],[1677, 163, 1663, 1671, 1645, 1644, 1643, 1119, 1113, 87, 1654, 1670])).
% 0.76/0.83 % SZS output end Proof
%------------------------------------------------------------------------------