TSTP Solution File: SYN511-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN511-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 23:56:05 EDT 2022
% Result : Unsatisfiable 0.65s 0.71s
% Output : Proof 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN511-1 : TPTP v8.1.0. Released v2.1.0.
% 0.00/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 04:48:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.65/0.71 % SZS status Unsatisfiable
% 0.65/0.71 % SZS output start Proof
% 0.65/0.71 tff(c2_1_type, type, (
% 0.65/0.71 c2_1: $i > $o)).
% 0.65/0.71 tff(a681_type, type, (
% 0.65/0.71 a681: $i)).
% 0.65/0.71 tff(hskp10_type, type, (
% 0.65/0.71 hskp10: $o)).
% 0.65/0.71 tff(c0_1_type, type, (
% 0.65/0.71 c0_1: $i > $o)).
% 0.65/0.71 tff(a680_type, type, (
% 0.65/0.71 a680: $i)).
% 0.65/0.71 tff(a678_type, type, (
% 0.65/0.71 a678: $i)).
% 0.65/0.71 tff(c3_1_type, type, (
% 0.65/0.71 c3_1: $i > $o)).
% 0.65/0.71 tff(c1_1_type, type, (
% 0.65/0.71 c1_1: $i > $o)).
% 0.65/0.71 tff(ndr1_0_type, type, (
% 0.65/0.71 ndr1_0: $o)).
% 0.65/0.71 tff(hskp28_type, type, (
% 0.65/0.71 hskp28: $o)).
% 0.65/0.71 tff(a683_type, type, (
% 0.65/0.71 a683: $i)).
% 0.65/0.71 tff(hskp11_type, type, (
% 0.65/0.71 hskp11: $o)).
% 0.65/0.71 tff(a675_type, type, (
% 0.65/0.71 a675: $i)).
% 0.65/0.71 tff(hskp7_type, type, (
% 0.65/0.71 hskp7: $o)).
% 0.65/0.71 tff(a760_type, type, (
% 0.65/0.71 a760: $i)).
% 0.65/0.71 tff(hskp25_type, type, (
% 0.65/0.71 hskp25: $o)).
% 0.65/0.71 tff(hskp5_type, type, (
% 0.65/0.71 hskp5: $o)).
% 0.65/0.71 tff(a673_type, type, (
% 0.65/0.71 a673: $i)).
% 0.65/0.71 tff(hskp30_type, type, (
% 0.65/0.71 hskp30: $o)).
% 0.65/0.71 tff(hskp8_type, type, (
% 0.65/0.71 hskp8: $o)).
% 0.65/0.71 tff(hskp9_type, type, (
% 0.65/0.71 hskp9: $o)).
% 0.65/0.71 tff(a703_type, type, (
% 0.65/0.71 a703: $i)).
% 0.65/0.71 tff(a688_type, type, (
% 0.65/0.71 a688: $i)).
% 0.65/0.71 tff(hskp13_type, type, (
% 0.65/0.71 hskp13: $o)).
% 0.65/0.71 tff(hskp17_type, type, (
% 0.65/0.71 hskp17: $o)).
% 0.65/0.71 tff(hskp14_type, type, (
% 0.65/0.71 hskp14: $o)).
% 0.65/0.71 tff(a696_type, type, (
% 0.65/0.71 a696: $i)).
% 0.65/0.71 tff(a679_type, type, (
% 0.65/0.71 a679: $i)).
% 0.65/0.71 tff(a670_type, type, (
% 0.65/0.71 a670: $i)).
% 0.65/0.71 tff(hskp2_type, type, (
% 0.65/0.71 hskp2: $o)).
% 0.65/0.71 tff(a702_type, type, (
% 0.65/0.71 a702: $i)).
% 0.65/0.71 tff(a669_type, type, (
% 0.65/0.71 a669: $i)).
% 0.65/0.71 tff(hskp1_type, type, (
% 0.65/0.71 hskp1: $o)).
% 0.65/0.71 tff(hskp16_type, type, (
% 0.65/0.71 hskp16: $o)).
% 0.65/0.71 tff(a715_type, type, (
% 0.65/0.71 a715: $i)).
% 0.65/0.71 tff(hskp21_type, type, (
% 0.65/0.71 hskp21: $o)).
% 0.65/0.71 tff(a725_type, type, (
% 0.65/0.71 a725: $i)).
% 0.65/0.71 tff(hskp29_type, type, (
% 0.65/0.71 hskp29: $o)).
% 0.65/0.71 tff(hskp0_type, type, (
% 0.65/0.71 hskp0: $o)).
% 0.65/0.71 tff(a668_type, type, (
% 0.65/0.71 a668: $i)).
% 0.65/0.71 tff(1,assumption,(c2_1(a678)), introduced(assumption)).
% 0.65/0.71 tff(2,plain,
% 0.65/0.71 (^[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))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V))))),
% 0.65/0.71 inference(bind,[status(th)],[])).
% 0.65/0.71 tff(3,plain,
% 0.65/0.71 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.71 inference(quant_intro,[status(thm)],[2])).
% 0.65/0.71 tff(4,plain,
% 0.65/0.71 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(5,plain,
% 0.65/0.71 (^[V: $i, U: $i] : 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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.65/0.71 inference(bind,[status(th)],[])).
% 0.65/0.71 tff(6,plain,
% 0.65/0.71 (![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.71 inference(quant_intro,[status(thm)],[5])).
% 0.65/0.71 tff(7,axiom,(![V: $i, U: $i] : (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 0.65/0.71 tff(8,plain,
% 0.65/0.71 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.65/0.71 tff(9,plain,
% 0.65/0.71 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.65/0.71 tff(10,plain,(
% 0.65/0.71 ![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.71 inference(skolemize,[status(sab)],[9])).
% 0.65/0.71 tff(11,plain,
% 0.65/0.71 (![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.65/0.71 tff(12,assumption,(~hskp28), introduced(assumption)).
% 0.65/0.71 tff(13,plain,
% 0.65/0.71 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W))))),
% 0.65/0.71 inference(bind,[status(th)],[])).
% 0.65/0.71 tff(14,plain,
% 0.65/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_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)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.65/0.71 inference(quant_intro,[status(thm)],[13])).
% 0.65/0.71 tff(15,plain,
% 0.65/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_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)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.65/0.71 inference(rewrite,[status(thm)],[])).
% 0.65/0.71 tff(16,plain,
% 0.65/0.71 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))))),
% 0.65/0.71 inference(bind,[status(th)],[])).
% 0.65/0.71 tff(17,plain,
% 0.65/0.71 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.65/0.71 inference(quant_intro,[status(thm)],[16])).
% 0.65/0.71 tff(18,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c0_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause204')).
% 0.65/0.71 tff(19,plain,
% 0.65/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.65/0.71 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.76/0.71 tff(20,plain,
% 0.76/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.76/0.71 tff(21,plain,(
% 0.76/0.71 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.76/0.71 inference(skolemize,[status(sab)],[20])).
% 0.76/0.71 tff(22,plain,
% 0.76/0.71 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.76/0.71 tff(23,plain,
% 0.76/0.71 (^[U: $i] : refl((hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.76/0.71 inference(bind,[status(th)],[])).
% 0.76/0.71 tff(24,plain,
% 0.76/0.71 (![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.71 inference(quant_intro,[status(thm)],[23])).
% 0.76/0.71 tff(25,plain,
% 0.76/0.71 (![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(26,plain,
% 0.76/0.71 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp10) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp10))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp10) <=> (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp10) <=> (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.76/0.71 inference(bind,[status(th)],[])).
% 0.76/0.71 tff(27,plain,
% 0.76/0.71 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp10) <=> ![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.71 inference(quant_intro,[status(thm)],[26])).
% 0.76/0.71 tff(28,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp28) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.76/0.71 tff(29,plain,
% 0.76/0.71 (![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.76/0.71 tff(30,plain,
% 0.76/0.71 (![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.76/0.71 tff(31,plain,(
% 0.76/0.71 ![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.71 inference(skolemize,[status(sab)],[30])).
% 0.76/0.71 tff(32,plain,
% 0.76/0.71 (![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.76/0.71 tff(33,plain,
% 0.76/0.71 (^[U: $i] : refl((hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))),
% 0.76/0.71 inference(bind,[status(th)],[])).
% 0.76/0.71 tff(34,plain,
% 0.76/0.71 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.76/0.71 inference(quant_intro,[status(thm)],[33])).
% 0.76/0.71 tff(35,plain,
% 0.76/0.71 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(36,plain,
% 0.76/0.71 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp7) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U)) | hskp7) <=> (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp7) <=> (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))))),
% 0.76/0.71 inference(bind,[status(th)],[])).
% 0.76/0.71 tff(37,plain,
% 0.76/0.71 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp7) <=> ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.76/0.71 inference(quant_intro,[status(thm)],[36])).
% 0.76/0.71 tff(38,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp28) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.76/0.71 tff(39,plain,
% 0.76/0.71 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.76/0.71 tff(40,plain,
% 0.76/0.71 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.76/0.71 tff(41,plain,(
% 0.76/0.71 ![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.76/0.71 inference(skolemize,[status(sab)],[40])).
% 0.76/0.71 tff(42,plain,
% 0.76/0.71 (![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.76/0.71 tff(43,assumption,(~hskp7), introduced(assumption)).
% 0.76/0.71 tff(44,assumption,(hskp5), introduced(assumption)).
% 0.76/0.71 tff(45,plain,
% 0.76/0.71 (((~hskp5) | (~c3_1(a673))) <=> ((~hskp5) | (~c3_1(a673)))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(46,plain,
% 0.76/0.71 (((~c3_1(a673)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a673)))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(47,axiom,((~c3_1(a673)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 0.76/0.71 tff(48,plain,
% 0.76/0.71 ((~hskp5) | (~c3_1(a673))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.76/0.71 tff(49,plain,
% 0.76/0.71 ((~hskp5) | (~c3_1(a673))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[48, 45])).
% 0.76/0.71 tff(50,plain,
% 0.76/0.71 (~c3_1(a673)),
% 0.76/0.71 inference(unit_resolution,[status(thm)],[49, 44])).
% 0.76/0.71 tff(51,plain,
% 0.76/0.71 (((~hskp5) | (~c2_1(a673))) <=> ((~hskp5) | (~c2_1(a673)))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(52,plain,
% 0.76/0.71 (((~c2_1(a673)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a673)))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(53,axiom,((~c2_1(a673)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.76/0.71 tff(54,plain,
% 0.76/0.71 ((~hskp5) | (~c2_1(a673))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.76/0.71 tff(55,plain,
% 0.76/0.71 ((~hskp5) | (~c2_1(a673))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[54, 51])).
% 0.76/0.71 tff(56,plain,
% 0.76/0.71 (~c2_1(a673)),
% 0.76/0.71 inference(unit_resolution,[status(thm)],[55, 44])).
% 0.76/0.71 tff(57,plain,
% 0.76/0.71 (((~hskp5) | (~c0_1(a673))) <=> ((~hskp5) | (~c0_1(a673)))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(58,plain,
% 0.76/0.71 (((~c0_1(a673)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a673)))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(59,axiom,((~c0_1(a673)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.76/0.71 tff(60,plain,
% 0.76/0.71 ((~hskp5) | (~c0_1(a673))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.76/0.71 tff(61,plain,
% 0.76/0.71 ((~hskp5) | (~c0_1(a673))),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[60, 57])).
% 0.76/0.71 tff(62,plain,
% 0.76/0.71 (~c0_1(a673)),
% 0.76/0.71 inference(unit_resolution,[status(thm)],[61, 44])).
% 0.76/0.71 tff(63,assumption,(~ndr1_0), introduced(assumption)).
% 0.76/0.71 tff(64,plain,
% 0.76/0.71 ((ndr1_0 | (~hskp11)) <=> (ndr1_0 | (~hskp11))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(65,plain,
% 0.76/0.71 (((~hskp11) | ndr1_0) <=> (ndr1_0 | (~hskp11))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(66,axiom,((~hskp11) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause20')).
% 0.76/0.71 tff(67,plain,
% 0.76/0.71 (ndr1_0 | (~hskp11)),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.76/0.71 tff(68,plain,
% 0.76/0.71 (ndr1_0 | (~hskp11)),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[67, 64])).
% 0.76/0.71 tff(69,plain,
% 0.76/0.71 (~hskp11),
% 0.76/0.71 inference(unit_resolution,[status(thm)],[68, 63])).
% 0.76/0.71 tff(70,plain,
% 0.76/0.71 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(71,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 0.76/0.71 tff(72,plain,
% 0.76/0.71 ((~hskp30) | ndr1_0),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.76/0.71 tff(73,plain,
% 0.76/0.71 ((~hskp30) | ndr1_0),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[72, 70])).
% 0.76/0.71 tff(74,plain,
% 0.76/0.71 ((~hskp30) | ndr1_0),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[73, 70])).
% 0.76/0.71 tff(75,plain,
% 0.76/0.71 ((~hskp30) | ndr1_0),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.76/0.71 tff(76,plain,
% 0.76/0.71 ((~hskp30) | ndr1_0),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[75, 70])).
% 0.76/0.71 tff(77,plain,
% 0.76/0.71 ((~hskp30) | ndr1_0),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[76, 70])).
% 0.76/0.71 tff(78,plain,
% 0.76/0.71 ((~hskp30) | ndr1_0),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.76/0.71 tff(79,plain,
% 0.76/0.71 ((~hskp30) | ndr1_0),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[78, 70])).
% 0.76/0.71 tff(80,plain,
% 0.76/0.71 (~hskp30),
% 0.76/0.71 inference(unit_resolution,[status(thm)],[79, 63])).
% 0.76/0.71 tff(81,plain,
% 0.76/0.71 ((ndr1_0 | (~hskp28)) <=> (ndr1_0 | (~hskp28))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(82,plain,
% 0.76/0.71 (((~hskp28) | ndr1_0) <=> (ndr1_0 | (~hskp28))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(83,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause3')).
% 0.76/0.71 tff(84,plain,
% 0.76/0.71 (ndr1_0 | (~hskp28)),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.76/0.71 tff(85,plain,
% 0.76/0.71 (ndr1_0 | (~hskp28)),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[84, 81])).
% 0.76/0.71 tff(86,plain,
% 0.76/0.71 (~hskp28),
% 0.76/0.71 inference(unit_resolution,[status(thm)],[85, 63])).
% 0.76/0.71 tff(87,plain,
% 0.76/0.71 ((hskp30 | hskp28 | hskp11) <=> (hskp30 | hskp28 | hskp11)),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(88,plain,
% 0.76/0.71 (((hskp28 | hskp30) | hskp11) <=> (hskp30 | hskp28 | hskp11)),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(89,axiom,((hskp28 | hskp30) | hskp11), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 0.76/0.71 tff(90,plain,
% 0.76/0.71 (hskp30 | hskp28 | hskp11),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.76/0.71 tff(91,plain,
% 0.76/0.71 (hskp30 | hskp28 | hskp11),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[90, 87])).
% 0.76/0.71 tff(92,plain,
% 0.76/0.71 (hskp30 | hskp28 | hskp11),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.76/0.71 tff(93,plain,
% 0.76/0.71 (hskp30 | hskp28 | hskp11),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[92, 87])).
% 0.76/0.71 tff(94,plain,
% 0.76/0.71 (hskp30 | hskp28 | hskp11),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[93, 87])).
% 0.76/0.71 tff(95,plain,
% 0.76/0.71 (hskp30 | hskp28 | hskp11),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.76/0.71 tff(96,plain,
% 0.76/0.71 (hskp30 | hskp28 | hskp11),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[95, 87])).
% 0.76/0.71 tff(97,plain,
% 0.76/0.71 (hskp30 | hskp28 | hskp11),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[96, 87])).
% 0.76/0.71 tff(98,plain,
% 0.76/0.71 ($false),
% 0.76/0.71 inference(unit_resolution,[status(thm)],[97, 86, 80, 69])).
% 0.76/0.71 tff(99,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.76/0.71 tff(100,plain,
% 0.76/0.71 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | c0_1(a673) | c2_1(a673) | c3_1(a673) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp7 | c0_1(a673) | c2_1(a673) | c3_1(a673) | (~ndr1_0))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(101,plain,
% 0.76/0.71 ((hskp28 | hskp7 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | c3_1(a673)) <=> (hskp28 | hskp7 | c0_1(a673) | c2_1(a673) | c3_1(a673) | (~ndr1_0))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(102,plain,
% 0.76/0.71 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | c3_1(a673))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | c0_1(a673) | c2_1(a673) | c3_1(a673) | (~ndr1_0)))),
% 0.76/0.71 inference(monotonicity,[status(thm)],[101])).
% 0.76/0.71 tff(103,plain,
% 0.76/0.71 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | c3_1(a673))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp7 | c0_1(a673) | c2_1(a673) | c3_1(a673) | (~ndr1_0))),
% 0.76/0.71 inference(transitivity,[status(thm)],[102, 100])).
% 0.76/0.71 tff(104,plain,
% 0.76/0.71 ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | c3_1(a673))),
% 0.76/0.71 inference(quant_inst,[status(thm)],[])).
% 0.76/0.71 tff(105,plain,
% 0.76/0.71 ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp7 | c0_1(a673) | c2_1(a673) | c3_1(a673) | (~ndr1_0)),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.76/0.71 tff(106,plain,
% 0.76/0.71 ($false),
% 0.76/0.71 inference(unit_resolution,[status(thm)],[105, 99, 12, 43, 62, 56, 50, 42])).
% 0.76/0.71 tff(107,plain,((~hskp5) | hskp28 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.76/0.71 tff(108,plain,
% 0.76/0.71 (~hskp5),
% 0.76/0.71 inference(unit_resolution,[status(thm)],[107, 43, 12])).
% 0.76/0.71 tff(109,plain,
% 0.76/0.71 ((hskp25 | hskp7 | hskp5) <=> (hskp25 | hskp7 | hskp5)),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(110,plain,
% 0.76/0.71 (((hskp25 | hskp7) | hskp5) <=> (hskp25 | hskp7 | hskp5)),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(111,plain,
% 0.76/0.71 ((hskp7 | hskp25) <=> (hskp25 | hskp7)),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(112,plain,
% 0.76/0.71 (((hskp7 | hskp25) | hskp5) <=> ((hskp25 | hskp7) | hskp5)),
% 0.76/0.71 inference(monotonicity,[status(thm)],[111])).
% 0.76/0.71 tff(113,plain,
% 0.76/0.71 (((hskp7 | hskp25) | hskp5) <=> (hskp25 | hskp7 | hskp5)),
% 0.76/0.71 inference(transitivity,[status(thm)],[112, 110])).
% 0.76/0.71 tff(114,axiom,((hskp7 | hskp25) | hskp5), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 0.76/0.71 tff(115,plain,
% 0.76/0.71 (hskp25 | hskp7 | hskp5),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.76/0.71 tff(116,plain,
% 0.76/0.71 (hskp25 | hskp7 | hskp5),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[115, 109])).
% 0.76/0.71 tff(117,plain,
% 0.76/0.71 (hskp25 | hskp7 | hskp5),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.76/0.71 tff(118,plain,
% 0.76/0.71 (hskp25 | hskp7 | hskp5),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[117, 109])).
% 0.76/0.71 tff(119,plain,
% 0.76/0.71 (hskp25 | hskp7 | hskp5),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[118, 109])).
% 0.76/0.71 tff(120,plain,
% 0.76/0.71 (hskp25 | hskp7 | hskp5),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[119, 109])).
% 0.76/0.71 tff(121,plain,
% 0.76/0.71 (hskp25 | hskp7 | hskp5),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[120, 109])).
% 0.76/0.71 tff(122,plain,
% 0.76/0.71 (hskp25 | hskp7 | hskp5),
% 0.76/0.71 inference(modus_ponens,[status(thm)],[121, 109])).
% 0.76/0.71 tff(123,plain,
% 0.76/0.71 (hskp25),
% 0.76/0.71 inference(unit_resolution,[status(thm)],[122, 108, 43])).
% 0.76/0.71 tff(124,plain,
% 0.76/0.71 (((~hskp25) | (~c3_1(a760))) <=> ((~hskp25) | (~c3_1(a760)))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(125,plain,
% 0.76/0.71 (((~c3_1(a760)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a760)))),
% 0.76/0.71 inference(rewrite,[status(thm)],[])).
% 0.76/0.71 tff(126,axiom,((~c3_1(a760)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.76/0.71 tff(127,plain,
% 0.76/0.72 ((~hskp25) | (~c3_1(a760))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.76/0.72 tff(128,plain,
% 0.76/0.72 ((~hskp25) | (~c3_1(a760))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[127, 124])).
% 0.76/0.72 tff(129,plain,
% 0.76/0.72 (~c3_1(a760)),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[128, 123])).
% 0.76/0.72 tff(130,plain,
% 0.76/0.72 (((~hskp25) | (~c0_1(a760))) <=> ((~hskp25) | (~c0_1(a760)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(131,plain,
% 0.76/0.72 (((~c0_1(a760)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a760)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(132,axiom,((~c0_1(a760)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.76/0.72 tff(133,plain,
% 0.76/0.72 ((~hskp25) | (~c0_1(a760))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.76/0.72 tff(134,plain,
% 0.76/0.72 ((~hskp25) | (~c0_1(a760))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[133, 130])).
% 0.76/0.72 tff(135,plain,
% 0.76/0.72 (~c0_1(a760)),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[134, 123])).
% 0.76/0.72 tff(136,plain,
% 0.76/0.72 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | c0_1(a760) | c3_1(a760) | (~ndr1_0) | c2_1(a760))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp7 | c0_1(a760) | c3_1(a760) | (~ndr1_0) | c2_1(a760))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(137,plain,
% 0.76/0.72 ((hskp28 | hskp7 | (~ndr1_0) | c2_1(a760) | c0_1(a760) | c3_1(a760)) <=> (hskp28 | hskp7 | c0_1(a760) | c3_1(a760) | (~ndr1_0) | c2_1(a760))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(138,plain,
% 0.76/0.72 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | (~ndr1_0) | c2_1(a760) | c0_1(a760) | c3_1(a760))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | c0_1(a760) | c3_1(a760) | (~ndr1_0) | c2_1(a760)))),
% 0.76/0.72 inference(monotonicity,[status(thm)],[137])).
% 0.76/0.72 tff(139,plain,
% 0.76/0.72 (((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | (~ndr1_0) | c2_1(a760) | c0_1(a760) | c3_1(a760))) <=> ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp7 | c0_1(a760) | c3_1(a760) | (~ndr1_0) | c2_1(a760))),
% 0.76/0.72 inference(transitivity,[status(thm)],[138, 136])).
% 0.76/0.72 tff(140,plain,
% 0.76/0.72 ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | (hskp28 | hskp7 | (~ndr1_0) | c2_1(a760) | c0_1(a760) | c3_1(a760))),
% 0.76/0.72 inference(quant_inst,[status(thm)],[])).
% 0.76/0.72 tff(141,plain,
% 0.76/0.72 ((~![U: $i] : (hskp28 | hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(U))) | hskp28 | hskp7 | c0_1(a760) | c3_1(a760) | (~ndr1_0) | c2_1(a760)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.76/0.72 tff(142,plain,
% 0.76/0.72 (c2_1(a760)),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[141, 99, 12, 43, 135, 129, 42])).
% 0.76/0.72 tff(143,plain,
% 0.76/0.72 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.76/0.72 inference(bind,[status(th)],[])).
% 0.76/0.72 tff(144,plain,
% 0.76/0.72 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.72 inference(quant_intro,[status(thm)],[143])).
% 0.76/0.72 tff(145,plain,
% 0.76/0.72 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(146,plain,
% 0.76/0.72 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.76/0.72 inference(bind,[status(th)],[])).
% 0.76/0.72 tff(147,plain,
% 0.76/0.72 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.72 inference(quant_intro,[status(thm)],[146])).
% 0.76/0.72 tff(148,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.76/0.72 tff(149,plain,
% 0.76/0.72 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.76/0.72 tff(150,plain,
% 0.76/0.72 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.76/0.72 tff(151,plain,(
% 0.76/0.72 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.72 inference(skolemize,[status(sab)],[150])).
% 0.76/0.72 tff(152,plain,
% 0.76/0.72 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.76/0.72 tff(153,plain,
% 0.76/0.72 (((~hskp25) | (~c1_1(a760))) <=> ((~hskp25) | (~c1_1(a760)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(154,plain,
% 0.76/0.72 (((~c1_1(a760)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a760)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(155,axiom,((~c1_1(a760)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 0.76/0.72 tff(156,plain,
% 0.76/0.72 ((~hskp25) | (~c1_1(a760))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.76/0.72 tff(157,plain,
% 0.76/0.72 ((~hskp25) | (~c1_1(a760))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[156, 153])).
% 0.76/0.72 tff(158,plain,
% 0.76/0.72 (~c1_1(a760)),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[157, 123])).
% 0.76/0.72 tff(159,plain,
% 0.76/0.72 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | (~ndr1_0) | (~c2_1(a760)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | (~ndr1_0) | (~c2_1(a760)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(160,plain,
% 0.76/0.72 ((hskp5 | (~ndr1_0) | c1_1(a760) | c3_1(a760) | (~c2_1(a760)) | c3_1(a760) | c1_1(a760) | c0_1(a760)) <=> (hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | (~ndr1_0) | (~c2_1(a760)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(161,plain,
% 0.76/0.72 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a760) | c3_1(a760) | (~c2_1(a760)) | c3_1(a760) | c1_1(a760) | c0_1(a760))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | (~ndr1_0) | (~c2_1(a760))))),
% 0.76/0.72 inference(monotonicity,[status(thm)],[160])).
% 0.76/0.72 tff(162,plain,
% 0.76/0.72 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a760) | c3_1(a760) | (~c2_1(a760)) | c3_1(a760) | c1_1(a760) | c0_1(a760))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | (~ndr1_0) | (~c2_1(a760)))),
% 0.76/0.72 inference(transitivity,[status(thm)],[161, 159])).
% 0.76/0.72 tff(163,plain,
% 0.76/0.72 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a760) | c3_1(a760) | (~c2_1(a760)) | c3_1(a760) | c1_1(a760) | c0_1(a760))),
% 0.76/0.72 inference(quant_inst,[status(thm)],[])).
% 0.76/0.72 tff(164,plain,
% 0.76/0.72 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | (~ndr1_0) | (~c2_1(a760))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.76/0.72 tff(165,plain,
% 0.76/0.72 ($false),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[164, 99, 108, 135, 158, 129, 152, 142])).
% 0.76/0.72 tff(166,plain,(hskp7 | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.76/0.72 tff(167,plain,
% 0.76/0.72 (hskp7),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[166, 12])).
% 0.76/0.72 tff(168,plain,
% 0.76/0.72 (((~hskp7) | (~c2_1(a675))) <=> ((~hskp7) | (~c2_1(a675)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(169,plain,
% 0.76/0.72 (((~c2_1(a675)) | (~hskp7)) <=> ((~hskp7) | (~c2_1(a675)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(170,axiom,((~c2_1(a675)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.76/0.72 tff(171,plain,
% 0.76/0.72 ((~hskp7) | (~c2_1(a675))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.76/0.72 tff(172,plain,
% 0.76/0.72 ((~hskp7) | (~c2_1(a675))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[171, 168])).
% 0.76/0.72 tff(173,plain,
% 0.76/0.72 (~c2_1(a675)),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[172, 167])).
% 0.76/0.72 tff(174,plain,
% 0.76/0.72 (((~hskp7) | c3_1(a675)) <=> ((~hskp7) | c3_1(a675))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(175,axiom,((~hskp7) | c3_1(a675)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.76/0.72 tff(176,plain,
% 0.76/0.72 ((~hskp7) | c3_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.76/0.72 tff(177,plain,
% 0.76/0.72 ((~hskp7) | c3_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[176, 174])).
% 0.76/0.72 tff(178,plain,
% 0.76/0.72 ((~hskp7) | c3_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[177, 174])).
% 0.76/0.72 tff(179,plain,
% 0.76/0.72 ((~hskp7) | c3_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.76/0.72 tff(180,plain,
% 0.76/0.72 ((~hskp7) | c3_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[179, 174])).
% 0.76/0.72 tff(181,plain,
% 0.76/0.72 ((~hskp7) | c3_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[180, 174])).
% 0.76/0.72 tff(182,plain,
% 0.76/0.72 ((~hskp7) | c3_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.76/0.72 tff(183,plain,
% 0.76/0.72 ((~hskp7) | c3_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[182, 174])).
% 0.76/0.72 tff(184,plain,
% 0.76/0.72 (c3_1(a675)),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[183, 167])).
% 0.76/0.72 tff(185,plain,
% 0.76/0.72 (((~hskp7) | c1_1(a675)) <=> ((~hskp7) | c1_1(a675))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(186,axiom,((~hskp7) | c1_1(a675)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.76/0.72 tff(187,plain,
% 0.76/0.72 ((~hskp7) | c1_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.76/0.72 tff(188,plain,
% 0.76/0.72 ((~hskp7) | c1_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[187, 185])).
% 0.76/0.72 tff(189,plain,
% 0.76/0.72 ((~hskp7) | c1_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[188, 185])).
% 0.76/0.72 tff(190,plain,
% 0.76/0.72 ((~hskp7) | c1_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.76/0.72 tff(191,plain,
% 0.76/0.72 ((~hskp7) | c1_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[190, 185])).
% 0.76/0.72 tff(192,plain,
% 0.76/0.72 ((~hskp7) | c1_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[191, 185])).
% 0.76/0.72 tff(193,plain,
% 0.76/0.72 ((~hskp7) | c1_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.76/0.72 tff(194,plain,
% 0.76/0.72 ((~hskp7) | c1_1(a675)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[193, 185])).
% 0.76/0.72 tff(195,plain,
% 0.76/0.72 (c1_1(a675)),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[194, 167])).
% 0.76/0.72 tff(196,plain,
% 0.76/0.72 (((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp10 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp10 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(197,plain,
% 0.76/0.72 ((hskp28 | hskp10 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675))) <=> (hskp28 | hskp10 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(198,plain,
% 0.76/0.72 (((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp10 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp10 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675))))),
% 0.76/0.72 inference(monotonicity,[status(thm)],[197])).
% 0.76/0.72 tff(199,plain,
% 0.76/0.72 (((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp10 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp10 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.76/0.72 inference(transitivity,[status(thm)],[198, 196])).
% 0.76/0.72 tff(200,plain,
% 0.76/0.72 ((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp28 | hskp10 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.76/0.72 inference(quant_inst,[status(thm)],[])).
% 0.76/0.72 tff(201,plain,
% 0.76/0.72 ((~![U: $i] : (hskp28 | hskp10 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp28 | hskp10 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.76/0.72 tff(202,plain,
% 0.76/0.72 (hskp10),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[201, 99, 12, 195, 184, 173, 32])).
% 0.76/0.72 tff(203,plain,
% 0.76/0.72 (((~hskp10) | (~c0_1(a681))) <=> ((~hskp10) | (~c0_1(a681)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(204,plain,
% 0.76/0.72 (((~c0_1(a681)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a681)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(205,axiom,((~c0_1(a681)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.76/0.72 tff(206,plain,
% 0.76/0.72 ((~hskp10) | (~c0_1(a681))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.76/0.72 tff(207,plain,
% 0.76/0.72 ((~hskp10) | (~c0_1(a681))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[206, 203])).
% 0.76/0.72 tff(208,plain,
% 0.76/0.72 (~c0_1(a681)),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[207, 202])).
% 0.76/0.72 tff(209,plain,
% 0.76/0.72 (((~hskp10) | c3_1(a681)) <=> ((~hskp10) | c3_1(a681))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(210,axiom,((~hskp10) | c3_1(a681)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.76/0.72 tff(211,plain,
% 0.76/0.72 ((~hskp10) | c3_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.76/0.72 tff(212,plain,
% 0.76/0.72 ((~hskp10) | c3_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[211, 209])).
% 0.76/0.72 tff(213,plain,
% 0.76/0.72 ((~hskp10) | c3_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[212, 209])).
% 0.76/0.72 tff(214,plain,
% 0.76/0.72 ((~hskp10) | c3_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.76/0.72 tff(215,plain,
% 0.76/0.72 ((~hskp10) | c3_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[214, 209])).
% 0.76/0.72 tff(216,plain,
% 0.76/0.72 ((~hskp10) | c3_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[215, 209])).
% 0.76/0.72 tff(217,plain,
% 0.76/0.72 ((~hskp10) | c3_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[216, 209])).
% 0.76/0.72 tff(218,plain,
% 0.76/0.72 ((~hskp10) | c3_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[217, 209])).
% 0.76/0.72 tff(219,plain,
% 0.76/0.72 (c3_1(a681)),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[218, 202])).
% 0.76/0.72 tff(220,plain,
% 0.76/0.72 (((~hskp10) | c2_1(a681)) <=> ((~hskp10) | c2_1(a681))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(221,axiom,((~hskp10) | c2_1(a681)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.76/0.72 tff(222,plain,
% 0.76/0.72 ((~hskp10) | c2_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.76/0.72 tff(223,plain,
% 0.76/0.72 ((~hskp10) | c2_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[222, 220])).
% 0.76/0.72 tff(224,plain,
% 0.76/0.72 ((~hskp10) | c2_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[223, 220])).
% 0.76/0.72 tff(225,plain,
% 0.76/0.72 ((~hskp10) | c2_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.76/0.72 tff(226,plain,
% 0.76/0.72 ((~hskp10) | c2_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[225, 220])).
% 0.76/0.72 tff(227,plain,
% 0.76/0.72 ((~hskp10) | c2_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[226, 220])).
% 0.76/0.72 tff(228,plain,
% 0.76/0.72 ((~hskp10) | c2_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[227, 220])).
% 0.76/0.72 tff(229,plain,
% 0.76/0.72 ((~hskp10) | c2_1(a681)),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[228, 220])).
% 0.76/0.72 tff(230,plain,
% 0.76/0.72 (c2_1(a681)),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[229, 202])).
% 0.76/0.72 tff(231,plain,
% 0.76/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | (~c1_1(a681)) | (~c3_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | (~c1_1(a681)) | (~c3_1(a681)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(232,plain,
% 0.76/0.72 (((~ndr1_0) | (~c2_1(a681)) | (~c3_1(a681)) | (~c1_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c1_1(a681))) <=> (c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | (~c1_1(a681)) | (~c3_1(a681)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(233,plain,
% 0.76/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a681)) | (~c3_1(a681)) | (~c1_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c1_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | (c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | (~c1_1(a681)) | (~c3_1(a681))))),
% 0.76/0.72 inference(monotonicity,[status(thm)],[232])).
% 0.76/0.72 tff(234,plain,
% 0.76/0.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a681)) | (~c3_1(a681)) | (~c1_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c1_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | (~c1_1(a681)) | (~c3_1(a681)))),
% 0.76/0.72 inference(transitivity,[status(thm)],[233, 231])).
% 0.76/0.72 tff(235,plain,
% 0.76/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a681)) | (~c3_1(a681)) | (~c1_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c0_1(a681) | (~c2_1(a681)) | (~c1_1(a681)))),
% 0.76/0.72 inference(quant_inst,[status(thm)],[])).
% 0.76/0.72 tff(236,plain,
% 0.76/0.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c1_1(W)))) | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | (~c1_1(a681)) | (~c3_1(a681))),
% 0.76/0.72 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.76/0.72 tff(237,plain,
% 0.76/0.72 (~c1_1(a681)),
% 0.76/0.72 inference(unit_resolution,[status(thm)],[236, 99, 230, 219, 208, 22])).
% 0.76/0.72 tff(238,plain,
% 0.76/0.72 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 0.76/0.72 inference(bind,[status(th)],[])).
% 0.76/0.72 tff(239,plain,
% 0.76/0.72 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.76/0.72 inference(quant_intro,[status(thm)],[238])).
% 0.76/0.72 tff(240,plain,
% 0.76/0.72 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.76/0.72 inference(rewrite,[status(thm)],[])).
% 0.76/0.72 tff(241,plain,
% 0.76/0.72 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 0.76/0.72 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(242,plain,
% 0.76/0.73 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[241])).
% 0.76/0.73 tff(243,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 0.76/0.73 tff(244,plain,
% 0.76/0.73 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.76/0.73 tff(245,plain,
% 0.76/0.73 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[244, 240])).
% 0.76/0.73 tff(246,plain,(
% 0.76/0.73 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.76/0.73 inference(skolemize,[status(sab)],[245])).
% 0.76/0.73 tff(247,plain,
% 0.76/0.73 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[246, 239])).
% 0.76/0.73 tff(248,plain,
% 0.76/0.73 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(249,plain,
% 0.76/0.73 ((hskp11 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681))) <=> (hskp11 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(250,plain,
% 0.76/0.73 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681))))),
% 0.76/0.73 inference(monotonicity,[status(thm)],[249])).
% 0.76/0.73 tff(251,plain,
% 0.76/0.73 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))),
% 0.76/0.73 inference(transitivity,[status(thm)],[250, 248])).
% 0.76/0.73 tff(252,plain,
% 0.76/0.73 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))),
% 0.76/0.73 inference(quant_inst,[status(thm)],[])).
% 0.76/0.73 tff(253,plain,
% 0.76/0.73 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.76/0.73 tff(254,plain,
% 0.76/0.73 (hskp11),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[253, 99, 230, 219, 208, 247, 237])).
% 0.76/0.73 tff(255,plain,
% 0.76/0.73 (((~hskp11) | c0_1(a683)) <=> ((~hskp11) | c0_1(a683))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(256,axiom,((~hskp11) | c0_1(a683)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.76/0.73 tff(257,plain,
% 0.76/0.73 ((~hskp11) | c0_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.76/0.73 tff(258,plain,
% 0.76/0.73 ((~hskp11) | c0_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[257, 255])).
% 0.76/0.73 tff(259,plain,
% 0.76/0.73 ((~hskp11) | c0_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[258, 255])).
% 0.76/0.73 tff(260,plain,
% 0.76/0.73 ((~hskp11) | c0_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[259, 255])).
% 0.76/0.73 tff(261,plain,
% 0.76/0.73 ((~hskp11) | c0_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[260, 255])).
% 0.76/0.73 tff(262,plain,
% 0.76/0.73 ((~hskp11) | c0_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[261, 255])).
% 0.76/0.73 tff(263,plain,
% 0.76/0.73 ((~hskp11) | c0_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[262, 255])).
% 0.76/0.73 tff(264,plain,
% 0.76/0.73 ((~hskp11) | c0_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[263, 255])).
% 0.76/0.73 tff(265,plain,
% 0.76/0.73 (c0_1(a683)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[264, 254])).
% 0.76/0.73 tff(266,plain,
% 0.76/0.73 (((~hskp11) | c3_1(a683)) <=> ((~hskp11) | c3_1(a683))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(267,axiom,((~hskp11) | c3_1(a683)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.76/0.73 tff(268,plain,
% 0.76/0.73 ((~hskp11) | c3_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.76/0.73 tff(269,plain,
% 0.76/0.73 ((~hskp11) | c3_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[268, 266])).
% 0.76/0.73 tff(270,plain,
% 0.76/0.73 ((~hskp11) | c3_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[269, 266])).
% 0.76/0.73 tff(271,plain,
% 0.76/0.73 ((~hskp11) | c3_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[270, 266])).
% 0.76/0.73 tff(272,plain,
% 0.76/0.73 ((~hskp11) | c3_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[271, 266])).
% 0.76/0.73 tff(273,plain,
% 0.76/0.73 ((~hskp11) | c3_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[272, 266])).
% 0.76/0.73 tff(274,plain,
% 0.76/0.73 ((~hskp11) | c3_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[273, 266])).
% 0.76/0.73 tff(275,plain,
% 0.76/0.73 ((~hskp11) | c3_1(a683)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[274, 266])).
% 0.76/0.73 tff(276,plain,
% 0.76/0.73 (c3_1(a683)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[275, 254])).
% 0.76/0.73 tff(277,plain,
% 0.76/0.73 (((~hskp11) | (~c2_1(a683))) <=> ((~hskp11) | (~c2_1(a683)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(278,plain,
% 0.76/0.73 (((~c2_1(a683)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a683)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(279,axiom,((~c2_1(a683)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.76/0.73 tff(280,plain,
% 0.76/0.73 ((~hskp11) | (~c2_1(a683))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.76/0.73 tff(281,plain,
% 0.76/0.73 ((~hskp11) | (~c2_1(a683))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[280, 277])).
% 0.76/0.73 tff(282,plain,
% 0.76/0.73 (~c2_1(a683)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[281, 254])).
% 0.76/0.73 tff(283,assumption,(hskp7), introduced(assumption)).
% 0.76/0.73 tff(284,plain,
% 0.76/0.73 (~c2_1(a675)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[172, 283])).
% 0.76/0.73 tff(285,plain,
% 0.76/0.73 (c3_1(a675)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[183, 283])).
% 0.76/0.73 tff(286,plain,
% 0.76/0.73 (c1_1(a675)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[194, 283])).
% 0.76/0.73 tff(287,plain,
% 0.76/0.73 (hskp10),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[201, 99, 12, 286, 285, 284, 32])).
% 0.76/0.73 tff(288,plain,
% 0.76/0.73 (~c0_1(a681)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[207, 287])).
% 0.76/0.73 tff(289,plain,
% 0.76/0.73 (c3_1(a681)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[218, 287])).
% 0.76/0.73 tff(290,plain,
% 0.76/0.73 (c2_1(a681)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[229, 287])).
% 0.76/0.73 tff(291,plain,
% 0.76/0.73 (~c1_1(a681)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[236, 99, 290, 289, 288, 22])).
% 0.76/0.73 tff(292,assumption,(c0_1(a683)), introduced(assumption)).
% 0.76/0.73 tff(293,assumption,(~c2_1(a683)), introduced(assumption)).
% 0.76/0.73 tff(294,assumption,(c3_1(a683)), introduced(assumption)).
% 0.76/0.73 tff(295,plain,
% 0.76/0.73 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W)))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(296,plain,
% 0.76/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[295])).
% 0.76/0.73 tff(297,plain,
% 0.76/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(298,plain,
% 0.76/0.73 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(299,plain,
% 0.76/0.73 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[298])).
% 0.76/0.73 tff(300,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c3_1(U)) | c2_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 0.76/0.73 tff(301,plain,
% 0.76/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.76/0.73 tff(302,plain,
% 0.76/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[301, 297])).
% 0.76/0.73 tff(303,plain,(
% 0.76/0.73 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.76/0.73 inference(skolemize,[status(sab)],[302])).
% 0.76/0.73 tff(304,plain,
% 0.76/0.73 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[303, 296])).
% 0.76/0.73 tff(305,assumption,(hskp9), introduced(assumption)).
% 0.76/0.73 tff(306,plain,
% 0.76/0.73 (((~hskp9) | (~c3_1(a680))) <=> ((~hskp9) | (~c3_1(a680)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(307,plain,
% 0.76/0.73 (((~c3_1(a680)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a680)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(308,axiom,((~c3_1(a680)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.76/0.73 tff(309,plain,
% 0.76/0.73 ((~hskp9) | (~c3_1(a680))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.76/0.73 tff(310,plain,
% 0.76/0.73 ((~hskp9) | (~c3_1(a680))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[309, 306])).
% 0.76/0.73 tff(311,plain,
% 0.76/0.73 (~c3_1(a680)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[310, 305])).
% 0.76/0.73 tff(312,plain,
% 0.76/0.73 (((~hskp9) | (~c1_1(a680))) <=> ((~hskp9) | (~c1_1(a680)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(313,plain,
% 0.76/0.73 (((~c1_1(a680)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a680)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(314,axiom,((~c1_1(a680)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 0.76/0.73 tff(315,plain,
% 0.76/0.73 ((~hskp9) | (~c1_1(a680))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.76/0.73 tff(316,plain,
% 0.76/0.73 ((~hskp9) | (~c1_1(a680))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[315, 312])).
% 0.76/0.73 tff(317,plain,
% 0.76/0.73 (~c1_1(a680)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[316, 305])).
% 0.76/0.73 tff(318,assumption,(~c0_1(a681)), introduced(assumption)).
% 0.76/0.73 tff(319,assumption,(c3_1(a681)), introduced(assumption)).
% 0.76/0.73 tff(320,assumption,(c2_1(a681)), introduced(assumption)).
% 0.76/0.73 tff(321,plain,
% 0.76/0.73 (~c1_1(a681)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[236, 99, 320, 319, 318, 22])).
% 0.76/0.73 tff(322,plain,
% 0.76/0.73 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(323,plain,
% 0.76/0.73 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[322])).
% 0.76/0.73 tff(324,plain,
% 0.76/0.73 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(325,plain,
% 0.76/0.73 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp13))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.76/0.73 inference(bind,[status(th)],[])).
% 0.76/0.73 tff(326,plain,
% 0.76/0.73 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.76/0.73 inference(quant_intro,[status(thm)],[325])).
% 0.76/0.73 tff(327,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 0.76/0.73 tff(328,plain,
% 0.76/0.73 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.76/0.73 tff(329,plain,
% 0.76/0.73 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[328, 324])).
% 0.76/0.73 tff(330,plain,(
% 0.76/0.73 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.76/0.73 inference(skolemize,[status(sab)],[329])).
% 0.76/0.73 tff(331,plain,
% 0.76/0.73 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[330, 323])).
% 0.76/0.73 tff(332,plain,
% 0.76/0.73 (((~hskp9) | c2_1(a680)) <=> ((~hskp9) | c2_1(a680))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(333,axiom,((~hskp9) | c2_1(a680)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 0.76/0.73 tff(334,plain,
% 0.76/0.73 ((~hskp9) | c2_1(a680)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.76/0.73 tff(335,plain,
% 0.76/0.73 ((~hskp9) | c2_1(a680)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[334, 332])).
% 0.76/0.73 tff(336,plain,
% 0.76/0.73 ((~hskp9) | c2_1(a680)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[335, 332])).
% 0.76/0.73 tff(337,plain,
% 0.76/0.73 ((~hskp9) | c2_1(a680)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[336, 332])).
% 0.76/0.73 tff(338,plain,
% 0.76/0.73 ((~hskp9) | c2_1(a680)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[337, 332])).
% 0.76/0.73 tff(339,plain,
% 0.76/0.73 ((~hskp9) | c2_1(a680)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[338, 332])).
% 0.76/0.73 tff(340,plain,
% 0.76/0.73 ((~hskp9) | c2_1(a680)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[339, 332])).
% 0.76/0.73 tff(341,plain,
% 0.76/0.73 ((~hskp9) | c2_1(a680)),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[340, 332])).
% 0.76/0.73 tff(342,plain,
% 0.76/0.73 (c2_1(a680)),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[341, 305])).
% 0.76/0.73 tff(343,plain,
% 0.76/0.73 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(344,plain,
% 0.76/0.73 ((hskp13 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c3_1(a680) | c1_1(a680) | (~c2_1(a680))) <=> (hskp13 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(345,plain,
% 0.76/0.73 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c3_1(a680) | c1_1(a680) | (~c2_1(a680)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681))))),
% 0.76/0.73 inference(monotonicity,[status(thm)],[344])).
% 0.76/0.73 tff(346,plain,
% 0.76/0.73 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c3_1(a680) | c1_1(a680) | (~c2_1(a680)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681)))),
% 0.76/0.73 inference(transitivity,[status(thm)],[345, 343])).
% 0.76/0.73 tff(347,plain,
% 0.76/0.73 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp13 | (~ndr1_0) | c1_1(a681) | (~c2_1(a681)) | (~c3_1(a681)) | c3_1(a680) | c1_1(a680) | (~c2_1(a680)))),
% 0.76/0.73 inference(quant_inst,[status(thm)],[])).
% 0.76/0.73 tff(348,plain,
% 0.76/0.73 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp13 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c2_1(a681)) | c1_1(a681) | (~c3_1(a681))),
% 0.76/0.73 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.76/0.73 tff(349,plain,
% 0.76/0.73 (hskp13),
% 0.76/0.73 inference(unit_resolution,[status(thm)],[348, 99, 320, 319, 342, 317, 311, 331, 321])).
% 0.76/0.73 tff(350,plain,
% 0.76/0.73 (((~hskp13) | (~c3_1(a688))) <=> ((~hskp13) | (~c3_1(a688)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.73 tff(351,plain,
% 0.76/0.73 (((~c3_1(a688)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a688)))),
% 0.76/0.73 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(352,axiom,((~c3_1(a688)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.76/0.74 tff(353,plain,
% 0.76/0.74 ((~hskp13) | (~c3_1(a688))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.76/0.74 tff(354,plain,
% 0.76/0.74 ((~hskp13) | (~c3_1(a688))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[353, 350])).
% 0.76/0.74 tff(355,plain,
% 0.76/0.74 (~c3_1(a688)),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[354, 349])).
% 0.76/0.74 tff(356,plain,
% 0.76/0.74 (((~hskp13) | c0_1(a688)) <=> ((~hskp13) | c0_1(a688))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(357,axiom,((~hskp13) | c0_1(a688)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.76/0.74 tff(358,plain,
% 0.76/0.74 ((~hskp13) | c0_1(a688)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.76/0.74 tff(359,plain,
% 0.76/0.74 ((~hskp13) | c0_1(a688)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[358, 356])).
% 0.76/0.74 tff(360,plain,
% 0.76/0.74 ((~hskp13) | c0_1(a688)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[359, 356])).
% 0.76/0.74 tff(361,plain,
% 0.76/0.74 ((~hskp13) | c0_1(a688)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[360, 356])).
% 0.76/0.74 tff(362,plain,
% 0.76/0.74 ((~hskp13) | c0_1(a688)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[361, 356])).
% 0.76/0.74 tff(363,plain,
% 0.76/0.74 ((~hskp13) | c0_1(a688)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[362, 356])).
% 0.76/0.74 tff(364,plain,
% 0.76/0.74 ((~hskp13) | c0_1(a688)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[363, 356])).
% 0.76/0.74 tff(365,plain,
% 0.76/0.74 ((~hskp13) | c0_1(a688)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[364, 356])).
% 0.76/0.74 tff(366,plain,
% 0.76/0.74 (c0_1(a688)),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[365, 349])).
% 0.76/0.74 tff(367,plain,
% 0.76/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a688) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a688)) | (~c0_1(a688)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a688) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a688)) | (~c0_1(a688)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(368,plain,
% 0.76/0.74 (((~ndr1_0) | c3_1(a688) | (~c2_1(a688)) | (~c0_1(a688)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680)) <=> (c3_1(a688) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a688)) | (~c0_1(a688)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(369,plain,
% 0.76/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a688) | (~c2_1(a688)) | (~c0_1(a688)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a688) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a688)) | (~c0_1(a688))))),
% 0.76/0.74 inference(monotonicity,[status(thm)],[368])).
% 0.76/0.74 tff(370,plain,
% 0.76/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a688) | (~c2_1(a688)) | (~c0_1(a688)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a688) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a688)) | (~c0_1(a688)))),
% 0.76/0.74 inference(transitivity,[status(thm)],[369, 367])).
% 0.76/0.74 tff(371,plain,
% 0.76/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a688) | (~c2_1(a688)) | (~c0_1(a688)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))),
% 0.76/0.74 inference(quant_inst,[status(thm)],[])).
% 0.76/0.74 tff(372,plain,
% 0.76/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a688) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a688)) | (~c0_1(a688))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.76/0.74 tff(373,plain,
% 0.76/0.74 (~c2_1(a688)),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[372, 99, 366, 292, 294, 342, 355, 293, 317, 311, 304])).
% 0.76/0.74 tff(374,plain,
% 0.76/0.74 (^[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)) | c0_1(W) | c3_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)) | c0_1(W) | c3_1(W) | (~c1_1(W))))),
% 0.76/0.74 inference(bind,[status(th)],[])).
% 0.76/0.74 tff(375,plain,
% 0.76/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.76/0.74 inference(quant_intro,[status(thm)],[374])).
% 0.76/0.74 tff(376,plain,
% 0.76/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(377,plain,
% 0.76/0.74 (^[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))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_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) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_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) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_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) | (~c1_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) | (~c1_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) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_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) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))))),
% 0.76/0.74 inference(bind,[status(th)],[])).
% 0.76/0.74 tff(378,plain,
% 0.76/0.74 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.76/0.74 inference(quant_intro,[status(thm)],[377])).
% 0.76/0.74 tff(379,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c1_1(W))) | c2_1(U)) | c2_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 0.76/0.74 tff(380,plain,
% 0.76/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.76/0.74 tff(381,plain,
% 0.76/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[380, 376])).
% 0.76/0.74 tff(382,plain,(
% 0.76/0.74 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.76/0.74 inference(skolemize,[status(sab)],[381])).
% 0.76/0.74 tff(383,plain,
% 0.76/0.74 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[382, 375])).
% 0.76/0.74 tff(384,assumption,(~c2_1(a675)), introduced(assumption)).
% 0.76/0.74 tff(385,assumption,(~c3_1(a680)), introduced(assumption)).
% 0.76/0.74 tff(386,assumption,(~c1_1(a680)), introduced(assumption)).
% 0.76/0.74 tff(387,assumption,(hskp14), introduced(assumption)).
% 0.76/0.74 tff(388,plain,
% 0.76/0.74 (((~hskp14) | (~c3_1(a696))) <=> ((~hskp14) | (~c3_1(a696)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(389,plain,
% 0.76/0.74 (((~c3_1(a696)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a696)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(390,axiom,((~c3_1(a696)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 0.76/0.74 tff(391,plain,
% 0.76/0.74 ((~hskp14) | (~c3_1(a696))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.76/0.74 tff(392,plain,
% 0.76/0.74 ((~hskp14) | (~c3_1(a696))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[391, 388])).
% 0.76/0.74 tff(393,plain,
% 0.76/0.74 (~c3_1(a696)),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[392, 387])).
% 0.76/0.74 tff(394,assumption,(c2_1(a680)), introduced(assumption)).
% 0.76/0.74 tff(395,plain,
% 0.76/0.74 (((~hskp14) | c2_1(a696)) <=> ((~hskp14) | c2_1(a696))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(396,axiom,((~hskp14) | c2_1(a696)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.76/0.74 tff(397,plain,
% 0.76/0.74 ((~hskp14) | c2_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.76/0.74 tff(398,plain,
% 0.76/0.74 ((~hskp14) | c2_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[397, 395])).
% 0.76/0.74 tff(399,plain,
% 0.76/0.74 ((~hskp14) | c2_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[398, 395])).
% 0.76/0.74 tff(400,plain,
% 0.76/0.74 ((~hskp14) | c2_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[399, 395])).
% 0.76/0.74 tff(401,plain,
% 0.76/0.74 ((~hskp14) | c2_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[400, 395])).
% 0.76/0.74 tff(402,plain,
% 0.76/0.74 ((~hskp14) | c2_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[401, 395])).
% 0.76/0.74 tff(403,plain,
% 0.76/0.74 ((~hskp14) | c2_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[402, 395])).
% 0.76/0.74 tff(404,plain,
% 0.76/0.74 ((~hskp14) | c2_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[403, 395])).
% 0.76/0.74 tff(405,plain,
% 0.76/0.74 (c2_1(a696)),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[404, 387])).
% 0.76/0.74 tff(406,plain,
% 0.76/0.74 (((~hskp14) | c0_1(a696)) <=> ((~hskp14) | c0_1(a696))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(407,axiom,((~hskp14) | c0_1(a696)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.76/0.74 tff(408,plain,
% 0.76/0.74 ((~hskp14) | c0_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.76/0.74 tff(409,plain,
% 0.76/0.74 ((~hskp14) | c0_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[408, 406])).
% 0.76/0.74 tff(410,plain,
% 0.76/0.74 ((~hskp14) | c0_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[409, 406])).
% 0.76/0.74 tff(411,plain,
% 0.76/0.74 ((~hskp14) | c0_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[410, 406])).
% 0.76/0.74 tff(412,plain,
% 0.76/0.74 ((~hskp14) | c0_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[411, 406])).
% 0.76/0.74 tff(413,plain,
% 0.76/0.74 ((~hskp14) | c0_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[412, 406])).
% 0.76/0.74 tff(414,plain,
% 0.76/0.74 ((~hskp14) | c0_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[413, 406])).
% 0.76/0.74 tff(415,plain,
% 0.76/0.74 ((~hskp14) | c0_1(a696)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[414, 406])).
% 0.76/0.74 tff(416,plain,
% 0.76/0.74 (c0_1(a696)),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[415, 387])).
% 0.76/0.74 tff(417,plain,
% 0.76/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a696) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a696)) | (~c0_1(a696)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a696)) | (~c0_1(a696)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(418,plain,
% 0.76/0.74 (((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680)) <=> (c3_1(a696) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a696)) | (~c0_1(a696)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(419,plain,
% 0.76/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a696) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a696)) | (~c0_1(a696))))),
% 0.76/0.74 inference(monotonicity,[status(thm)],[418])).
% 0.76/0.74 tff(420,plain,
% 0.76/0.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a696)) | (~c0_1(a696)))),
% 0.76/0.74 inference(transitivity,[status(thm)],[419, 417])).
% 0.76/0.74 tff(421,plain,
% 0.76/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a683) | (~c3_1(a683)) | (~c0_1(a683)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))),
% 0.76/0.74 inference(quant_inst,[status(thm)],[])).
% 0.76/0.74 tff(422,plain,
% 0.76/0.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | c2_1(a683) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c2_1(a696)) | (~c0_1(a696))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.76/0.74 tff(423,plain,
% 0.76/0.74 ($false),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[422, 99, 416, 405, 292, 294, 394, 393, 293, 386, 385, 304])).
% 0.76/0.74 tff(424,plain,((~hskp14) | (~c0_1(a683)) | (~c3_1(a683)) | (~c2_1(a680)) | c2_1(a683) | c1_1(a680) | c3_1(a680)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.74 tff(425,plain,
% 0.76/0.74 (~hskp14),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[424, 342, 294, 292, 293, 317, 311])).
% 0.76/0.74 tff(426,plain,
% 0.76/0.74 (^[U: $i] : refl((hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.76/0.74 inference(bind,[status(th)],[])).
% 0.76/0.74 tff(427,plain,
% 0.76/0.74 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.74 inference(quant_intro,[status(thm)],[426])).
% 0.76/0.74 tff(428,plain,
% 0.76/0.74 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(429,plain,
% 0.76/0.74 (^[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)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp14) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp14) | hskp17) <=> ((hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite(((hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp14) | hskp17) <=> (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.76/0.74 inference(bind,[status(th)],[])).
% 0.76/0.74 tff(430,plain,
% 0.76/0.74 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp14) | hskp17) <=> ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.74 inference(quant_intro,[status(thm)],[429])).
% 0.76/0.74 tff(431,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp14) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 0.76/0.74 tff(432,plain,
% 0.76/0.74 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.76/0.74 tff(433,plain,
% 0.76/0.74 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[432, 428])).
% 0.76/0.74 tff(434,plain,(
% 0.76/0.74 ![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.74 inference(skolemize,[status(sab)],[433])).
% 0.76/0.74 tff(435,plain,
% 0.76/0.74 (![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[434, 427])).
% 0.76/0.74 tff(436,assumption,(c3_1(a675)), introduced(assumption)).
% 0.76/0.74 tff(437,assumption,(c1_1(a675)), introduced(assumption)).
% 0.76/0.74 tff(438,plain,
% 0.76/0.74 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(439,plain,
% 0.76/0.74 ((hskp17 | hskp14 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675))) <=> (hskp17 | hskp14 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(440,plain,
% 0.76/0.74 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675))))),
% 0.76/0.74 inference(monotonicity,[status(thm)],[439])).
% 0.76/0.74 tff(441,plain,
% 0.76/0.74 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.76/0.74 inference(transitivity,[status(thm)],[440, 438])).
% 0.76/0.74 tff(442,plain,
% 0.76/0.74 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.76/0.74 inference(quant_inst,[status(thm)],[])).
% 0.76/0.74 tff(443,plain,
% 0.76/0.74 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[442, 441])).
% 0.76/0.74 tff(444,plain,
% 0.76/0.74 (hskp17 | hskp14),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[443, 99, 437, 436, 384, 435])).
% 0.76/0.74 tff(445,plain,
% 0.76/0.74 (hskp17),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[444, 425])).
% 0.76/0.74 tff(446,plain,
% 0.76/0.74 (((~hskp17) | (~c0_1(a703))) <=> ((~hskp17) | (~c0_1(a703)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(447,plain,
% 0.76/0.74 (((~c0_1(a703)) | (~hskp17)) <=> ((~hskp17) | (~c0_1(a703)))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(448,axiom,((~c0_1(a703)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.76/0.74 tff(449,plain,
% 0.76/0.74 ((~hskp17) | (~c0_1(a703))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[448, 447])).
% 0.76/0.74 tff(450,plain,
% 0.76/0.74 ((~hskp17) | (~c0_1(a703))),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[449, 446])).
% 0.76/0.74 tff(451,plain,
% 0.76/0.74 (~c0_1(a703)),
% 0.76/0.74 inference(unit_resolution,[status(thm)],[450, 445])).
% 0.76/0.74 tff(452,plain,
% 0.76/0.74 (((~hskp13) | c1_1(a688)) <=> ((~hskp13) | c1_1(a688))),
% 0.76/0.74 inference(rewrite,[status(thm)],[])).
% 0.76/0.74 tff(453,axiom,((~hskp13) | c1_1(a688)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.76/0.74 tff(454,plain,
% 0.76/0.74 ((~hskp13) | c1_1(a688)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.76/0.74 tff(455,plain,
% 0.76/0.74 ((~hskp13) | c1_1(a688)),
% 0.76/0.74 inference(modus_ponens,[status(thm)],[454, 452])).
% 0.76/0.74 tff(456,plain,
% 0.76/0.75 ((~hskp13) | c1_1(a688)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[455, 452])).
% 0.76/0.75 tff(457,plain,
% 0.76/0.75 ((~hskp13) | c1_1(a688)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[456, 452])).
% 0.76/0.75 tff(458,plain,
% 0.76/0.75 ((~hskp13) | c1_1(a688)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[457, 452])).
% 0.76/0.75 tff(459,plain,
% 0.76/0.75 ((~hskp13) | c1_1(a688)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[458, 452])).
% 0.76/0.75 tff(460,plain,
% 0.76/0.75 ((~hskp13) | c1_1(a688)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[459, 452])).
% 0.76/0.75 tff(461,plain,
% 0.76/0.75 ((~hskp13) | c1_1(a688)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[460, 452])).
% 0.76/0.75 tff(462,plain,
% 0.76/0.75 (c1_1(a688)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[461, 349])).
% 0.76/0.75 tff(463,plain,
% 0.76/0.75 (((~hskp17) | c1_1(a703)) <=> ((~hskp17) | c1_1(a703))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(464,axiom,((~hskp17) | c1_1(a703)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 0.76/0.75 tff(465,plain,
% 0.76/0.75 ((~hskp17) | c1_1(a703)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.76/0.75 tff(466,plain,
% 0.76/0.75 ((~hskp17) | c1_1(a703)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[465, 463])).
% 0.76/0.75 tff(467,plain,
% 0.76/0.75 ((~hskp17) | c1_1(a703)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[466, 463])).
% 0.76/0.75 tff(468,plain,
% 0.76/0.75 ((~hskp17) | c1_1(a703)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[467, 463])).
% 0.76/0.75 tff(469,plain,
% 0.76/0.75 ((~hskp17) | c1_1(a703)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[468, 463])).
% 0.76/0.75 tff(470,plain,
% 0.76/0.75 ((~hskp17) | c1_1(a703)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[469, 463])).
% 0.76/0.75 tff(471,plain,
% 0.76/0.75 ((~hskp17) | c1_1(a703)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[470, 463])).
% 0.76/0.75 tff(472,plain,
% 0.76/0.75 ((~hskp17) | c1_1(a703)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[471, 463])).
% 0.76/0.75 tff(473,plain,
% 0.76/0.75 (c1_1(a703)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[472, 445])).
% 0.76/0.75 tff(474,plain,
% 0.76/0.75 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c0_1(a688)) | (~c1_1(a688)) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c0_1(a688)) | (~c1_1(a688)) | c3_1(a703) | (~c1_1(a703)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(475,plain,
% 0.76/0.75 (((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c1_1(a688)) | (~c0_1(a688)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703))) <=> (c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c0_1(a688)) | (~c1_1(a688)) | c3_1(a703) | (~c1_1(a703)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(476,plain,
% 0.76/0.75 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c1_1(a688)) | (~c0_1(a688)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c0_1(a688)) | (~c1_1(a688)) | c3_1(a703) | (~c1_1(a703))))),
% 0.76/0.75 inference(monotonicity,[status(thm)],[475])).
% 0.76/0.75 tff(477,plain,
% 0.76/0.75 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c1_1(a688)) | (~c0_1(a688)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c0_1(a688)) | (~c1_1(a688)) | c3_1(a703) | (~c1_1(a703)))),
% 0.76/0.75 inference(transitivity,[status(thm)],[476, 474])).
% 0.76/0.75 tff(478,plain,
% 0.76/0.75 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c1_1(a688)) | (~c0_1(a688)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(479,plain,
% 0.76/0.75 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a688) | (~c0_1(a688)) | (~c1_1(a688)) | c3_1(a703) | (~c1_1(a703))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.76/0.75 tff(480,plain,
% 0.76/0.75 (c3_1(a703)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[479, 99, 473, 366, 462, 437, 436, 451, 384, 383, 373])).
% 0.76/0.75 tff(481,plain,
% 0.76/0.75 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(482,plain,
% 0.76/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[481])).
% 0.76/0.75 tff(483,plain,
% 0.76/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(484,plain,
% 0.76/0.75 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(485,plain,
% 0.76/0.75 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[484])).
% 0.76/0.75 tff(486,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 0.76/0.75 tff(487,plain,
% 0.76/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[486, 485])).
% 0.76/0.75 tff(488,plain,
% 0.76/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[487, 483])).
% 0.76/0.75 tff(489,plain,(
% 0.76/0.75 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.75 inference(skolemize,[status(sab)],[488])).
% 0.76/0.75 tff(490,plain,
% 0.76/0.75 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[489, 482])).
% 0.76/0.75 tff(491,plain,
% 0.76/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a703) | c2_1(a683) | c0_1(a681) | (~ndr1_0) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c2_1(a683) | c0_1(a681) | (~ndr1_0) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(492,plain,
% 0.76/0.75 (((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681))) <=> (c0_1(a703) | c2_1(a683) | c0_1(a681) | (~ndr1_0) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(493,plain,
% 0.76/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a703) | c2_1(a683) | c0_1(a681) | (~ndr1_0) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c3_1(a703)) | (~c1_1(a703))))),
% 0.76/0.75 inference(monotonicity,[status(thm)],[492])).
% 0.76/0.75 tff(494,plain,
% 0.76/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c2_1(a683) | c0_1(a681) | (~ndr1_0) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.76/0.75 inference(transitivity,[status(thm)],[493, 491])).
% 0.76/0.75 tff(495,plain,
% 0.76/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(496,plain,
% 0.76/0.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c2_1(a683) | c0_1(a681) | (~ndr1_0) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c3_1(a703)) | (~c1_1(a703))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[495, 494])).
% 0.76/0.75 tff(497,plain,
% 0.76/0.75 ($false),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[496, 99, 473, 292, 294, 319, 451, 293, 318, 490, 321, 480])).
% 0.76/0.75 tff(498,plain,((~hskp9) | (~c0_1(a683)) | (~c3_1(a683)) | (~c3_1(a681)) | c2_1(a683) | c0_1(a681) | (~c1_1(a675)) | (~c3_1(a675)) | c2_1(a675) | (~c2_1(a681))), inference(lemma,lemma(discharge,[]))).
% 0.76/0.75 tff(499,plain,
% 0.76/0.75 (~hskp9),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[498, 289, 294, 292, 293, 288, 286, 285, 284, 290])).
% 0.76/0.75 tff(500,plain,
% 0.76/0.75 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(501,plain,
% 0.76/0.75 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[500])).
% 0.76/0.75 tff(502,plain,
% 0.76/0.75 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(503,plain,
% 0.76/0.75 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.76/0.75 inference(bind,[status(th)],[])).
% 0.76/0.75 tff(504,plain,
% 0.76/0.75 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.75 inference(quant_intro,[status(thm)],[503])).
% 0.76/0.75 tff(505,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 0.76/0.75 tff(506,plain,
% 0.76/0.75 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.76/0.75 tff(507,plain,
% 0.76/0.75 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[506, 502])).
% 0.76/0.75 tff(508,plain,(
% 0.76/0.75 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.75 inference(skolemize,[status(sab)],[507])).
% 0.76/0.75 tff(509,plain,
% 0.76/0.75 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[508, 501])).
% 0.76/0.75 tff(510,plain,
% 0.76/0.75 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(511,plain,
% 0.76/0.75 ((hskp9 | hskp8 | (~ndr1_0) | c1_1(a681) | c0_1(a681) | (~c2_1(a681))) <=> (hskp9 | hskp8 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(512,plain,
% 0.76/0.75 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a681) | c0_1(a681) | (~c2_1(a681)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681)))),
% 0.76/0.75 inference(monotonicity,[status(thm)],[511])).
% 0.76/0.75 tff(513,plain,
% 0.76/0.75 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a681) | c0_1(a681) | (~c2_1(a681)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681))),
% 0.76/0.75 inference(transitivity,[status(thm)],[512, 510])).
% 0.76/0.75 tff(514,plain,
% 0.76/0.75 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a681) | c0_1(a681) | (~c2_1(a681)))),
% 0.76/0.75 inference(quant_inst,[status(thm)],[])).
% 0.76/0.75 tff(515,plain,
% 0.76/0.75 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a681) | (~ndr1_0) | (~c2_1(a681)) | c1_1(a681)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.76/0.75 tff(516,plain,
% 0.76/0.75 (hskp9 | hskp8),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[515, 99, 290, 288, 509, 291])).
% 0.76/0.75 tff(517,plain,
% 0.76/0.75 (hskp8),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[516, 499])).
% 0.76/0.75 tff(518,plain,
% 0.76/0.75 (((~hskp8) | (~c0_1(a679))) <=> ((~hskp8) | (~c0_1(a679)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(519,plain,
% 0.76/0.75 (((~c0_1(a679)) | (~hskp8)) <=> ((~hskp8) | (~c0_1(a679)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(520,axiom,((~c0_1(a679)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.76/0.75 tff(521,plain,
% 0.76/0.75 ((~hskp8) | (~c0_1(a679))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[520, 519])).
% 0.76/0.75 tff(522,plain,
% 0.76/0.75 ((~hskp8) | (~c0_1(a679))),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[521, 518])).
% 0.76/0.75 tff(523,plain,
% 0.76/0.75 (~c0_1(a679)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[522, 517])).
% 0.76/0.75 tff(524,assumption,(hskp8), introduced(assumption)).
% 0.76/0.75 tff(525,plain,
% 0.76/0.75 (((~hskp8) | c1_1(a679)) <=> ((~hskp8) | c1_1(a679))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(526,axiom,((~hskp8) | c1_1(a679)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.76/0.75 tff(527,plain,
% 0.76/0.75 ((~hskp8) | c1_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[526, 525])).
% 0.76/0.75 tff(528,plain,
% 0.76/0.75 ((~hskp8) | c1_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[527, 525])).
% 0.76/0.75 tff(529,plain,
% 0.76/0.75 ((~hskp8) | c1_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[528, 525])).
% 0.76/0.75 tff(530,plain,
% 0.76/0.75 ((~hskp8) | c1_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[529, 525])).
% 0.76/0.75 tff(531,plain,
% 0.76/0.75 ((~hskp8) | c1_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[530, 525])).
% 0.76/0.75 tff(532,plain,
% 0.76/0.75 ((~hskp8) | c1_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[531, 525])).
% 0.76/0.75 tff(533,plain,
% 0.76/0.75 ((~hskp8) | c1_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[532, 525])).
% 0.76/0.75 tff(534,plain,
% 0.76/0.75 ((~hskp8) | c1_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[533, 525])).
% 0.76/0.75 tff(535,plain,
% 0.76/0.75 (c1_1(a679)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[534, 524])).
% 0.76/0.75 tff(536,plain,
% 0.76/0.75 (((~hskp8) | c3_1(a679)) <=> ((~hskp8) | c3_1(a679))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(537,axiom,((~hskp8) | c3_1(a679)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.76/0.75 tff(538,plain,
% 0.76/0.75 ((~hskp8) | c3_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.76/0.75 tff(539,plain,
% 0.76/0.75 ((~hskp8) | c3_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[538, 536])).
% 0.76/0.75 tff(540,plain,
% 0.76/0.75 ((~hskp8) | c3_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[539, 536])).
% 0.76/0.75 tff(541,plain,
% 0.76/0.75 ((~hskp8) | c3_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[540, 536])).
% 0.76/0.75 tff(542,plain,
% 0.76/0.75 ((~hskp8) | c3_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[541, 536])).
% 0.76/0.75 tff(543,plain,
% 0.76/0.75 ((~hskp8) | c3_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[542, 536])).
% 0.76/0.75 tff(544,plain,
% 0.76/0.75 ((~hskp8) | c3_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[543, 536])).
% 0.76/0.75 tff(545,plain,
% 0.76/0.75 ((~hskp8) | c3_1(a679)),
% 0.76/0.75 inference(modus_ponens,[status(thm)],[544, 536])).
% 0.76/0.75 tff(546,plain,
% 0.76/0.75 (c3_1(a679)),
% 0.76/0.75 inference(unit_resolution,[status(thm)],[545, 524])).
% 0.76/0.75 tff(547,assumption,(~c1_1(a681)), introduced(assumption)).
% 0.76/0.75 tff(548,assumption,(~c0_1(a679)), introduced(assumption)).
% 0.76/0.75 tff(549,plain,
% 0.76/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a683) | c0_1(a681) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a683) | c0_1(a681) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(550,plain,
% 0.76/0.75 (((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681))) <=> (c2_1(a683) | c0_1(a681) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)))),
% 0.76/0.75 inference(rewrite,[status(thm)],[])).
% 0.76/0.75 tff(551,plain,
% 0.76/0.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a683) | c0_1(a681) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683))))),
% 0.76/0.76 inference(monotonicity,[status(thm)],[550])).
% 0.76/0.76 tff(552,plain,
% 0.76/0.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a683) | c0_1(a681) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683)))),
% 0.76/0.76 inference(transitivity,[status(thm)],[551, 549])).
% 0.76/0.76 tff(553,plain,
% 0.76/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a681) | c0_1(a681) | (~c3_1(a681)))),
% 0.76/0.76 inference(quant_inst,[status(thm)],[])).
% 0.76/0.76 tff(554,plain,
% 0.76/0.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a683) | c0_1(a681) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | c1_1(a681) | (~c3_1(a681)) | (~c3_1(a683)) | (~c0_1(a683))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[553, 552])).
% 0.76/0.76 tff(555,plain,
% 0.76/0.76 ((~c1_1(a679)) | (~c3_1(a679))),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[554, 99, 292, 294, 319, 293, 318, 548, 490, 547])).
% 0.76/0.76 tff(556,plain,
% 0.76/0.76 ($false),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[555, 546, 535])).
% 0.76/0.76 tff(557,plain,((~hskp8) | (~c0_1(a683)) | (~c3_1(a683)) | (~c3_1(a681)) | c2_1(a683) | c0_1(a681) | c0_1(a679) | c1_1(a681)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.76 tff(558,plain,
% 0.76/0.76 ($false),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[557, 523, 517, 294, 289, 293, 288, 292, 291])).
% 0.76/0.76 tff(559,plain,((~hskp7) | (~c3_1(a683)) | c2_1(a683) | (~c0_1(a683)) | hskp28), inference(lemma,lemma(discharge,[]))).
% 0.76/0.76 tff(560,plain,
% 0.76/0.76 ($false),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[559, 282, 276, 167, 265, 12])).
% 0.76/0.76 tff(561,plain,(hskp28), inference(lemma,lemma(discharge,[]))).
% 0.76/0.76 tff(562,plain,
% 0.76/0.76 (((~hskp28) | c3_1(a678)) <=> ((~hskp28) | c3_1(a678))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(563,axiom,((~hskp28) | c3_1(a678)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.76/0.76 tff(564,plain,
% 0.76/0.76 ((~hskp28) | c3_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[563, 562])).
% 0.76/0.76 tff(565,plain,
% 0.76/0.76 ((~hskp28) | c3_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[564, 562])).
% 0.76/0.76 tff(566,plain,
% 0.76/0.76 ((~hskp28) | c3_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[565, 562])).
% 0.76/0.76 tff(567,plain,
% 0.76/0.76 ((~hskp28) | c3_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[566, 562])).
% 0.76/0.76 tff(568,plain,
% 0.76/0.76 ((~hskp28) | c3_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[567, 562])).
% 0.76/0.76 tff(569,plain,
% 0.76/0.76 ((~hskp28) | c3_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[568, 562])).
% 0.76/0.76 tff(570,plain,
% 0.76/0.76 ((~hskp28) | c3_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[569, 562])).
% 0.76/0.76 tff(571,plain,
% 0.76/0.76 ((~hskp28) | c3_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[570, 562])).
% 0.76/0.76 tff(572,plain,
% 0.76/0.76 (c3_1(a678)),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[571, 561])).
% 0.76/0.76 tff(573,plain,
% 0.76/0.76 (((~hskp28) | c1_1(a678)) <=> ((~hskp28) | c1_1(a678))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(574,axiom,((~hskp28) | c1_1(a678)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 0.76/0.76 tff(575,plain,
% 0.76/0.76 ((~hskp28) | c1_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[574, 573])).
% 0.76/0.76 tff(576,plain,
% 0.76/0.76 ((~hskp28) | c1_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[575, 573])).
% 0.76/0.76 tff(577,plain,
% 0.76/0.76 ((~hskp28) | c1_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[576, 573])).
% 0.76/0.76 tff(578,plain,
% 0.76/0.76 ((~hskp28) | c1_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[577, 573])).
% 0.76/0.76 tff(579,plain,
% 0.76/0.76 ((~hskp28) | c1_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[578, 573])).
% 0.76/0.76 tff(580,plain,
% 0.76/0.76 ((~hskp28) | c1_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[579, 573])).
% 0.76/0.76 tff(581,plain,
% 0.76/0.76 ((~hskp28) | c1_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[580, 573])).
% 0.76/0.76 tff(582,plain,
% 0.76/0.76 ((~hskp28) | c1_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[581, 573])).
% 0.76/0.76 tff(583,plain,
% 0.76/0.76 (c1_1(a678)),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[582, 561])).
% 0.76/0.76 tff(584,plain,
% 0.76/0.76 (((~hskp28) | c0_1(a678)) <=> ((~hskp28) | c0_1(a678))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(585,axiom,((~hskp28) | c0_1(a678)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.76/0.76 tff(586,plain,
% 0.76/0.76 ((~hskp28) | c0_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.76/0.76 tff(587,plain,
% 0.76/0.76 ((~hskp28) | c0_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[586, 584])).
% 0.76/0.76 tff(588,plain,
% 0.76/0.76 ((~hskp28) | c0_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[587, 584])).
% 0.76/0.76 tff(589,plain,
% 0.76/0.76 ((~hskp28) | c0_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[588, 584])).
% 0.76/0.76 tff(590,plain,
% 0.76/0.76 ((~hskp28) | c0_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[589, 584])).
% 0.76/0.76 tff(591,plain,
% 0.76/0.76 ((~hskp28) | c0_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[590, 584])).
% 0.76/0.76 tff(592,plain,
% 0.76/0.76 ((~hskp28) | c0_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[591, 584])).
% 0.76/0.76 tff(593,plain,
% 0.76/0.76 ((~hskp28) | c0_1(a678)),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[592, 584])).
% 0.76/0.76 tff(594,plain,
% 0.76/0.76 (c0_1(a678)),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[593, 561])).
% 0.76/0.76 tff(595,plain,
% 0.76/0.76 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(596,plain,
% 0.76/0.76 (((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678))) <=> ((~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(597,plain,
% 0.76/0.76 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678))))),
% 0.76/0.76 inference(monotonicity,[status(thm)],[596])).
% 0.76/0.76 tff(598,plain,
% 0.76/0.76 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)))),
% 0.76/0.76 inference(transitivity,[status(thm)],[597, 595])).
% 0.76/0.76 tff(599,plain,
% 0.76/0.76 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c2_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | (~c2_1(a678)) | (~c3_1(a678)) | (~c0_1(a678)))),
% 0.76/0.76 inference(quant_inst,[status(thm)],[])).
% 0.76/0.76 tff(600,plain,
% 0.76/0.76 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))) | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)) | (~c3_1(a678))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[599, 598])).
% 0.76/0.76 tff(601,plain,
% 0.76/0.76 ($false),
% 0.76/0.76 inference(unit_resolution,[status(thm)],[600, 99, 594, 583, 572, 11, 1])).
% 0.76/0.76 tff(602,plain,(~c2_1(a678)), inference(lemma,lemma(discharge,[]))).
% 0.76/0.76 tff(603,assumption,(~hskp9), introduced(assumption)).
% 0.76/0.76 tff(604,assumption,(~hskp2), introduced(assumption)).
% 0.76/0.76 tff(605,plain,
% 0.76/0.76 (^[U: $i] : refl((hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(606,plain,
% 0.76/0.76 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[605])).
% 0.76/0.76 tff(607,plain,
% 0.76/0.76 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(608,plain,
% 0.76/0.76 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp9))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) <=> (hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp2) <=> ((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp2))), rewrite(((hskp9 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U))) | hskp2) <=> (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp2) <=> (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(609,plain,
% 0.76/0.76 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp2) <=> ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[608])).
% 0.76/0.76 tff(610,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp9) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 0.76/0.76 tff(611,plain,
% 0.76/0.76 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.76/0.76 tff(612,plain,
% 0.76/0.76 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[611, 607])).
% 0.76/0.76 tff(613,plain,(
% 0.76/0.76 ![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.76/0.76 inference(skolemize,[status(sab)],[612])).
% 0.76/0.76 tff(614,plain,
% 0.76/0.76 (![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[613, 606])).
% 0.76/0.76 tff(615,plain,
% 0.76/0.76 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(616,plain,
% 0.76/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[615])).
% 0.76/0.76 tff(617,plain,
% 0.76/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(618,plain,
% 0.76/0.76 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(619,plain,
% 0.76/0.76 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[618])).
% 0.76/0.76 tff(620,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c2_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 0.76/0.76 tff(621,plain,
% 0.76/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[620, 619])).
% 0.76/0.76 tff(622,plain,
% 0.76/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[621, 617])).
% 0.76/0.76 tff(623,plain,(
% 0.76/0.76 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.76 inference(skolemize,[status(sab)],[622])).
% 0.76/0.76 tff(624,plain,
% 0.76/0.76 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))),
% 0.76/0.76 inference(modus_ponens,[status(thm)],[623, 616])).
% 0.76/0.76 tff(625,assumption,(~hskp11), introduced(assumption)).
% 0.76/0.76 tff(626,assumption,(~hskp5), introduced(assumption)).
% 0.76/0.76 tff(627,plain,
% 0.76/0.76 (^[U: $i] : refl((hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))),
% 0.76/0.76 inference(bind,[status(th)],[])).
% 0.76/0.76 tff(628,plain,
% 0.76/0.76 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.76/0.76 inference(quant_intro,[status(thm)],[627])).
% 0.76/0.76 tff(629,plain,
% 0.76/0.76 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.76/0.76 inference(rewrite,[status(thm)],[])).
% 0.76/0.76 tff(630,plain,
% 0.76/0.76 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp9) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp9))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp9) <=> (hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp9) | hskp5) <=> ((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp5))), rewrite(((hskp9 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U))) | hskp5) <=> (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp9) | hskp5) <=> (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))))),
% 0.81/0.76 inference(bind,[status(th)],[])).
% 0.81/0.76 tff(631,plain,
% 0.81/0.76 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp9) | hskp5) <=> ![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.81/0.76 inference(quant_intro,[status(thm)],[630])).
% 0.81/0.76 tff(632,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp9) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 0.81/0.76 tff(633,plain,
% 0.81/0.76 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.81/0.76 tff(634,plain,
% 0.81/0.76 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[633, 629])).
% 0.81/0.76 tff(635,plain,(
% 0.81/0.76 ![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.81/0.76 inference(skolemize,[status(sab)],[634])).
% 0.81/0.76 tff(636,plain,
% 0.81/0.76 (![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[635, 628])).
% 0.81/0.76 tff(637,plain,
% 0.81/0.76 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp9 | hskp5 | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(638,plain,
% 0.81/0.76 ((hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a678)) | (~c0_1(a678)) | (~c1_1(a678))) <=> (hskp9 | hskp5 | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(639,plain,
% 0.81/0.76 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a678)) | (~c0_1(a678)) | (~c1_1(a678)))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678))))),
% 0.81/0.76 inference(monotonicity,[status(thm)],[638])).
% 0.81/0.76 tff(640,plain,
% 0.81/0.76 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a678)) | (~c0_1(a678)) | (~c1_1(a678)))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp9 | hskp5 | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678)))),
% 0.81/0.76 inference(transitivity,[status(thm)],[639, 637])).
% 0.81/0.76 tff(641,plain,
% 0.81/0.76 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a678)) | (~c0_1(a678)) | (~c1_1(a678)))),
% 0.81/0.76 inference(quant_inst,[status(thm)],[])).
% 0.81/0.76 tff(642,plain,
% 0.81/0.76 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp9 | hskp5 | (~ndr1_0) | (~c1_1(a678)) | (~c2_1(a678)) | (~c0_1(a678))),
% 0.81/0.76 inference(modus_ponens,[status(thm)],[641, 640])).
% 0.81/0.76 tff(643,plain,
% 0.81/0.76 (hskp9 | hskp5 | (~c2_1(a678))),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[642, 99, 594, 583, 636])).
% 0.81/0.76 tff(644,plain,
% 0.81/0.76 (~c2_1(a678)),
% 0.81/0.76 inference(unit_resolution,[status(thm)],[643, 603, 626])).
% 0.81/0.76 tff(645,plain,
% 0.81/0.76 (((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a696)) | (~c0_1(a696)) | (~c1_1(a696)))) <=> ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a696)) | (~c0_1(a696)) | (~c1_1(a696)))),
% 0.81/0.76 inference(rewrite,[status(thm)],[])).
% 0.81/0.76 tff(646,plain,
% 0.81/0.76 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a696)) | (~c0_1(a696)) | (~c1_1(a696)))),
% 0.81/0.77 inference(quant_inst,[status(thm)],[])).
% 0.81/0.77 tff(647,plain,
% 0.81/0.77 ((~![U: $i] : (hskp9 | hskp5 | (~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(U)))) | hskp9 | hskp5 | (~ndr1_0) | (~c2_1(a696)) | (~c0_1(a696)) | (~c1_1(a696))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.81/0.77 tff(648,plain,
% 0.81/0.77 (~c1_1(a696)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[647, 99, 603, 626, 416, 405, 636])).
% 0.81/0.77 tff(649,plain,
% 0.81/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a696) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a696)) | (~c0_1(a696)) | c1_1(a696))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a696)) | (~c0_1(a696)) | c1_1(a696))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(650,plain,
% 0.81/0.77 (((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a696) | (~c2_1(a696)) | c3_1(a696)) <=> (c3_1(a696) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a696)) | (~c0_1(a696)) | c1_1(a696))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(651,plain,
% 0.81/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a696) | (~c2_1(a696)) | c3_1(a696))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a696) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a696)) | (~c0_1(a696)) | c1_1(a696)))),
% 0.81/0.77 inference(monotonicity,[status(thm)],[650])).
% 0.81/0.77 tff(652,plain,
% 0.81/0.77 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a696) | (~c2_1(a696)) | c3_1(a696))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a696)) | (~c0_1(a696)) | c1_1(a696))),
% 0.81/0.77 inference(transitivity,[status(thm)],[651, 649])).
% 0.81/0.77 tff(653,plain,
% 0.81/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a696) | (~c2_1(a696)) | c3_1(a696))),
% 0.81/0.77 inference(quant_inst,[status(thm)],[])).
% 0.81/0.77 tff(654,plain,
% 0.81/0.77 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a696)) | (~c0_1(a696)) | c1_1(a696)),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[653, 652])).
% 0.81/0.77 tff(655,plain,
% 0.81/0.77 ($false),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[654, 99, 594, 572, 416, 405, 393, 304, 644, 648])).
% 0.81/0.77 tff(656,plain,((~hskp14) | hskp9 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.81/0.77 tff(657,plain,
% 0.81/0.77 (~hskp14),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[656, 603, 626])).
% 0.81/0.77 tff(658,plain,
% 0.81/0.77 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c3_1(a678)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c3_1(a678)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(659,plain,
% 0.81/0.77 ((hskp17 | hskp14 | (~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678))) <=> (hskp17 | hskp14 | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c3_1(a678)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(660,plain,
% 0.81/0.77 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c3_1(a678))))),
% 0.81/0.77 inference(monotonicity,[status(thm)],[659])).
% 0.81/0.77 tff(661,plain,
% 0.81/0.77 (((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)))) <=> ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c3_1(a678)))),
% 0.81/0.77 inference(transitivity,[status(thm)],[660, 658])).
% 0.81/0.77 tff(662,plain,
% 0.81/0.77 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp17 | hskp14 | (~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)))),
% 0.81/0.77 inference(quant_inst,[status(thm)],[])).
% 0.81/0.77 tff(663,plain,
% 0.81/0.77 ((~![U: $i] : (hskp17 | hskp14 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp17 | hskp14 | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c3_1(a678))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.81/0.77 tff(664,plain,
% 0.81/0.77 (hskp17 | hskp14 | c2_1(a678)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[663, 99, 583, 572, 435])).
% 0.81/0.77 tff(665,plain,
% 0.81/0.77 (hskp17),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[664, 657, 644])).
% 0.81/0.77 tff(666,plain,
% 0.81/0.77 (~c0_1(a703)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[450, 665])).
% 0.81/0.77 tff(667,plain,
% 0.81/0.77 (c1_1(a703)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[472, 665])).
% 0.81/0.77 tff(668,plain,
% 0.81/0.77 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c3_1(a703) | (~c1_1(a703)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(669,plain,
% 0.81/0.77 (((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703))) <=> (c0_1(a703) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c3_1(a703) | (~c1_1(a703)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(670,plain,
% 0.81/0.77 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c3_1(a703) | (~c1_1(a703))))),
% 0.81/0.77 inference(monotonicity,[status(thm)],[669])).
% 0.81/0.77 tff(671,plain,
% 0.81/0.77 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c3_1(a703) | (~c1_1(a703)))),
% 0.81/0.77 inference(transitivity,[status(thm)],[670, 668])).
% 0.81/0.77 tff(672,plain,
% 0.81/0.77 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))),
% 0.81/0.77 inference(quant_inst,[status(thm)],[])).
% 0.81/0.77 tff(673,plain,
% 0.81/0.77 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c3_1(a703) | (~c1_1(a703))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.81/0.77 tff(674,plain,
% 0.81/0.77 (c3_1(a703)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[673, 99, 594, 583, 572, 667, 666, 383, 644])).
% 0.81/0.77 tff(675,plain,
% 0.81/0.77 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.81/0.77 inference(bind,[status(th)],[])).
% 0.81/0.77 tff(676,plain,
% 0.81/0.77 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.77 inference(quant_intro,[status(thm)],[675])).
% 0.81/0.77 tff(677,plain,
% 0.81/0.77 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(678,plain,
% 0.81/0.77 (^[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) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.81/0.77 inference(bind,[status(th)],[])).
% 0.81/0.77 tff(679,plain,
% 0.81/0.77 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.77 inference(quant_intro,[status(thm)],[678])).
% 0.81/0.77 tff(680,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 0.81/0.77 tff(681,plain,
% 0.81/0.77 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.81/0.77 tff(682,plain,
% 0.81/0.77 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[681, 677])).
% 0.81/0.77 tff(683,plain,(
% 0.81/0.77 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.77 inference(skolemize,[status(sab)],[682])).
% 0.81/0.77 tff(684,plain,
% 0.81/0.77 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[683, 676])).
% 0.81/0.77 tff(685,plain,
% 0.81/0.77 (((~hskp17) | (~c2_1(a703))) <=> ((~hskp17) | (~c2_1(a703)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(686,plain,
% 0.81/0.77 (((~c2_1(a703)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a703)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(687,axiom,((~c2_1(a703)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.81/0.77 tff(688,plain,
% 0.81/0.77 ((~hskp17) | (~c2_1(a703))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[687, 686])).
% 0.81/0.77 tff(689,plain,
% 0.81/0.77 ((~hskp17) | (~c2_1(a703))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[688, 685])).
% 0.81/0.77 tff(690,plain,
% 0.81/0.77 (~c2_1(a703)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[689, 665])).
% 0.81/0.77 tff(691,plain,
% 0.81/0.77 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a703) | c2_1(a703) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a703) | c2_1(a703) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a703)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(692,plain,
% 0.81/0.77 ((hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | c2_1(a703) | (~c3_1(a703))) <=> (hskp7 | c0_1(a703) | c2_1(a703) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a703)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(693,plain,
% 0.81/0.77 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | c2_1(a703) | (~c3_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a703) | c2_1(a703) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a703))))),
% 0.81/0.77 inference(monotonicity,[status(thm)],[692])).
% 0.81/0.77 tff(694,plain,
% 0.81/0.77 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | c2_1(a703) | (~c3_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a703) | c2_1(a703) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a703)))),
% 0.81/0.77 inference(transitivity,[status(thm)],[693, 691])).
% 0.81/0.77 tff(695,plain,
% 0.81/0.77 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | c2_1(a703) | (~c3_1(a703)))),
% 0.81/0.77 inference(quant_inst,[status(thm)],[])).
% 0.81/0.77 tff(696,plain,
% 0.81/0.77 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a703) | c2_1(a703) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a703))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.81/0.77 tff(697,plain,
% 0.81/0.77 ($false),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[696, 99, 43, 594, 572, 666, 690, 684, 644, 674])).
% 0.81/0.77 tff(698,plain,(hskp9 | hskp7 | hskp5), inference(lemma,lemma(discharge,[]))).
% 0.81/0.77 tff(699,plain,
% 0.81/0.77 (hskp9),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[698, 626, 43])).
% 0.81/0.77 tff(700,plain,
% 0.81/0.77 (~c3_1(a680)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[310, 699])).
% 0.81/0.77 tff(701,plain,
% 0.81/0.77 (~c1_1(a680)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[316, 699])).
% 0.81/0.77 tff(702,plain,
% 0.81/0.77 (hskp25),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[122, 626, 43])).
% 0.81/0.77 tff(703,plain,
% 0.81/0.77 (~c3_1(a760)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[128, 702])).
% 0.81/0.77 tff(704,plain,
% 0.81/0.77 (~c1_1(a760)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[157, 702])).
% 0.81/0.77 tff(705,plain,
% 0.81/0.77 (~c0_1(a760)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[134, 702])).
% 0.81/0.77 tff(706,plain,
% 0.81/0.77 (c2_1(a680)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[341, 699])).
% 0.81/0.77 tff(707,plain,
% 0.81/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(708,plain,
% 0.81/0.77 ((hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a760) | c1_1(a760) | c0_1(a760)) <=> (hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)))),
% 0.81/0.77 inference(rewrite,[status(thm)],[])).
% 0.81/0.77 tff(709,plain,
% 0.81/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a760) | c1_1(a760) | c0_1(a760))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680))))),
% 0.81/0.77 inference(monotonicity,[status(thm)],[708])).
% 0.81/0.77 tff(710,plain,
% 0.81/0.77 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a760) | c1_1(a760) | c0_1(a760))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)))),
% 0.81/0.77 inference(transitivity,[status(thm)],[709, 707])).
% 0.81/0.77 tff(711,plain,
% 0.81/0.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a760) | c1_1(a760) | c0_1(a760))),
% 0.81/0.77 inference(quant_inst,[status(thm)],[])).
% 0.81/0.77 tff(712,plain,
% 0.81/0.77 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c0_1(a760) | c1_1(a760) | c3_1(a760) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680))),
% 0.81/0.77 inference(modus_ponens,[status(thm)],[711, 710])).
% 0.81/0.77 tff(713,plain,
% 0.81/0.77 ($false),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[712, 99, 626, 706, 705, 704, 703, 701, 700, 152])).
% 0.81/0.77 tff(714,plain,(hskp5 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.81/0.77 tff(715,plain,
% 0.81/0.77 (hskp5),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[714, 43])).
% 0.81/0.77 tff(716,plain,
% 0.81/0.77 (~c3_1(a673)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[49, 715])).
% 0.81/0.77 tff(717,plain,
% 0.81/0.77 (~c0_1(a673)),
% 0.81/0.77 inference(unit_resolution,[status(thm)],[61, 715])).
% 0.81/0.77 tff(718,plain,
% 0.81/0.77 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a673)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a673)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(719,plain,
% 0.81/0.78 (((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673))) <=> (c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a673)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(720,plain,
% 0.81/0.78 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a673))))),
% 0.81/0.78 inference(monotonicity,[status(thm)],[719])).
% 0.81/0.78 tff(721,plain,
% 0.81/0.78 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a673)))),
% 0.81/0.78 inference(transitivity,[status(thm)],[720, 718])).
% 0.81/0.78 tff(722,plain,
% 0.81/0.78 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c3_1(a678)) | (~c1_1(a678)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))),
% 0.81/0.78 inference(quant_inst,[status(thm)],[])).
% 0.81/0.78 tff(723,plain,
% 0.81/0.78 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a673))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[722, 721])).
% 0.81/0.78 tff(724,plain,
% 0.81/0.78 (~c1_1(a673)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[723, 99, 594, 583, 572, 717, 716, 383, 602])).
% 0.81/0.78 tff(725,plain,
% 0.81/0.78 (~c2_1(a673)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[55, 715])).
% 0.81/0.78 tff(726,assumption,(~c1_1(a673)), introduced(assumption)).
% 0.81/0.78 tff(727,plain,
% 0.81/0.78 (^[U: $i] : refl((hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 0.81/0.78 inference(bind,[status(th)],[])).
% 0.81/0.78 tff(728,plain,
% 0.81/0.78 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.81/0.78 inference(quant_intro,[status(thm)],[727])).
% 0.81/0.78 tff(729,plain,
% 0.81/0.78 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(730,plain,
% 0.81/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite(((hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 0.81/0.78 inference(bind,[status(th)],[])).
% 0.81/0.78 tff(731,plain,
% 0.81/0.78 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2) <=> ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.81/0.78 inference(quant_intro,[status(thm)],[730])).
% 0.81/0.78 tff(732,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp1) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.81/0.78 tff(733,plain,
% 0.81/0.78 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[732, 731])).
% 0.81/0.78 tff(734,plain,
% 0.81/0.78 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[733, 729])).
% 0.81/0.78 tff(735,plain,(
% 0.81/0.78 ![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.81/0.78 inference(skolemize,[status(sab)],[734])).
% 0.81/0.78 tff(736,plain,
% 0.81/0.78 (![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[735, 728])).
% 0.81/0.78 tff(737,assumption,(~c2_1(a673)), introduced(assumption)).
% 0.81/0.78 tff(738,assumption,(~c0_1(a673)), introduced(assumption)).
% 0.81/0.78 tff(739,plain,
% 0.81/0.78 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | c1_1(a673))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | c1_1(a673))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(740,plain,
% 0.81/0.78 ((hskp2 | hskp1 | (~ndr1_0) | c2_1(a673) | c1_1(a673) | c0_1(a673)) <=> (hskp2 | hskp1 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | c1_1(a673))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(741,plain,
% 0.81/0.78 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a673) | c1_1(a673) | c0_1(a673))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | c1_1(a673)))),
% 0.81/0.78 inference(monotonicity,[status(thm)],[740])).
% 0.81/0.78 tff(742,plain,
% 0.81/0.78 (((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a673) | c1_1(a673) | c0_1(a673))) <=> ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | c1_1(a673))),
% 0.81/0.78 inference(transitivity,[status(thm)],[741, 739])).
% 0.81/0.78 tff(743,plain,
% 0.81/0.78 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp2 | hskp1 | (~ndr1_0) | c2_1(a673) | c1_1(a673) | c0_1(a673))),
% 0.81/0.78 inference(quant_inst,[status(thm)],[])).
% 0.81/0.78 tff(744,plain,
% 0.81/0.78 ((~![U: $i] : (hskp2 | hskp1 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp2 | hskp1 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | c1_1(a673)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[743, 742])).
% 0.81/0.78 tff(745,plain,
% 0.81/0.78 (hskp2 | hskp1),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[744, 99, 738, 737, 736, 726])).
% 0.81/0.78 tff(746,plain,
% 0.81/0.78 (hskp1),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[745, 604])).
% 0.81/0.78 tff(747,plain,
% 0.81/0.78 (((~hskp1) | (~c2_1(a669))) <=> ((~hskp1) | (~c2_1(a669)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(748,plain,
% 0.81/0.78 (((~c2_1(a669)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a669)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(749,axiom,((~c2_1(a669)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 0.81/0.78 tff(750,plain,
% 0.81/0.78 ((~hskp1) | (~c2_1(a669))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[749, 748])).
% 0.81/0.78 tff(751,plain,
% 0.81/0.78 ((~hskp1) | (~c2_1(a669))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[750, 747])).
% 0.81/0.78 tff(752,plain,
% 0.81/0.78 (~c2_1(a669)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[751, 746])).
% 0.81/0.78 tff(753,plain,
% 0.81/0.78 (((~hskp1) | (~c1_1(a669))) <=> ((~hskp1) | (~c1_1(a669)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(754,plain,
% 0.81/0.78 (((~c1_1(a669)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a669)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(755,axiom,((~c1_1(a669)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.81/0.78 tff(756,plain,
% 0.81/0.78 ((~hskp1) | (~c1_1(a669))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[755, 754])).
% 0.81/0.78 tff(757,plain,
% 0.81/0.78 ((~hskp1) | (~c1_1(a669))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[756, 753])).
% 0.81/0.78 tff(758,plain,
% 0.81/0.78 (~c1_1(a669)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[757, 746])).
% 0.81/0.78 tff(759,plain,
% 0.81/0.78 (((~hskp1) | c0_1(a669)) <=> ((~hskp1) | c0_1(a669))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(760,axiom,((~hskp1) | c0_1(a669)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.81/0.78 tff(761,plain,
% 0.81/0.78 ((~hskp1) | c0_1(a669)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[760, 759])).
% 0.81/0.78 tff(762,plain,
% 0.81/0.78 ((~hskp1) | c0_1(a669)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[761, 759])).
% 0.81/0.78 tff(763,plain,
% 0.81/0.78 ((~hskp1) | c0_1(a669)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[762, 759])).
% 0.81/0.78 tff(764,plain,
% 0.81/0.78 ((~hskp1) | c0_1(a669)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[763, 759])).
% 0.81/0.78 tff(765,plain,
% 0.81/0.78 ((~hskp1) | c0_1(a669)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[764, 759])).
% 0.81/0.78 tff(766,plain,
% 0.81/0.78 ((~hskp1) | c0_1(a669)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[765, 759])).
% 0.81/0.78 tff(767,plain,
% 0.81/0.78 ((~hskp1) | c0_1(a669)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[766, 759])).
% 0.81/0.78 tff(768,plain,
% 0.81/0.78 ((~hskp1) | c0_1(a669)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[767, 759])).
% 0.81/0.78 tff(769,plain,
% 0.81/0.78 (c0_1(a669)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[768, 746])).
% 0.81/0.78 tff(770,plain,
% 0.81/0.78 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | c1_1(a669) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c1_1(a669) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(771,plain,
% 0.81/0.78 ((hskp9 | hskp2 | (~ndr1_0) | c2_1(a669) | c1_1(a669) | (~c0_1(a669))) <=> (hskp9 | hskp2 | c1_1(a669) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(772,plain,
% 0.81/0.78 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a669) | c1_1(a669) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | c1_1(a669) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669))))),
% 0.81/0.78 inference(monotonicity,[status(thm)],[771])).
% 0.81/0.78 tff(773,plain,
% 0.81/0.78 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a669) | c1_1(a669) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c1_1(a669) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)))),
% 0.81/0.78 inference(transitivity,[status(thm)],[772, 770])).
% 0.81/0.78 tff(774,plain,
% 0.81/0.78 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a669) | c1_1(a669) | (~c0_1(a669)))),
% 0.81/0.78 inference(quant_inst,[status(thm)],[])).
% 0.81/0.78 tff(775,plain,
% 0.81/0.78 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c1_1(a669) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[774, 773])).
% 0.81/0.78 tff(776,plain,
% 0.81/0.78 ($false),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[775, 99, 603, 604, 769, 758, 752, 614])).
% 0.81/0.78 tff(777,plain,(hskp2 | hskp9 | c0_1(a673) | c2_1(a673) | c1_1(a673)), inference(lemma,lemma(discharge,[]))).
% 0.81/0.78 tff(778,plain,
% 0.81/0.78 (hskp2),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[777, 603, 717, 725, 724])).
% 0.81/0.78 tff(779,plain,
% 0.81/0.78 (((~hskp2) | (~c1_1(a670))) <=> ((~hskp2) | (~c1_1(a670)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(780,plain,
% 0.81/0.78 (((~c1_1(a670)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a670)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(781,axiom,((~c1_1(a670)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.81/0.78 tff(782,plain,
% 0.81/0.78 ((~hskp2) | (~c1_1(a670))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[781, 780])).
% 0.81/0.78 tff(783,plain,
% 0.81/0.78 ((~hskp2) | (~c1_1(a670))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[782, 779])).
% 0.81/0.78 tff(784,plain,
% 0.81/0.78 (~c1_1(a670)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[783, 778])).
% 0.81/0.78 tff(785,plain,
% 0.81/0.78 (((~hskp2) | (~c0_1(a670))) <=> ((~hskp2) | (~c0_1(a670)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(786,plain,
% 0.81/0.78 (((~c0_1(a670)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a670)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(787,axiom,((~c0_1(a670)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.81/0.78 tff(788,plain,
% 0.81/0.78 ((~hskp2) | (~c0_1(a670))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[787, 786])).
% 0.81/0.78 tff(789,plain,
% 0.81/0.78 ((~hskp2) | (~c0_1(a670))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[788, 785])).
% 0.81/0.78 tff(790,plain,
% 0.81/0.78 (~c0_1(a670)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[789, 778])).
% 0.81/0.78 tff(791,assumption,(~c2_1(a678)), introduced(assumption)).
% 0.81/0.78 tff(792,assumption,(hskp2), introduced(assumption)).
% 0.81/0.78 tff(793,plain,
% 0.81/0.78 (~c0_1(a670)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[789, 792])).
% 0.81/0.78 tff(794,plain,
% 0.81/0.78 (((~hskp2) | c3_1(a670)) <=> ((~hskp2) | c3_1(a670))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(795,axiom,((~hskp2) | c3_1(a670)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.81/0.78 tff(796,plain,
% 0.81/0.78 ((~hskp2) | c3_1(a670)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[795, 794])).
% 0.81/0.78 tff(797,plain,
% 0.81/0.78 ((~hskp2) | c3_1(a670)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[796, 794])).
% 0.81/0.78 tff(798,plain,
% 0.81/0.78 ((~hskp2) | c3_1(a670)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[797, 794])).
% 0.81/0.78 tff(799,plain,
% 0.81/0.78 ((~hskp2) | c3_1(a670)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[798, 794])).
% 0.81/0.78 tff(800,plain,
% 0.81/0.78 ((~hskp2) | c3_1(a670)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[799, 794])).
% 0.81/0.78 tff(801,plain,
% 0.81/0.78 ((~hskp2) | c3_1(a670)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[800, 794])).
% 0.81/0.78 tff(802,plain,
% 0.81/0.78 ((~hskp2) | c3_1(a670)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[801, 794])).
% 0.81/0.78 tff(803,plain,
% 0.81/0.78 ((~hskp2) | c3_1(a670)),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[802, 794])).
% 0.81/0.78 tff(804,plain,
% 0.81/0.78 (c3_1(a670)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[803, 792])).
% 0.81/0.78 tff(805,plain,
% 0.81/0.78 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(806,plain,
% 0.81/0.78 ((hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a670) | c2_1(a670) | (~c3_1(a670))) <=> (hskp7 | c0_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(807,plain,
% 0.81/0.78 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a670) | c2_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670))))),
% 0.81/0.78 inference(monotonicity,[status(thm)],[806])).
% 0.81/0.78 tff(808,plain,
% 0.81/0.78 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a670) | c2_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))),
% 0.81/0.78 inference(transitivity,[status(thm)],[807, 805])).
% 0.81/0.78 tff(809,plain,
% 0.81/0.78 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a670) | c2_1(a670) | (~c3_1(a670)))),
% 0.81/0.78 inference(quant_inst,[status(thm)],[])).
% 0.81/0.78 tff(810,plain,
% 0.81/0.78 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[809, 808])).
% 0.81/0.78 tff(811,plain,
% 0.81/0.78 (c2_1(a670)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[810, 99, 43, 594, 572, 804, 793, 684, 791])).
% 0.81/0.78 tff(812,plain,
% 0.81/0.78 (~c1_1(a670)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[783, 792])).
% 0.81/0.78 tff(813,assumption,(~hskp8), introduced(assumption)).
% 0.81/0.78 tff(814,plain,
% 0.81/0.78 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(815,plain,
% 0.81/0.78 ((hskp9 | hskp8 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c2_1(a670))) <=> (hskp9 | hskp8 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)))),
% 0.81/0.78 inference(rewrite,[status(thm)],[])).
% 0.81/0.78 tff(816,plain,
% 0.81/0.78 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670))))),
% 0.81/0.78 inference(monotonicity,[status(thm)],[815])).
% 0.81/0.78 tff(817,plain,
% 0.81/0.78 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)))),
% 0.81/0.78 inference(transitivity,[status(thm)],[816, 814])).
% 0.81/0.78 tff(818,plain,
% 0.81/0.78 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)))),
% 0.81/0.78 inference(quant_inst,[status(thm)],[])).
% 0.81/0.78 tff(819,plain,
% 0.81/0.78 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670))),
% 0.81/0.78 inference(modus_ponens,[status(thm)],[818, 817])).
% 0.81/0.78 tff(820,plain,
% 0.81/0.78 ($false),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[819, 99, 603, 813, 793, 812, 509, 811])).
% 0.81/0.78 tff(821,plain,((~hskp2) | hskp9 | hskp8 | hskp7 | c2_1(a678)), inference(lemma,lemma(discharge,[]))).
% 0.81/0.78 tff(822,plain,
% 0.81/0.78 ((~hskp2) | hskp9 | hskp8 | hskp7),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[821, 602])).
% 0.81/0.78 tff(823,plain,
% 0.81/0.78 (hskp8),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[822, 778, 603, 43])).
% 0.81/0.78 tff(824,plain,
% 0.81/0.78 (~c0_1(a679)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[522, 823])).
% 0.81/0.78 tff(825,plain,
% 0.81/0.78 (c3_1(a670)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[803, 778])).
% 0.81/0.78 tff(826,plain,
% 0.81/0.78 (c3_1(a679)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[545, 823])).
% 0.81/0.78 tff(827,plain,
% 0.81/0.78 (c1_1(a679)),
% 0.81/0.78 inference(unit_resolution,[status(thm)],[534, 823])).
% 0.81/0.79 tff(828,plain,
% 0.81/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)))),
% 0.81/0.79 inference(rewrite,[status(thm)],[])).
% 0.81/0.79 tff(829,plain,
% 0.81/0.79 (((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670))) <=> (c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)))),
% 0.81/0.79 inference(rewrite,[status(thm)],[])).
% 0.81/0.79 tff(830,plain,
% 0.81/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679))))),
% 0.81/0.79 inference(monotonicity,[status(thm)],[829])).
% 0.81/0.79 tff(831,plain,
% 0.81/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)))),
% 0.81/0.79 inference(transitivity,[status(thm)],[830, 828])).
% 0.81/0.79 tff(832,plain,
% 0.81/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))),
% 0.81/0.79 inference(quant_inst,[status(thm)],[])).
% 0.81/0.79 tff(833,plain,
% 0.81/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[832, 831])).
% 0.81/0.79 tff(834,plain,
% 0.81/0.79 ($false),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[833, 99, 594, 572, 827, 826, 825, 824, 790, 784, 490, 602])).
% 0.81/0.79 tff(835,plain,(hskp9 | hskp7), inference(lemma,lemma(discharge,[]))).
% 0.81/0.79 tff(836,plain,
% 0.81/0.79 (hskp9),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[835, 43])).
% 0.81/0.79 tff(837,plain,
% 0.81/0.79 (~c3_1(a680)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[310, 836])).
% 0.81/0.79 tff(838,plain,
% 0.81/0.79 (~c1_1(a680)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[316, 836])).
% 0.81/0.79 tff(839,assumption,(~hskp14), introduced(assumption)).
% 0.81/0.79 tff(840,plain,
% 0.81/0.79 (hskp17),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[664, 791, 839])).
% 0.81/0.79 tff(841,plain,
% 0.81/0.79 (~c0_1(a703)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[450, 840])).
% 0.81/0.79 tff(842,plain,
% 0.81/0.79 (c1_1(a703)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[472, 840])).
% 0.81/0.79 tff(843,plain,
% 0.81/0.79 (c3_1(a703)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[673, 99, 594, 583, 572, 842, 841, 383, 791])).
% 0.81/0.79 tff(844,plain,
% 0.81/0.79 (~c2_1(a703)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[689, 840])).
% 0.81/0.79 tff(845,plain,
% 0.81/0.79 ($false),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[696, 99, 43, 594, 572, 841, 844, 684, 791, 843])).
% 0.81/0.79 tff(846,plain,(c2_1(a678) | hskp7 | hskp14), inference(lemma,lemma(discharge,[]))).
% 0.81/0.79 tff(847,plain,
% 0.81/0.79 (hskp7 | hskp14),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[846, 602])).
% 0.81/0.79 tff(848,plain,
% 0.81/0.79 (hskp14),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[847, 43])).
% 0.81/0.79 tff(849,plain,
% 0.81/0.79 (~c3_1(a696)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[392, 848])).
% 0.81/0.79 tff(850,plain,
% 0.81/0.79 (c2_1(a680)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[341, 836])).
% 0.81/0.79 tff(851,plain,
% 0.81/0.79 (c2_1(a696)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[404, 848])).
% 0.81/0.79 tff(852,plain,
% 0.81/0.79 (c0_1(a696)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[415, 848])).
% 0.81/0.79 tff(853,plain,
% 0.81/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a696) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c2_1(a696)) | (~c0_1(a696)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c2_1(a696)) | (~c0_1(a696)))),
% 0.81/0.79 inference(rewrite,[status(thm)],[])).
% 0.81/0.79 tff(854,plain,
% 0.81/0.79 (((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680)) <=> (c3_1(a696) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c2_1(a696)) | (~c0_1(a696)))),
% 0.81/0.79 inference(rewrite,[status(thm)],[])).
% 0.81/0.79 tff(855,plain,
% 0.81/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c3_1(a696) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c2_1(a696)) | (~c0_1(a696))))),
% 0.81/0.79 inference(monotonicity,[status(thm)],[854])).
% 0.81/0.79 tff(856,plain,
% 0.81/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c2_1(a696)) | (~c0_1(a696)))),
% 0.81/0.79 inference(transitivity,[status(thm)],[855, 853])).
% 0.81/0.79 tff(857,plain,
% 0.81/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a696) | (~c2_1(a696)) | (~c0_1(a696)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))),
% 0.81/0.79 inference(quant_inst,[status(thm)],[])).
% 0.81/0.79 tff(858,plain,
% 0.81/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c3_1(a696) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c2_1(a696)) | (~c0_1(a696))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[857, 856])).
% 0.81/0.79 tff(859,plain,
% 0.81/0.79 ($false),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[858, 99, 594, 572, 852, 851, 850, 849, 838, 837, 304, 602])).
% 0.81/0.79 tff(860,plain,(hskp7), inference(lemma,lemma(discharge,[]))).
% 0.81/0.79 tff(861,plain,
% 0.81/0.79 (~c2_1(a675)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[172, 860])).
% 0.81/0.79 tff(862,assumption,(hskp17), introduced(assumption)).
% 0.81/0.79 tff(863,plain,
% 0.81/0.79 (~c0_1(a703)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[450, 862])).
% 0.81/0.79 tff(864,plain,
% 0.81/0.79 (c3_1(a675)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[183, 860])).
% 0.81/0.79 tff(865,plain,
% 0.81/0.79 (c1_1(a675)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[194, 860])).
% 0.81/0.79 tff(866,plain,
% 0.81/0.79 (c1_1(a703)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[472, 862])).
% 0.81/0.79 tff(867,plain,
% 0.81/0.79 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a675)) | (~c1_1(a675)) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a675)) | (~c1_1(a675)) | c3_1(a703) | (~c1_1(a703)))),
% 0.81/0.79 inference(rewrite,[status(thm)],[])).
% 0.81/0.79 tff(868,plain,
% 0.81/0.79 (((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703))) <=> (c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a675)) | (~c1_1(a675)) | c3_1(a703) | (~c1_1(a703)))),
% 0.81/0.79 inference(rewrite,[status(thm)],[])).
% 0.81/0.79 tff(869,plain,
% 0.81/0.79 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a675)) | (~c1_1(a675)) | c3_1(a703) | (~c1_1(a703))))),
% 0.81/0.79 inference(monotonicity,[status(thm)],[868])).
% 0.81/0.79 tff(870,plain,
% 0.81/0.79 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a675)) | (~c1_1(a675)) | c3_1(a703) | (~c1_1(a703)))),
% 0.81/0.79 inference(transitivity,[status(thm)],[869, 867])).
% 0.81/0.79 tff(871,plain,
% 0.81/0.79 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))),
% 0.81/0.79 inference(quant_inst,[status(thm)],[])).
% 0.81/0.79 tff(872,plain,
% 0.81/0.79 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a675) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a675)) | (~c1_1(a675)) | c3_1(a703) | (~c1_1(a703))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[871, 870])).
% 0.81/0.79 tff(873,plain,
% 0.81/0.79 (c3_1(a703)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[872, 99, 594, 583, 866, 865, 864, 863, 861, 383, 602])).
% 0.81/0.79 tff(874,plain,
% 0.81/0.79 (~c2_1(a703)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[689, 862])).
% 0.81/0.79 tff(875,plain,
% 0.81/0.79 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 0.81/0.79 inference(bind,[status(th)],[])).
% 0.81/0.79 tff(876,plain,
% 0.81/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_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)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.79 inference(quant_intro,[status(thm)],[875])).
% 0.81/0.79 tff(877,plain,
% 0.81/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_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)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.79 inference(rewrite,[status(thm)],[])).
% 0.81/0.79 tff(878,plain,
% 0.81/0.79 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 0.81/0.79 inference(bind,[status(th)],[])).
% 0.81/0.79 tff(879,plain,
% 0.81/0.79 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.79 inference(quant_intro,[status(thm)],[878])).
% 0.81/0.79 tff(880,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c1_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause201')).
% 0.81/0.79 tff(881,plain,
% 0.81/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[880, 879])).
% 0.81/0.79 tff(882,plain,
% 0.81/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[881, 877])).
% 0.81/0.79 tff(883,plain,(
% 0.81/0.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.79 inference(skolemize,[status(sab)],[882])).
% 0.81/0.79 tff(884,plain,
% 0.81/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[883, 876])).
% 0.81/0.79 tff(885,assumption,(hskp16), introduced(assumption)).
% 0.81/0.79 tff(886,plain,
% 0.81/0.79 (((~hskp16) | (~c1_1(a702))) <=> ((~hskp16) | (~c1_1(a702)))),
% 0.81/0.79 inference(rewrite,[status(thm)],[])).
% 0.81/0.79 tff(887,plain,
% 0.81/0.79 (((~c1_1(a702)) | (~hskp16)) <=> ((~hskp16) | (~c1_1(a702)))),
% 0.81/0.79 inference(rewrite,[status(thm)],[])).
% 0.81/0.79 tff(888,axiom,((~c1_1(a702)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.81/0.79 tff(889,plain,
% 0.81/0.79 ((~hskp16) | (~c1_1(a702))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[888, 887])).
% 0.81/0.79 tff(890,plain,
% 0.81/0.79 ((~hskp16) | (~c1_1(a702))),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[889, 886])).
% 0.81/0.79 tff(891,plain,
% 0.81/0.79 (~c1_1(a702)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[890, 885])).
% 0.81/0.79 tff(892,assumption,(~c2_1(a703)), introduced(assumption)).
% 0.81/0.79 tff(893,assumption,(~c0_1(a703)), introduced(assumption)).
% 0.81/0.79 tff(894,plain,
% 0.81/0.79 (((~hskp16) | c3_1(a702)) <=> ((~hskp16) | c3_1(a702))),
% 0.81/0.79 inference(rewrite,[status(thm)],[])).
% 0.81/0.79 tff(895,axiom,((~hskp16) | c3_1(a702)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 0.81/0.79 tff(896,plain,
% 0.81/0.79 ((~hskp16) | c3_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[895, 894])).
% 0.81/0.79 tff(897,plain,
% 0.81/0.79 ((~hskp16) | c3_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[896, 894])).
% 0.81/0.79 tff(898,plain,
% 0.81/0.79 ((~hskp16) | c3_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[897, 894])).
% 0.81/0.79 tff(899,plain,
% 0.81/0.79 ((~hskp16) | c3_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[898, 894])).
% 0.81/0.79 tff(900,plain,
% 0.81/0.79 ((~hskp16) | c3_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[899, 894])).
% 0.81/0.79 tff(901,plain,
% 0.81/0.79 ((~hskp16) | c3_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[900, 894])).
% 0.81/0.79 tff(902,plain,
% 0.81/0.79 ((~hskp16) | c3_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[901, 894])).
% 0.81/0.79 tff(903,plain,
% 0.81/0.79 ((~hskp16) | c3_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[902, 894])).
% 0.81/0.79 tff(904,plain,
% 0.81/0.79 (c3_1(a702)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[903, 885])).
% 0.81/0.79 tff(905,plain,
% 0.81/0.79 (((~hskp16) | c2_1(a702)) <=> ((~hskp16) | c2_1(a702))),
% 0.81/0.79 inference(rewrite,[status(thm)],[])).
% 0.81/0.79 tff(906,axiom,((~hskp16) | c2_1(a702)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 0.81/0.79 tff(907,plain,
% 0.81/0.79 ((~hskp16) | c2_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[906, 905])).
% 0.81/0.79 tff(908,plain,
% 0.81/0.79 ((~hskp16) | c2_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[907, 905])).
% 0.81/0.79 tff(909,plain,
% 0.81/0.79 ((~hskp16) | c2_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[908, 905])).
% 0.81/0.79 tff(910,plain,
% 0.81/0.79 ((~hskp16) | c2_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[909, 905])).
% 0.81/0.79 tff(911,plain,
% 0.81/0.79 ((~hskp16) | c2_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[910, 905])).
% 0.81/0.79 tff(912,plain,
% 0.81/0.79 ((~hskp16) | c2_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[911, 905])).
% 0.81/0.79 tff(913,plain,
% 0.81/0.79 ((~hskp16) | c2_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[912, 905])).
% 0.81/0.79 tff(914,plain,
% 0.81/0.79 ((~hskp16) | c2_1(a702)),
% 0.81/0.79 inference(modus_ponens,[status(thm)],[913, 905])).
% 0.81/0.79 tff(915,plain,
% 0.81/0.79 (c2_1(a702)),
% 0.81/0.79 inference(unit_resolution,[status(thm)],[914, 885])).
% 0.81/0.79 tff(916,assumption,(c1_1(a703)), introduced(assumption)).
% 0.81/0.79 tff(917,plain,
% 0.81/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a703) | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a703) | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | (~c1_1(a703)))),
% 0.81/0.79 inference(rewrite,[status(thm)],[])).
% 0.81/0.79 tff(918,plain,
% 0.81/0.79 (((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703))) <=> (c0_1(a703) | c2_1(a703) | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | (~c1_1(a703)))),
% 0.81/0.79 inference(rewrite,[status(thm)],[])).
% 0.81/0.79 tff(919,plain,
% 0.81/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a703) | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | (~c1_1(a703))))),
% 0.81/0.79 inference(monotonicity,[status(thm)],[918])).
% 0.81/0.79 tff(920,plain,
% 0.81/0.79 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a703) | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | (~c1_1(a703)))),
% 0.81/0.79 inference(transitivity,[status(thm)],[919, 917])).
% 0.81/0.79 tff(921,plain,
% 0.81/0.79 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703)))),
% 0.81/0.79 inference(quant_inst,[status(thm)],[])).
% 0.81/0.80 tff(922,plain,
% 0.81/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a703) | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | (~c1_1(a703))),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[921, 920])).
% 0.81/0.80 tff(923,plain,
% 0.81/0.80 (~c0_1(a702)),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[922, 99, 916, 915, 904, 893, 892, 891, 884])).
% 0.81/0.80 tff(924,plain,
% 0.81/0.80 (c3_1(a703)),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[872, 99, 594, 583, 916, 865, 864, 893, 861, 383, 602])).
% 0.81/0.80 tff(925,plain,
% 0.81/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a703) | c1_1(a702) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a702) | (~c3_1(a702)) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c1_1(a702) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a702) | (~c3_1(a702)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(926,plain,
% 0.81/0.80 (((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702))) <=> (c0_1(a703) | c1_1(a702) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a702) | (~c3_1(a702)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(927,plain,
% 0.81/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a703) | c1_1(a702) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a702) | (~c3_1(a702)) | (~c3_1(a703)) | (~c1_1(a703))))),
% 0.81/0.80 inference(monotonicity,[status(thm)],[926])).
% 0.81/0.80 tff(928,plain,
% 0.81/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c1_1(a702) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a702) | (~c3_1(a702)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.80 inference(transitivity,[status(thm)],[927, 925])).
% 0.81/0.80 tff(929,plain,
% 0.81/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))),
% 0.81/0.80 inference(quant_inst,[status(thm)],[])).
% 0.81/0.80 tff(930,plain,
% 0.81/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c1_1(a702) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a702) | (~c3_1(a702)) | (~c3_1(a703)) | (~c1_1(a703))),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[929, 928])).
% 0.81/0.80 tff(931,plain,
% 0.81/0.80 ($false),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[930, 99, 594, 572, 916, 904, 893, 891, 490, 602, 924, 923])).
% 0.81/0.80 tff(932,plain,((~hskp16) | (~c1_1(a703)) | c0_1(a703) | c2_1(a703)), inference(lemma,lemma(discharge,[]))).
% 0.81/0.80 tff(933,plain,
% 0.81/0.80 (~hskp16),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[932, 866, 863, 874])).
% 0.81/0.80 tff(934,plain,
% 0.81/0.80 ((hskp21 | hskp11 | hskp2) <=> (hskp21 | hskp11 | hskp2)),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(935,plain,
% 0.81/0.80 (((hskp11 | hskp21) | hskp2) <=> (hskp21 | hskp11 | hskp2)),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(936,axiom,((hskp11 | hskp21) | hskp2), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 0.81/0.80 tff(937,plain,
% 0.81/0.80 (hskp21 | hskp11 | hskp2),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[936, 935])).
% 0.81/0.80 tff(938,plain,
% 0.81/0.80 (hskp21 | hskp11 | hskp2),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[937, 934])).
% 0.81/0.80 tff(939,plain,
% 0.81/0.80 (hskp21 | hskp11 | hskp2),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[938, 934])).
% 0.81/0.80 tff(940,plain,
% 0.81/0.80 (hskp21 | hskp11 | hskp2),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[939, 934])).
% 0.81/0.80 tff(941,plain,
% 0.81/0.80 (hskp21 | hskp11 | hskp2),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[940, 934])).
% 0.81/0.80 tff(942,plain,
% 0.81/0.80 (hskp21 | hskp11 | hskp2),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[941, 934])).
% 0.81/0.80 tff(943,plain,
% 0.81/0.80 (hskp21 | hskp11 | hskp2),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[942, 934])).
% 0.81/0.80 tff(944,plain,
% 0.81/0.80 (hskp21 | hskp11 | hskp2),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[943, 934])).
% 0.81/0.80 tff(945,plain,
% 0.81/0.80 (hskp21),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[944, 604, 625])).
% 0.81/0.80 tff(946,plain,
% 0.81/0.80 (((~hskp21) | (~c2_1(a715))) <=> ((~hskp21) | (~c2_1(a715)))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(947,plain,
% 0.81/0.80 (((~c2_1(a715)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a715)))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(948,axiom,((~c2_1(a715)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.81/0.80 tff(949,plain,
% 0.81/0.80 ((~hskp21) | (~c2_1(a715))),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[948, 947])).
% 0.81/0.80 tff(950,plain,
% 0.81/0.80 ((~hskp21) | (~c2_1(a715))),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[949, 946])).
% 0.81/0.80 tff(951,plain,
% 0.81/0.80 (~c2_1(a715)),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[950, 945])).
% 0.81/0.80 tff(952,plain,
% 0.81/0.80 (((~hskp21) | c0_1(a715)) <=> ((~hskp21) | c0_1(a715))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(953,axiom,((~hskp21) | c0_1(a715)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 0.81/0.80 tff(954,plain,
% 0.81/0.80 ((~hskp21) | c0_1(a715)),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.81/0.80 tff(955,plain,
% 0.81/0.80 ((~hskp21) | c0_1(a715)),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[954, 952])).
% 0.81/0.80 tff(956,plain,
% 0.81/0.80 ((~hskp21) | c0_1(a715)),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[955, 952])).
% 0.81/0.80 tff(957,plain,
% 0.81/0.80 ((~hskp21) | c0_1(a715)),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[956, 952])).
% 0.81/0.80 tff(958,plain,
% 0.81/0.80 ((~hskp21) | c0_1(a715)),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[957, 952])).
% 0.81/0.80 tff(959,plain,
% 0.81/0.80 ((~hskp21) | c0_1(a715)),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[958, 952])).
% 0.81/0.80 tff(960,plain,
% 0.81/0.80 ((~hskp21) | c0_1(a715)),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[959, 952])).
% 0.81/0.80 tff(961,plain,
% 0.81/0.80 ((~hskp21) | c0_1(a715)),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[960, 952])).
% 0.81/0.80 tff(962,plain,
% 0.81/0.80 (c0_1(a715)),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[961, 945])).
% 0.81/0.80 tff(963,plain,
% 0.81/0.80 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | c2_1(a715) | (~ndr1_0) | (~c0_1(a715)) | c1_1(a715))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c2_1(a715) | (~ndr1_0) | (~c0_1(a715)) | c1_1(a715))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(964,plain,
% 0.81/0.80 ((hskp9 | hskp2 | (~ndr1_0) | c2_1(a715) | c1_1(a715) | (~c0_1(a715))) <=> (hskp9 | hskp2 | c2_1(a715) | (~ndr1_0) | (~c0_1(a715)) | c1_1(a715))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(965,plain,
% 0.81/0.80 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a715) | c1_1(a715) | (~c0_1(a715)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | c2_1(a715) | (~ndr1_0) | (~c0_1(a715)) | c1_1(a715)))),
% 0.81/0.80 inference(monotonicity,[status(thm)],[964])).
% 0.81/0.80 tff(966,plain,
% 0.81/0.80 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a715) | c1_1(a715) | (~c0_1(a715)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c2_1(a715) | (~ndr1_0) | (~c0_1(a715)) | c1_1(a715))),
% 0.81/0.80 inference(transitivity,[status(thm)],[965, 963])).
% 0.81/0.80 tff(967,plain,
% 0.81/0.80 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a715) | c1_1(a715) | (~c0_1(a715)))),
% 0.81/0.80 inference(quant_inst,[status(thm)],[])).
% 0.81/0.80 tff(968,plain,
% 0.81/0.80 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c2_1(a715) | (~ndr1_0) | (~c0_1(a715)) | c1_1(a715)),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[967, 966])).
% 0.81/0.80 tff(969,plain,
% 0.81/0.80 (c1_1(a715)),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[968, 99, 603, 604, 962, 951, 614])).
% 0.81/0.80 tff(970,plain,
% 0.81/0.80 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 0.81/0.80 inference(bind,[status(th)],[])).
% 0.81/0.80 tff(971,plain,
% 0.81/0.80 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/0.80 inference(quant_intro,[status(thm)],[970])).
% 0.81/0.80 tff(972,plain,
% 0.81/0.80 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(973,plain,
% 0.81/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 0.81/0.80 inference(bind,[status(th)],[])).
% 0.81/0.80 tff(974,plain,
% 0.81/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/0.80 inference(quant_intro,[status(thm)],[973])).
% 0.81/0.80 tff(975,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 0.81/0.80 tff(976,plain,
% 0.81/0.80 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[975, 974])).
% 0.81/0.80 tff(977,plain,
% 0.81/0.80 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[976, 972])).
% 0.81/0.80 tff(978,plain,(
% 0.81/0.80 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/0.80 inference(skolemize,[status(sab)],[977])).
% 0.81/0.80 tff(979,plain,
% 0.81/0.80 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[978, 971])).
% 0.81/0.80 tff(980,plain,
% 0.81/0.80 (((~hskp21) | (~c3_1(a715))) <=> ((~hskp21) | (~c3_1(a715)))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(981,plain,
% 0.81/0.80 (((~c3_1(a715)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a715)))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(982,axiom,((~c3_1(a715)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.81/0.80 tff(983,plain,
% 0.81/0.80 ((~hskp21) | (~c3_1(a715))),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[982, 981])).
% 0.81/0.80 tff(984,plain,
% 0.81/0.80 ((~hskp21) | (~c3_1(a715))),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[983, 980])).
% 0.81/0.80 tff(985,plain,
% 0.81/0.80 (~c3_1(a715)),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[984, 945])).
% 0.81/0.80 tff(986,assumption,(~hskp16), introduced(assumption)).
% 0.81/0.80 tff(987,plain,
% 0.81/0.80 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c3_1(a715) | c0_1(a703) | (~ndr1_0) | (~c3_1(a703)) | (~c1_1(a703)) | (~c0_1(a715)) | (~c1_1(a715)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c3_1(a715) | c0_1(a703) | (~ndr1_0) | (~c3_1(a703)) | (~c1_1(a703)) | (~c0_1(a715)) | (~c1_1(a715)))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(988,plain,
% 0.81/0.80 ((hskp16 | (~ndr1_0) | c3_1(a715) | (~c0_1(a715)) | (~c1_1(a715)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703))) <=> (hskp16 | c3_1(a715) | c0_1(a703) | (~ndr1_0) | (~c3_1(a703)) | (~c1_1(a703)) | (~c0_1(a715)) | (~c1_1(a715)))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(989,plain,
% 0.81/0.80 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a715) | (~c0_1(a715)) | (~c1_1(a715)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c3_1(a715) | c0_1(a703) | (~ndr1_0) | (~c3_1(a703)) | (~c1_1(a703)) | (~c0_1(a715)) | (~c1_1(a715))))),
% 0.81/0.80 inference(monotonicity,[status(thm)],[988])).
% 0.81/0.80 tff(990,plain,
% 0.81/0.80 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a715) | (~c0_1(a715)) | (~c1_1(a715)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c3_1(a715) | c0_1(a703) | (~ndr1_0) | (~c3_1(a703)) | (~c1_1(a703)) | (~c0_1(a715)) | (~c1_1(a715)))),
% 0.81/0.80 inference(transitivity,[status(thm)],[989, 987])).
% 0.81/0.80 tff(991,plain,
% 0.81/0.80 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a715) | (~c0_1(a715)) | (~c1_1(a715)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.80 inference(quant_inst,[status(thm)],[])).
% 0.81/0.80 tff(992,plain,
% 0.81/0.80 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c3_1(a715) | c0_1(a703) | (~ndr1_0) | (~c3_1(a703)) | (~c1_1(a703)) | (~c0_1(a715)) | (~c1_1(a715))),
% 0.81/0.80 inference(modus_ponens,[status(thm)],[991, 990])).
% 0.81/0.80 tff(993,plain,
% 0.81/0.80 ($false),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[992, 99, 986, 962, 916, 985, 893, 979, 924, 969])).
% 0.81/0.80 tff(994,plain,(hskp2 | hskp16 | (~c1_1(a703)) | c0_1(a703) | hskp9 | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.81/0.80 tff(995,plain,
% 0.81/0.80 (hskp2),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[994, 933, 866, 863, 603, 625])).
% 0.81/0.80 tff(996,plain,
% 0.81/0.80 (~c1_1(a670)),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[783, 995])).
% 0.81/0.80 tff(997,plain,
% 0.81/0.80 (~c0_1(a670)),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[789, 995])).
% 0.81/0.80 tff(998,plain,
% 0.81/0.80 (c3_1(a670)),
% 0.81/0.80 inference(unit_resolution,[status(thm)],[803, 995])).
% 0.81/0.80 tff(999,plain,
% 0.81/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a703) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(1000,plain,
% 0.81/0.80 (((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670))) <=> (c0_1(a703) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.80 inference(rewrite,[status(thm)],[])).
% 0.81/0.80 tff(1001,plain,
% 0.81/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a703) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c3_1(a703)) | (~c1_1(a703))))),
% 0.81/0.80 inference(monotonicity,[status(thm)],[1000])).
% 0.81/0.80 tff(1002,plain,
% 0.81/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.80 inference(transitivity,[status(thm)],[1001, 999])).
% 0.81/0.80 tff(1003,plain,
% 0.81/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))),
% 0.81/0.80 inference(quant_inst,[status(thm)],[])).
% 0.81/0.80 tff(1004,plain,
% 0.81/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a703) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c3_1(a670)) | (~c3_1(a703)) | (~c1_1(a703))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 0.81/0.81 tff(1005,plain,
% 0.81/0.81 ($false),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[1004, 99, 594, 572, 866, 998, 863, 997, 996, 490, 602, 873])).
% 0.81/0.81 tff(1006,plain,((~hskp17) | hskp9 | hskp11), inference(lemma,lemma(discharge,[]))).
% 0.81/0.81 tff(1007,plain,
% 0.81/0.81 (~hskp17),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[1006, 625, 603])).
% 0.81/0.81 tff(1008,plain,
% 0.81/0.81 (hskp17 | hskp14),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[664, 602])).
% 0.81/0.81 tff(1009,plain,
% 0.81/0.81 (hskp14),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[1008, 1007])).
% 0.81/0.81 tff(1010,plain,
% 0.81/0.81 (hskp5),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[656, 1009, 603])).
% 0.81/0.81 tff(1011,plain,
% 0.81/0.81 (~c2_1(a673)),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[55, 1010])).
% 0.81/0.81 tff(1012,plain,
% 0.81/0.81 (~c0_1(a673)),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[61, 1010])).
% 0.81/0.81 tff(1013,plain,
% 0.81/0.81 (~c3_1(a673)),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[49, 1010])).
% 0.81/0.81 tff(1014,plain,
% 0.81/0.81 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a675) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a673)) | (~c3_1(a675)) | (~c1_1(a675)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a675) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a673)) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(1015,plain,
% 0.81/0.81 (((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673))) <=> (c2_1(a675) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a673)) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(1016,plain,
% 0.81/0.81 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a675) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a673)) | (~c3_1(a675)) | (~c1_1(a675))))),
% 0.81/0.81 inference(monotonicity,[status(thm)],[1015])).
% 0.81/0.81 tff(1017,plain,
% 0.81/0.81 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a675) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a673)) | (~c3_1(a675)) | (~c1_1(a675)))),
% 0.81/0.81 inference(transitivity,[status(thm)],[1016, 1014])).
% 0.81/0.81 tff(1018,plain,
% 0.81/0.81 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))),
% 0.81/0.81 inference(quant_inst,[status(thm)],[])).
% 0.81/0.81 tff(1019,plain,
% 0.81/0.81 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a675) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a673)) | (~c3_1(a675)) | (~c1_1(a675))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 0.81/0.81 tff(1020,plain,
% 0.81/0.81 (~c1_1(a673)),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[1019, 99, 594, 583, 865, 864, 861, 1012, 1013, 383, 602])).
% 0.81/0.81 tff(1021,plain,
% 0.81/0.81 (hskp2),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[777, 1020, 1012, 1011, 603])).
% 0.81/0.81 tff(1022,plain,
% 0.81/0.81 (~c1_1(a670)),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[783, 1021])).
% 0.81/0.81 tff(1023,plain,
% 0.81/0.81 (~c0_1(a670)),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[789, 1021])).
% 0.81/0.81 tff(1024,plain,
% 0.81/0.81 (c3_1(a670)),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[803, 1021])).
% 0.81/0.81 tff(1025,plain,
% 0.81/0.81 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(1026,plain,
% 0.81/0.81 ((hskp11 | (~ndr1_0) | c1_1(a670) | (~c2_1(a670)) | (~c3_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670))) <=> (hskp11 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(1027,plain,
% 0.81/0.81 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a670) | (~c2_1(a670)) | (~c3_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670))))),
% 0.81/0.81 inference(monotonicity,[status(thm)],[1026])).
% 0.81/0.81 tff(1028,plain,
% 0.81/0.81 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a670) | (~c2_1(a670)) | (~c3_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))),
% 0.81/0.81 inference(transitivity,[status(thm)],[1027, 1025])).
% 0.81/0.81 tff(1029,plain,
% 0.81/0.81 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a670) | (~c2_1(a670)) | (~c3_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))),
% 0.81/0.81 inference(quant_inst,[status(thm)],[])).
% 0.81/0.81 tff(1030,plain,
% 0.81/0.81 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 0.81/0.81 tff(1031,plain,
% 0.81/0.81 (~c2_1(a670)),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[1030, 99, 625, 1024, 1023, 1022, 247])).
% 0.81/0.81 tff(1032,plain,
% 0.81/0.81 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.81/0.81 inference(bind,[status(th)],[])).
% 0.81/0.81 tff(1033,plain,
% 0.81/0.81 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.81 inference(quant_intro,[status(thm)],[1032])).
% 0.81/0.81 tff(1034,plain,
% 0.81/0.81 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(1035,plain,
% 0.81/0.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.81/0.81 inference(bind,[status(th)],[])).
% 0.81/0.81 tff(1036,plain,
% 0.81/0.81 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.81 inference(quant_intro,[status(thm)],[1035])).
% 0.81/0.81 tff(1037,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 0.81/0.81 tff(1038,plain,
% 0.81/0.81 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[1037, 1036])).
% 0.81/0.81 tff(1039,plain,
% 0.81/0.81 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[1038, 1034])).
% 0.81/0.81 tff(1040,plain,(
% 0.81/0.81 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.81 inference(skolemize,[status(sab)],[1039])).
% 0.81/0.81 tff(1041,plain,
% 0.81/0.81 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[1040, 1033])).
% 0.81/0.81 tff(1042,plain,
% 0.81/0.81 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(1043,plain,
% 0.81/0.81 ((hskp16 | (~ndr1_0) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | c1_1(a670) | c2_1(a670) | (~c3_1(a670))) <=> (hskp16 | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(1044,plain,
% 0.81/0.81 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | c1_1(a670) | c2_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670))))),
% 0.81/0.81 inference(monotonicity,[status(thm)],[1043])).
% 0.81/0.81 tff(1045,plain,
% 0.81/0.81 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | c1_1(a670) | c2_1(a670) | (~c3_1(a670)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670)))),
% 0.81/0.81 inference(transitivity,[status(thm)],[1044, 1042])).
% 0.81/0.81 tff(1046,plain,
% 0.81/0.81 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | (~c0_1(a678)) | (~c3_1(a678)) | (~c1_1(a678)) | c1_1(a670) | c2_1(a670) | (~c3_1(a670)))),
% 0.81/0.81 inference(quant_inst,[status(thm)],[])).
% 0.81/0.81 tff(1047,plain,
% 0.81/0.81 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c0_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | (~c0_1(a678)) | (~c3_1(a678)) | c2_1(a670) | (~c3_1(a670))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[1046, 1045])).
% 0.81/0.81 tff(1048,plain,
% 0.81/0.81 (hskp16 | c2_1(a670)),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[1047, 99, 594, 583, 572, 1024, 1022, 1041])).
% 0.81/0.81 tff(1049,plain,
% 0.81/0.81 (hskp16),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[1048, 1031])).
% 0.81/0.81 tff(1050,plain,
% 0.81/0.81 (c3_1(a702)),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[903, 1049])).
% 0.81/0.81 tff(1051,plain,
% 0.81/0.81 (c2_1(a702)),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[914, 1049])).
% 0.81/0.81 tff(1052,plain,
% 0.81/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a670)) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a670)) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(1053,plain,
% 0.81/0.81 (((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670))) <=> (c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a670)) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(1054,plain,
% 0.81/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a670)) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702))))),
% 0.81/0.81 inference(monotonicity,[status(thm)],[1053])).
% 0.81/0.81 tff(1055,plain,
% 0.81/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a670)) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)))),
% 0.81/0.81 inference(transitivity,[status(thm)],[1054, 1052])).
% 0.81/0.81 tff(1056,plain,
% 0.81/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702)) | c2_1(a678) | (~c1_1(a678)) | (~c0_1(a678)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))),
% 0.81/0.81 inference(quant_inst,[status(thm)],[])).
% 0.81/0.81 tff(1057,plain,
% 0.81/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a670)) | (~c2_1(a702)) | (~c0_1(a702)) | (~c3_1(a702))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 0.81/0.81 tff(1058,plain,
% 0.81/0.81 (~c0_1(a702)),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[1057, 99, 594, 583, 1051, 1050, 1024, 1023, 1022, 624, 602])).
% 0.81/0.81 tff(1059,plain,
% 0.81/0.81 (~c1_1(a702)),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[890, 1049])).
% 0.81/0.81 tff(1060,plain,
% 0.81/0.81 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702) | (~c3_1(a702)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(1061,plain,
% 0.81/0.81 ((hskp11 | (~ndr1_0) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702))) <=> (hskp11 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702) | (~c3_1(a702)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(1062,plain,
% 0.81/0.81 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702) | (~c3_1(a702))))),
% 0.81/0.81 inference(monotonicity,[status(thm)],[1061])).
% 0.81/0.81 tff(1063,plain,
% 0.81/0.81 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702) | (~c3_1(a702)))),
% 0.81/0.81 inference(transitivity,[status(thm)],[1062, 1060])).
% 0.81/0.81 tff(1064,plain,
% 0.81/0.81 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a702) | (~c2_1(a702)) | (~c3_1(a702)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))),
% 0.81/0.81 inference(quant_inst,[status(thm)],[])).
% 0.81/0.81 tff(1065,plain,
% 0.81/0.81 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp11 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702) | (~c3_1(a702))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[1064, 1063])).
% 0.81/0.81 tff(1066,plain,
% 0.81/0.81 ($false),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[1065, 99, 625, 1051, 1050, 1059, 247, 1058])).
% 0.81/0.82 tff(1067,plain,(hskp11 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.81/0.82 tff(1068,plain,
% 0.81/0.82 (hskp11),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[1067, 603])).
% 0.81/0.82 tff(1069,plain,
% 0.81/0.82 (~c2_1(a683)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[281, 1068])).
% 0.81/0.82 tff(1070,plain,
% 0.81/0.82 (c0_1(a683)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[264, 1068])).
% 0.81/0.82 tff(1071,plain,
% 0.81/0.82 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | c2_1(a683) | (~ndr1_0) | (~c0_1(a683)) | c1_1(a683))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c2_1(a683) | (~ndr1_0) | (~c0_1(a683)) | c1_1(a683))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1072,plain,
% 0.81/0.82 ((hskp9 | hskp2 | (~ndr1_0) | c2_1(a683) | c1_1(a683) | (~c0_1(a683))) <=> (hskp9 | hskp2 | c2_1(a683) | (~ndr1_0) | (~c0_1(a683)) | c1_1(a683))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1073,plain,
% 0.81/0.82 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a683) | c1_1(a683) | (~c0_1(a683)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | c2_1(a683) | (~ndr1_0) | (~c0_1(a683)) | c1_1(a683)))),
% 0.81/0.82 inference(monotonicity,[status(thm)],[1072])).
% 0.81/0.82 tff(1074,plain,
% 0.81/0.82 (((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a683) | c1_1(a683) | (~c0_1(a683)))) <=> ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c2_1(a683) | (~ndr1_0) | (~c0_1(a683)) | c1_1(a683))),
% 0.81/0.82 inference(transitivity,[status(thm)],[1073, 1071])).
% 0.81/0.82 tff(1075,plain,
% 0.81/0.82 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp9 | hskp2 | (~ndr1_0) | c2_1(a683) | c1_1(a683) | (~c0_1(a683)))),
% 0.81/0.82 inference(quant_inst,[status(thm)],[])).
% 0.81/0.82 tff(1076,plain,
% 0.81/0.82 ((~![U: $i] : (hskp9 | hskp2 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)))) | hskp9 | hskp2 | c2_1(a683) | (~ndr1_0) | (~c0_1(a683)) | c1_1(a683)),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1075, 1074])).
% 0.81/0.82 tff(1077,plain,
% 0.81/0.82 (hskp2 | c1_1(a683)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[1076, 99, 603, 1070, 1069, 614])).
% 0.81/0.82 tff(1078,plain,
% 0.81/0.82 (c1_1(a683)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[1077, 604])).
% 0.81/0.82 tff(1079,plain,
% 0.81/0.82 (c1_1(a673)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[777, 62, 604, 56, 603])).
% 0.81/0.82 tff(1080,plain,
% 0.81/0.82 (c3_1(a683)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[275, 1068])).
% 0.81/0.82 tff(1081,plain,
% 0.81/0.82 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a683) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a673)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a683) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a673)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1082,plain,
% 0.81/0.82 (((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673))) <=> (c2_1(a683) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a673)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1083,plain,
% 0.81/0.82 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a683) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a673)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683))))),
% 0.81/0.82 inference(monotonicity,[status(thm)],[1082])).
% 0.81/0.82 tff(1084,plain,
% 0.81/0.82 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a683) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a673)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)))),
% 0.81/0.82 inference(transitivity,[status(thm)],[1083, 1081])).
% 0.81/0.82 tff(1085,plain,
% 0.81/0.82 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a673) | c3_1(a673) | (~c1_1(a673)))),
% 0.81/0.82 inference(quant_inst,[status(thm)],[])).
% 0.81/0.82 tff(1086,plain,
% 0.81/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a683) | c0_1(a673) | c3_1(a673) | (~ndr1_0) | (~c1_1(a673)) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 0.81/0.82 tff(1087,plain,
% 0.81/0.82 ($false),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[1086, 99, 1070, 1080, 1069, 62, 50, 383, 1078, 1079])).
% 0.81/0.82 tff(1088,plain,((~hskp5) | hskp2 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.81/0.82 tff(1089,plain,
% 0.81/0.82 (~hskp5),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[1088, 604, 603])).
% 0.81/0.82 tff(1090,plain,
% 0.81/0.82 (~hskp14),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[656, 1089, 603])).
% 0.81/0.82 tff(1091,plain,
% 0.81/0.82 (hskp17),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[1008, 1090])).
% 0.81/0.82 tff(1092,plain,
% 0.81/0.82 (~c0_1(a703)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[450, 1091])).
% 0.81/0.82 tff(1093,plain,
% 0.81/0.82 (c1_1(a703)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[472, 1091])).
% 0.81/0.82 tff(1094,plain,
% 0.81/0.82 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a683) | (~ndr1_0) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a683) | (~ndr1_0) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)) | c3_1(a703) | (~c1_1(a703)))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1095,plain,
% 0.81/0.82 (((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703))) <=> (c0_1(a703) | c2_1(a683) | (~ndr1_0) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)) | c3_1(a703) | (~c1_1(a703)))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1096,plain,
% 0.81/0.82 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a683) | (~ndr1_0) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)) | c3_1(a703) | (~c1_1(a703))))),
% 0.81/0.82 inference(monotonicity,[status(thm)],[1095])).
% 0.81/0.82 tff(1097,plain,
% 0.81/0.82 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a683) | (~ndr1_0) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)) | c3_1(a703) | (~c1_1(a703)))),
% 0.81/0.82 inference(transitivity,[status(thm)],[1096, 1094])).
% 0.81/0.82 tff(1098,plain,
% 0.81/0.82 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c3_1(a683)) | (~c1_1(a683)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a703) | c3_1(a703) | (~c1_1(a703)))),
% 0.81/0.82 inference(quant_inst,[status(thm)],[])).
% 0.81/0.82 tff(1099,plain,
% 0.81/0.82 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a683) | (~ndr1_0) | (~c3_1(a683)) | (~c0_1(a683)) | (~c1_1(a683)) | c3_1(a703) | (~c1_1(a703))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1098, 1097])).
% 0.81/0.82 tff(1100,plain,
% 0.81/0.82 (c3_1(a703)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[1099, 99, 1093, 1070, 1080, 1092, 1069, 383, 1078])).
% 0.81/0.82 tff(1101,plain,
% 0.81/0.82 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W))))),
% 0.81/0.82 inference(bind,[status(th)],[])).
% 0.81/0.82 tff(1102,plain,
% 0.81/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_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)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.82 inference(quant_intro,[status(thm)],[1101])).
% 0.81/0.82 tff(1103,plain,
% 0.81/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_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)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1104,plain,
% 0.81/0.82 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))))),
% 0.81/0.82 inference(bind,[status(th)],[])).
% 0.81/0.82 tff(1105,plain,
% 0.81/0.82 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_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)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.82 inference(quant_intro,[status(thm)],[1104])).
% 0.81/0.82 tff(1106,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | (~c1_1(W))) | c0_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 0.81/0.82 tff(1107,plain,
% 0.81/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 0.81/0.82 tff(1108,plain,
% 0.81/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1107, 1103])).
% 0.81/0.82 tff(1109,plain,(
% 0.81/0.82 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.82 inference(skolemize,[status(sab)],[1108])).
% 0.81/0.82 tff(1110,plain,
% 0.81/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1109, 1102])).
% 0.81/0.82 tff(1111,plain,
% 0.81/0.82 (~c2_1(a703)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[689, 1091])).
% 0.81/0.82 tff(1112,plain,
% 0.81/0.82 (~hskp16),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[932, 1092, 1093, 1111])).
% 0.81/0.82 tff(1113,assumption,(c3_1(a703)), introduced(assumption)).
% 0.81/0.82 tff(1114,assumption,(hskp0), introduced(assumption)).
% 0.81/0.82 tff(1115,plain,
% 0.81/0.82 (((~hskp0) | (~c3_1(a668))) <=> ((~hskp0) | (~c3_1(a668)))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1116,plain,
% 0.81/0.82 (((~c3_1(a668)) | (~hskp0)) <=> ((~hskp0) | (~c3_1(a668)))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1117,axiom,((~c3_1(a668)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 0.81/0.82 tff(1118,plain,
% 0.81/0.82 ((~hskp0) | (~c3_1(a668))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 0.81/0.82 tff(1119,plain,
% 0.81/0.82 ((~hskp0) | (~c3_1(a668))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1118, 1115])).
% 0.81/0.82 tff(1120,plain,
% 0.81/0.82 (~c3_1(a668)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[1119, 1114])).
% 0.81/0.82 tff(1121,plain,
% 0.81/0.82 (((~hskp0) | c1_1(a668)) <=> ((~hskp0) | c1_1(a668))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1122,axiom,((~hskp0) | c1_1(a668)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 0.81/0.82 tff(1123,plain,
% 0.81/0.82 ((~hskp0) | c1_1(a668)),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.81/0.82 tff(1124,plain,
% 0.81/0.82 ((~hskp0) | c1_1(a668)),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1123, 1121])).
% 0.81/0.82 tff(1125,plain,
% 0.81/0.82 ((~hskp0) | c1_1(a668)),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1124, 1121])).
% 0.81/0.82 tff(1126,plain,
% 0.81/0.82 ((~hskp0) | c1_1(a668)),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1125, 1121])).
% 0.81/0.82 tff(1127,plain,
% 0.81/0.82 ((~hskp0) | c1_1(a668)),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1126, 1121])).
% 0.81/0.82 tff(1128,plain,
% 0.81/0.82 ((~hskp0) | c1_1(a668)),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1127, 1121])).
% 0.81/0.82 tff(1129,plain,
% 0.81/0.82 ((~hskp0) | c1_1(a668)),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1128, 1121])).
% 0.81/0.82 tff(1130,plain,
% 0.81/0.82 ((~hskp0) | c1_1(a668)),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1129, 1121])).
% 0.81/0.82 tff(1131,plain,
% 0.81/0.82 (c1_1(a668)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[1130, 1114])).
% 0.81/0.82 tff(1132,plain,
% 0.81/0.82 (~hskp16),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[932, 893, 916, 892])).
% 0.81/0.82 tff(1133,plain,
% 0.81/0.82 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a703) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c0_1(a668)) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a703) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c0_1(a668)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1134,plain,
% 0.81/0.82 ((hskp16 | (~ndr1_0) | c3_1(a668) | (~c0_1(a668)) | (~c1_1(a668)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703))) <=> (hskp16 | c0_1(a703) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c0_1(a668)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1135,plain,
% 0.81/0.82 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a668) | (~c0_1(a668)) | (~c1_1(a668)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | c0_1(a703) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c0_1(a668)) | (~c3_1(a703)) | (~c1_1(a703))))),
% 0.81/0.82 inference(monotonicity,[status(thm)],[1134])).
% 0.81/0.82 tff(1136,plain,
% 0.81/0.82 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a668) | (~c0_1(a668)) | (~c1_1(a668)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a703) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c0_1(a668)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.82 inference(transitivity,[status(thm)],[1135, 1133])).
% 0.81/0.82 tff(1137,plain,
% 0.81/0.82 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a668) | (~c0_1(a668)) | (~c1_1(a668)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.82 inference(quant_inst,[status(thm)],[])).
% 0.81/0.82 tff(1138,plain,
% 0.81/0.82 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp16 | c0_1(a703) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c0_1(a668)) | (~c3_1(a703)) | (~c1_1(a703))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 0.81/0.82 tff(1139,plain,
% 0.81/0.82 (~c0_1(a668)),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[1138, 99, 1132, 916, 1131, 893, 1120, 979, 1113])).
% 0.81/0.82 tff(1140,assumption,(c1_1(a683)), introduced(assumption)).
% 0.81/0.82 tff(1141,plain,
% 0.81/0.82 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a703) | c2_1(a683) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | c0_1(a668) | (~c0_1(a683)) | (~c1_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a703) | c2_1(a683) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | c0_1(a668) | (~c0_1(a683)) | (~c1_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1142,plain,
% 0.81/0.82 (((~ndr1_0) | c2_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a668) | c3_1(a668) | (~c1_1(a668))) <=> (c2_1(a703) | c2_1(a683) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | c0_1(a668) | (~c0_1(a683)) | (~c1_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.82 inference(rewrite,[status(thm)],[])).
% 0.81/0.82 tff(1143,plain,
% 0.81/0.82 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a668) | c3_1(a668) | (~c1_1(a668)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | (c2_1(a703) | c2_1(a683) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | c0_1(a668) | (~c0_1(a683)) | (~c1_1(a683)) | (~c3_1(a703)) | (~c1_1(a703))))),
% 0.81/0.82 inference(monotonicity,[status(thm)],[1142])).
% 0.81/0.82 tff(1144,plain,
% 0.81/0.82 (((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a668) | c3_1(a668) | (~c1_1(a668)))) <=> ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a703) | c2_1(a683) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | c0_1(a668) | (~c0_1(a683)) | (~c1_1(a683)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.82 inference(transitivity,[status(thm)],[1143, 1141])).
% 0.81/0.82 tff(1145,plain,
% 0.81/0.82 ((~![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)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c2_1(a683) | (~c1_1(a683)) | (~c0_1(a683)) | c0_1(a668) | c3_1(a668) | (~c1_1(a668)))),
% 0.81/0.82 inference(quant_inst,[status(thm)],[])).
% 0.81/0.82 tff(1146,plain,
% 0.81/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W) | (~c1_1(W)))) | c2_1(a703) | c2_1(a683) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | c0_1(a668) | (~c0_1(a683)) | (~c1_1(a683)) | (~c3_1(a703)) | (~c1_1(a703))),
% 0.81/0.82 inference(modus_ponens,[status(thm)],[1145, 1144])).
% 0.81/0.82 tff(1147,plain,
% 0.81/0.82 ($false),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[1146, 99, 916, 292, 1131, 892, 293, 1120, 383, 1140, 1139, 1113])).
% 0.81/0.82 tff(1148,plain,((~hskp0) | (~c1_1(a703)) | (~c0_1(a683)) | c2_1(a703) | c2_1(a683) | (~c1_1(a683)) | (~c3_1(a703)) | c0_1(a703)), inference(lemma,lemma(discharge,[]))).
% 0.81/0.82 tff(1149,plain,
% 0.81/0.82 (~hskp0),
% 0.81/0.82 inference(unit_resolution,[status(thm)],[1148, 1093, 1070, 1111, 1069, 1078, 1100, 1092])).
% 0.81/0.82 tff(1150,plain,
% 0.81/0.82 ((hskp29 | hskp16 | hskp0) <=> (hskp29 | hskp16 | hskp0)),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1151,plain,
% 0.81/0.83 (((hskp29 | hskp0) | hskp16) <=> (hskp29 | hskp16 | hskp0)),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1152,plain,
% 0.81/0.83 ((hskp29 | hskp0) <=> (hskp29 | hskp0)),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1153,plain,
% 0.81/0.83 (((hskp29 | hskp0) | hskp16) <=> ((hskp29 | hskp0) | hskp16)),
% 0.81/0.83 inference(monotonicity,[status(thm)],[1152])).
% 0.81/0.83 tff(1154,plain,
% 0.81/0.83 (((hskp29 | hskp0) | hskp16) <=> (hskp29 | hskp16 | hskp0)),
% 0.81/0.83 inference(transitivity,[status(thm)],[1153, 1151])).
% 0.81/0.83 tff(1155,axiom,((hskp29 | hskp0) | hskp16), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 0.81/0.83 tff(1156,plain,
% 0.81/0.83 (hskp29 | hskp16 | hskp0),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1155, 1154])).
% 0.81/0.83 tff(1157,plain,
% 0.81/0.83 (hskp29 | hskp16 | hskp0),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1156, 1150])).
% 0.81/0.83 tff(1158,plain,
% 0.81/0.83 (hskp29 | hskp16 | hskp0),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1157, 1150])).
% 0.81/0.83 tff(1159,plain,
% 0.81/0.83 (hskp29 | hskp16 | hskp0),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1158, 1150])).
% 0.81/0.83 tff(1160,plain,
% 0.81/0.83 (hskp29 | hskp16 | hskp0),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1159, 1150])).
% 0.81/0.83 tff(1161,plain,
% 0.81/0.83 (hskp29 | hskp16 | hskp0),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1160, 1150])).
% 0.81/0.83 tff(1162,plain,
% 0.81/0.83 (hskp29 | hskp16 | hskp0),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1161, 1150])).
% 0.81/0.83 tff(1163,plain,
% 0.81/0.83 (hskp29 | hskp16 | hskp0),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1162, 1150])).
% 0.81/0.83 tff(1164,plain,
% 0.81/0.83 (hskp29),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1163, 1149, 1112])).
% 0.81/0.83 tff(1165,plain,
% 0.81/0.83 (((~hskp29) | c3_1(a725)) <=> ((~hskp29) | c3_1(a725))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1166,axiom,((~hskp29) | c3_1(a725)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.81/0.83 tff(1167,plain,
% 0.81/0.83 ((~hskp29) | c3_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1166, 1165])).
% 0.81/0.83 tff(1168,plain,
% 0.81/0.83 ((~hskp29) | c3_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1167, 1165])).
% 0.81/0.83 tff(1169,plain,
% 0.81/0.83 ((~hskp29) | c3_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1168, 1165])).
% 0.81/0.83 tff(1170,plain,
% 0.81/0.83 ((~hskp29) | c3_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1169, 1165])).
% 0.81/0.83 tff(1171,plain,
% 0.81/0.83 ((~hskp29) | c3_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1170, 1165])).
% 0.81/0.83 tff(1172,plain,
% 0.81/0.83 ((~hskp29) | c3_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1171, 1165])).
% 0.81/0.83 tff(1173,plain,
% 0.81/0.83 ((~hskp29) | c3_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1172, 1165])).
% 0.81/0.83 tff(1174,plain,
% 0.81/0.83 ((~hskp29) | c3_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1173, 1165])).
% 0.81/0.83 tff(1175,plain,
% 0.81/0.83 (c3_1(a725)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1174, 1164])).
% 0.81/0.83 tff(1176,plain,
% 0.81/0.83 (((~hskp29) | c2_1(a725)) <=> ((~hskp29) | c2_1(a725))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1177,axiom,((~hskp29) | c2_1(a725)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 0.81/0.83 tff(1178,plain,
% 0.81/0.83 ((~hskp29) | c2_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1177, 1176])).
% 0.81/0.83 tff(1179,plain,
% 0.81/0.83 ((~hskp29) | c2_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1178, 1176])).
% 0.81/0.83 tff(1180,plain,
% 0.81/0.83 ((~hskp29) | c2_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1179, 1176])).
% 0.81/0.83 tff(1181,plain,
% 0.81/0.83 ((~hskp29) | c2_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1180, 1176])).
% 0.81/0.83 tff(1182,plain,
% 0.81/0.83 ((~hskp29) | c2_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1181, 1176])).
% 0.81/0.83 tff(1183,plain,
% 0.81/0.83 ((~hskp29) | c2_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1182, 1176])).
% 0.81/0.83 tff(1184,plain,
% 0.81/0.83 ((~hskp29) | c2_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1183, 1176])).
% 0.81/0.83 tff(1185,plain,
% 0.81/0.83 ((~hskp29) | c2_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1184, 1176])).
% 0.81/0.83 tff(1186,plain,
% 0.81/0.83 (c2_1(a725)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1185, 1164])).
% 0.81/0.83 tff(1187,plain,
% 0.81/0.83 (((~hskp29) | c1_1(a725)) <=> ((~hskp29) | c1_1(a725))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1188,axiom,((~hskp29) | c1_1(a725)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.81/0.83 tff(1189,plain,
% 0.81/0.83 ((~hskp29) | c1_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 0.81/0.83 tff(1190,plain,
% 0.81/0.83 ((~hskp29) | c1_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1189, 1187])).
% 0.81/0.83 tff(1191,plain,
% 0.81/0.83 ((~hskp29) | c1_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1190, 1187])).
% 0.81/0.83 tff(1192,plain,
% 0.81/0.83 ((~hskp29) | c1_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1191, 1187])).
% 0.81/0.83 tff(1193,plain,
% 0.81/0.83 ((~hskp29) | c1_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1192, 1187])).
% 0.81/0.83 tff(1194,plain,
% 0.81/0.83 ((~hskp29) | c1_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1193, 1187])).
% 0.81/0.83 tff(1195,plain,
% 0.81/0.83 ((~hskp29) | c1_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1194, 1187])).
% 0.81/0.83 tff(1196,plain,
% 0.81/0.83 ((~hskp29) | c1_1(a725)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1195, 1187])).
% 0.81/0.83 tff(1197,plain,
% 0.81/0.83 (c1_1(a725)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1196, 1164])).
% 0.81/0.83 tff(1198,plain,
% 0.81/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a703) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | (~c3_1(a703)) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a703) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1199,plain,
% 0.81/0.83 (((~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703))) <=> (c0_1(a703) | c2_1(a703) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1200,plain,
% 0.81/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | (c0_1(a703) | c2_1(a703) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | (~c3_1(a703)) | (~c1_1(a703))))),
% 0.81/0.83 inference(monotonicity,[status(thm)],[1199])).
% 0.81/0.83 tff(1201,plain,
% 0.81/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a703) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | (~c3_1(a703)) | (~c1_1(a703)))),
% 0.81/0.83 inference(transitivity,[status(thm)],[1200, 1198])).
% 0.81/0.83 tff(1202,plain,
% 0.81/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | ((~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | c0_1(a703) | (~c3_1(a703)) | (~c1_1(a703)) | c0_1(a703) | c2_1(a703) | (~c1_1(a703)))),
% 0.81/0.83 inference(quant_inst,[status(thm)],[])).
% 0.81/0.83 tff(1203,plain,
% 0.81/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c0_1(W) | c2_1(W) | (~c1_1(W)))) | c0_1(a703) | c2_1(a703) | (~ndr1_0) | (~c2_1(a725)) | (~c3_1(a725)) | (~c1_1(a725)) | (~c3_1(a703)) | (~c1_1(a703))),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 0.81/0.83 tff(1204,plain,
% 0.81/0.83 ($false),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1203, 99, 1197, 1186, 1175, 1093, 1092, 1111, 1110, 1100])).
% 0.81/0.83 tff(1205,plain,(hskp2 | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.81/0.83 tff(1206,plain,
% 0.81/0.83 (hskp2),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1205, 603])).
% 0.81/0.83 tff(1207,plain,
% 0.81/0.83 (~c1_1(a670)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[783, 1206])).
% 0.81/0.83 tff(1208,plain,
% 0.81/0.83 (~c0_1(a670)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[789, 1206])).
% 0.81/0.83 tff(1209,plain,
% 0.81/0.83 (c3_1(a670)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[803, 1206])).
% 0.81/0.83 tff(1210,plain,
% 0.81/0.83 (~c0_1(a702)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1057, 99, 594, 583, 915, 904, 1209, 1208, 1207, 624, 602])).
% 0.81/0.83 tff(1211,plain,
% 0.81/0.83 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1212,plain,
% 0.81/0.83 ((hskp9 | hskp8 | (~ndr1_0) | c1_1(a702) | c0_1(a702) | (~c2_1(a702))) <=> (hskp9 | hskp8 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1213,plain,
% 0.81/0.83 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a702) | c0_1(a702) | (~c2_1(a702)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702)))),
% 0.81/0.83 inference(monotonicity,[status(thm)],[1212])).
% 0.81/0.83 tff(1214,plain,
% 0.81/0.83 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a702) | c0_1(a702) | (~c2_1(a702)))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702))),
% 0.81/0.83 inference(transitivity,[status(thm)],[1213, 1211])).
% 0.81/0.83 tff(1215,plain,
% 0.81/0.83 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp9 | hskp8 | (~ndr1_0) | c1_1(a702) | c0_1(a702) | (~c2_1(a702)))),
% 0.81/0.83 inference(quant_inst,[status(thm)],[])).
% 0.81/0.83 tff(1216,plain,
% 0.81/0.83 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp9 | hskp8 | c1_1(a702) | (~ndr1_0) | (~c2_1(a702)) | c0_1(a702)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1215, 1214])).
% 0.81/0.83 tff(1217,plain,
% 0.81/0.83 (hskp8),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1216, 99, 603, 915, 891, 509, 1210])).
% 0.81/0.83 tff(1218,plain,
% 0.81/0.83 (~c0_1(a679)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[522, 1217])).
% 0.81/0.83 tff(1219,plain,
% 0.81/0.83 (c3_1(a679)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[545, 1217])).
% 0.81/0.83 tff(1220,plain,
% 0.81/0.83 (c1_1(a679)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[534, 1217])).
% 0.81/0.83 tff(1221,plain,
% 0.81/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a702) | c2_1(a683) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a702) | c2_1(a683) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)) | c0_1(a702) | (~c3_1(a702)))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1222,plain,
% 0.81/0.83 (((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702))) <=> (c1_1(a702) | c2_1(a683) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)) | c0_1(a702) | (~c3_1(a702)))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1223,plain,
% 0.81/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c1_1(a702) | c2_1(a683) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)) | c0_1(a702) | (~c3_1(a702))))),
% 0.81/0.83 inference(monotonicity,[status(thm)],[1222])).
% 0.81/0.83 tff(1224,plain,
% 0.81/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a702) | c2_1(a683) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)) | c0_1(a702) | (~c3_1(a702)))),
% 0.81/0.83 inference(transitivity,[status(thm)],[1223, 1221])).
% 0.81/0.83 tff(1225,plain,
% 0.81/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a702) | c0_1(a702) | (~c3_1(a702)))),
% 0.81/0.83 inference(quant_inst,[status(thm)],[])).
% 0.81/0.83 tff(1226,plain,
% 0.81/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c1_1(a702) | c2_1(a683) | c0_1(a679) | (~ndr1_0) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)) | c0_1(a702) | (~c3_1(a702))),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1225, 1224])).
% 0.81/0.83 tff(1227,plain,
% 0.81/0.83 ($false),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1226, 99, 904, 1070, 1080, 1220, 1219, 891, 1069, 1218, 490, 1210])).
% 0.81/0.83 tff(1228,plain,((~hskp16) | hskp9), inference(lemma,lemma(discharge,[]))).
% 0.81/0.83 tff(1229,plain,
% 0.81/0.83 (~hskp16),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1228, 603])).
% 0.81/0.83 tff(1230,plain,
% 0.81/0.83 (hskp16 | c2_1(a670)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1047, 99, 594, 583, 572, 1209, 1207, 1041])).
% 0.81/0.83 tff(1231,plain,
% 0.81/0.83 (c2_1(a670)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1230, 1229])).
% 0.81/0.83 tff(1232,plain,
% 0.81/0.83 (hskp8 | (~c2_1(a670))),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[819, 99, 603, 1208, 1207, 509])).
% 0.81/0.83 tff(1233,plain,
% 0.81/0.83 (hskp8),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1232, 1231])).
% 0.81/0.83 tff(1234,plain,
% 0.81/0.83 (~c0_1(a679)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[522, 1233])).
% 0.81/0.83 tff(1235,plain,
% 0.81/0.83 (c3_1(a679)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[545, 1233])).
% 0.81/0.83 tff(1236,plain,
% 0.81/0.83 (c1_1(a679)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[534, 1233])).
% 0.81/0.83 tff(1237,plain,
% 0.81/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a683) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a683) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1238,plain,
% 0.81/0.83 (((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670))) <=> (c2_1(a683) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1239,plain,
% 0.81/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | (c2_1(a683) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683))))),
% 0.81/0.83 inference(monotonicity,[status(thm)],[1238])).
% 0.81/0.83 tff(1240,plain,
% 0.81/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a683) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683)))),
% 0.81/0.83 inference(transitivity,[status(thm)],[1239, 1237])).
% 0.81/0.83 tff(1241,plain,
% 0.81/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a683) | (~c0_1(a683)) | (~c3_1(a683)) | c0_1(a679) | (~c3_1(a679)) | (~c1_1(a679)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))),
% 0.81/0.83 inference(quant_inst,[status(thm)],[])).
% 0.81/0.83 tff(1242,plain,
% 0.81/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)) | c1_1(W) | c0_1(W) | (~c3_1(W)))) | c2_1(a683) | c0_1(a679) | c0_1(a670) | c1_1(a670) | (~ndr1_0) | (~c3_1(a670)) | (~c1_1(a679)) | (~c3_1(a679)) | (~c3_1(a683)) | (~c0_1(a683))),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1241, 1240])).
% 0.81/0.83 tff(1243,plain,
% 0.81/0.83 ($false),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1242, 99, 1070, 1080, 1236, 1235, 1209, 1069, 1234, 1208, 1207, 490])).
% 0.81/0.83 tff(1244,plain,(hskp9), inference(lemma,lemma(discharge,[]))).
% 0.81/0.83 tff(1245,plain,
% 0.81/0.83 (~c3_1(a680)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[310, 1244])).
% 0.81/0.83 tff(1246,plain,
% 0.81/0.83 (~c1_1(a680)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[316, 1244])).
% 0.81/0.83 tff(1247,plain,
% 0.81/0.83 (c2_1(a680)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[341, 1244])).
% 0.81/0.83 tff(1248,plain,
% 0.81/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c0_1(a680)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c0_1(a680)))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1249,plain,
% 0.81/0.83 (((~ndr1_0) | c3_1(a680) | (~c2_1(a680)) | (~c0_1(a680)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680)) <=> (c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c0_1(a680)))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1250,plain,
% 0.81/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a680) | (~c2_1(a680)) | (~c0_1(a680)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | (c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c0_1(a680))))),
% 0.81/0.83 inference(monotonicity,[status(thm)],[1249])).
% 0.81/0.83 tff(1251,plain,
% 0.81/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a680) | (~c2_1(a680)) | (~c0_1(a680)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c0_1(a680)))),
% 0.81/0.83 inference(transitivity,[status(thm)],[1250, 1248])).
% 0.81/0.83 tff(1252,plain,
% 0.81/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | ((~ndr1_0) | c3_1(a680) | (~c2_1(a680)) | (~c0_1(a680)) | c2_1(a678) | (~c3_1(a678)) | (~c0_1(a678)) | c1_1(a680) | (~c2_1(a680)) | c3_1(a680))),
% 0.81/0.83 inference(quant_inst,[status(thm)],[])).
% 0.81/0.83 tff(1253,plain,
% 0.81/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | c3_1(W))) | c1_1(a680) | c3_1(a680) | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c3_1(a678)) | (~c2_1(a680)) | (~c0_1(a680))),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 0.81/0.83 tff(1254,plain,
% 0.81/0.83 (~c0_1(a680)),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1253, 99, 594, 572, 1247, 1246, 1245, 304, 602])).
% 0.81/0.83 tff(1255,plain,
% 0.81/0.83 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.81/0.83 inference(bind,[status(th)],[])).
% 0.81/0.83 tff(1256,plain,
% 0.81/0.83 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/0.83 inference(quant_intro,[status(thm)],[1255])).
% 0.81/0.83 tff(1257,plain,
% 0.81/0.83 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1258,plain,
% 0.81/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | 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) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.81/0.83 inference(bind,[status(th)],[])).
% 0.81/0.83 tff(1259,plain,
% 0.81/0.83 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/0.83 inference(quant_intro,[status(thm)],[1258])).
% 0.81/0.83 tff(1260,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 0.81/0.83 tff(1261,plain,
% 0.81/0.83 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 0.81/0.83 tff(1262,plain,
% 0.81/0.83 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1261, 1257])).
% 0.81/0.83 tff(1263,plain,(
% 0.81/0.83 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/0.83 inference(skolemize,[status(sab)],[1262])).
% 0.81/0.83 tff(1264,plain,
% 0.81/0.83 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1263, 1256])).
% 0.81/0.83 tff(1265,plain,
% 0.81/0.83 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | c0_1(a680))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | c0_1(a680))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1266,plain,
% 0.81/0.83 ((hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a680) | c1_1(a680) | c0_1(a680)) <=> (hskp5 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | c0_1(a680))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(1267,plain,
% 0.81/0.83 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a680) | c1_1(a680) | c0_1(a680))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | c0_1(a680)))),
% 0.81/0.83 inference(monotonicity,[status(thm)],[1266])).
% 0.81/0.83 tff(1268,plain,
% 0.81/0.83 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a680) | c1_1(a680) | c0_1(a680))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | c0_1(a680))),
% 0.81/0.83 inference(transitivity,[status(thm)],[1267, 1265])).
% 0.81/0.83 tff(1269,plain,
% 0.81/0.83 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp5 | (~ndr1_0) | c1_1(a680) | c3_1(a680) | (~c2_1(a680)) | c3_1(a680) | c1_1(a680) | c0_1(a680))),
% 0.81/0.83 inference(quant_inst,[status(thm)],[])).
% 0.81/0.83 tff(1270,plain,
% 0.81/0.83 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp5 | c1_1(a680) | c3_1(a680) | (~ndr1_0) | (~c2_1(a680)) | c0_1(a680)),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[1269, 1268])).
% 0.81/0.83 tff(1271,plain,
% 0.81/0.83 (hskp5),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[1270, 99, 1247, 1246, 1245, 152, 1254])).
% 0.81/0.84 tff(1272,plain,
% 0.81/0.84 (~c3_1(a673)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[49, 1271])).
% 0.81/0.84 tff(1273,plain,
% 0.81/0.84 (~c0_1(a673)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[61, 1271])).
% 0.81/0.84 tff(1274,plain,
% 0.81/0.84 (~c1_1(a673)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[1019, 99, 594, 583, 865, 864, 861, 1273, 1272, 383, 602])).
% 0.81/0.84 tff(1275,plain,
% 0.81/0.84 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 0.81/0.84 inference(bind,[status(th)],[])).
% 0.81/0.84 tff(1276,plain,
% 0.81/0.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.81/0.84 inference(quant_intro,[status(thm)],[1275])).
% 0.81/0.84 tff(1277,plain,
% 0.81/0.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.81/0.84 inference(rewrite,[status(thm)],[])).
% 0.81/0.84 tff(1278,plain,
% 0.81/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 0.81/0.84 inference(bind,[status(th)],[])).
% 0.81/0.84 tff(1279,plain,
% 0.81/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.81/0.84 inference(quant_intro,[status(thm)],[1278])).
% 0.81/0.84 tff(1280,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 0.81/0.84 tff(1281,plain,
% 0.81/0.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 0.81/0.84 tff(1282,plain,
% 0.81/0.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[1281, 1277])).
% 0.81/0.84 tff(1283,plain,(
% 0.81/0.84 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.81/0.84 inference(skolemize,[status(sab)],[1282])).
% 0.81/0.84 tff(1284,plain,
% 0.81/0.84 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[1283, 1276])).
% 0.81/0.84 tff(1285,plain,
% 0.81/0.84 (~c2_1(a673)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[55, 1271])).
% 0.81/0.84 tff(1286,plain,
% 0.81/0.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | c1_1(a673))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | c1_1(a673))),
% 0.81/0.84 inference(rewrite,[status(thm)],[])).
% 0.81/0.84 tff(1287,plain,
% 0.81/0.84 ((hskp0 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a678)) | c1_1(a673) | c0_1(a673) | c2_1(a673)) <=> (hskp0 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | c1_1(a673))),
% 0.81/0.84 inference(rewrite,[status(thm)],[])).
% 0.81/0.84 tff(1288,plain,
% 0.81/0.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a678)) | c1_1(a673) | c0_1(a673) | c2_1(a673))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | c1_1(a673)))),
% 0.81/0.84 inference(monotonicity,[status(thm)],[1287])).
% 0.81/0.84 tff(1289,plain,
% 0.81/0.84 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a678)) | c1_1(a673) | c0_1(a673) | c2_1(a673))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | c1_1(a673))),
% 0.81/0.84 inference(transitivity,[status(thm)],[1288, 1286])).
% 0.81/0.84 tff(1290,plain,
% 0.81/0.84 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a678) | (~c0_1(a678)) | (~c1_1(a678)) | c1_1(a673) | c0_1(a673) | c2_1(a673))),
% 0.81/0.84 inference(quant_inst,[status(thm)],[])).
% 0.81/0.84 tff(1291,plain,
% 0.81/0.84 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp0 | c0_1(a673) | c2_1(a673) | (~ndr1_0) | (~c1_1(a678)) | c2_1(a678) | (~c0_1(a678)) | c1_1(a673)),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 0.81/0.84 tff(1292,plain,
% 0.81/0.84 (hskp0),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[1291, 99, 594, 583, 1273, 1285, 1284, 602, 1274])).
% 0.81/0.84 tff(1293,plain,
% 0.81/0.84 (~c3_1(a668)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[1119, 1292])).
% 0.81/0.84 tff(1294,plain,
% 0.81/0.84 (((~hskp0) | (~c2_1(a668))) <=> ((~hskp0) | (~c2_1(a668)))),
% 0.81/0.84 inference(rewrite,[status(thm)],[])).
% 0.81/0.84 tff(1295,plain,
% 0.81/0.84 (((~c2_1(a668)) | (~hskp0)) <=> ((~hskp0) | (~c2_1(a668)))),
% 0.81/0.84 inference(rewrite,[status(thm)],[])).
% 0.81/0.84 tff(1296,axiom,((~c2_1(a668)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 0.81/0.84 tff(1297,plain,
% 0.81/0.84 ((~hskp0) | (~c2_1(a668))),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 0.81/0.84 tff(1298,plain,
% 0.81/0.84 ((~hskp0) | (~c2_1(a668))),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[1297, 1294])).
% 0.81/0.84 tff(1299,plain,
% 0.81/0.84 (~c2_1(a668)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[1298, 1292])).
% 0.81/0.84 tff(1300,plain,
% 0.81/0.84 (c1_1(a668)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[1130, 1292])).
% 0.81/0.84 tff(1301,plain,
% 0.81/0.84 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c3_1(a680) | c2_1(a668) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c2_1(a680)) | c0_1(a680))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c3_1(a680) | c2_1(a668) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c2_1(a680)) | c0_1(a680))),
% 0.81/0.84 inference(rewrite,[status(thm)],[])).
% 0.81/0.84 tff(1302,plain,
% 0.81/0.84 ((hskp10 | (~ndr1_0) | c2_1(a668) | c3_1(a668) | (~c1_1(a668)) | c3_1(a680) | c0_1(a680) | (~c2_1(a680))) <=> (hskp10 | c3_1(a680) | c2_1(a668) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c2_1(a680)) | c0_1(a680))),
% 0.81/0.84 inference(rewrite,[status(thm)],[])).
% 0.81/0.84 tff(1303,plain,
% 0.81/0.84 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a668) | c3_1(a668) | (~c1_1(a668)) | c3_1(a680) | c0_1(a680) | (~c2_1(a680)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | c3_1(a680) | c2_1(a668) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c2_1(a680)) | c0_1(a680)))),
% 0.81/0.84 inference(monotonicity,[status(thm)],[1302])).
% 0.81/0.84 tff(1304,plain,
% 0.81/0.84 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a668) | c3_1(a668) | (~c1_1(a668)) | c3_1(a680) | c0_1(a680) | (~c2_1(a680)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c3_1(a680) | c2_1(a668) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c2_1(a680)) | c0_1(a680))),
% 0.81/0.84 inference(transitivity,[status(thm)],[1303, 1301])).
% 0.81/0.84 tff(1305,plain,
% 0.81/0.84 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp10 | (~ndr1_0) | c2_1(a668) | c3_1(a668) | (~c1_1(a668)) | c3_1(a680) | c0_1(a680) | (~c2_1(a680)))),
% 0.81/0.84 inference(quant_inst,[status(thm)],[])).
% 0.81/0.84 tff(1306,plain,
% 0.81/0.84 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp10 | c3_1(a680) | c2_1(a668) | c3_1(a668) | (~ndr1_0) | (~c1_1(a668)) | (~c2_1(a680)) | c0_1(a680)),
% 0.81/0.84 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 0.81/0.84 tff(1307,plain,
% 0.81/0.84 (hskp10),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[1306, 99, 1247, 1300, 1245, 1299, 1293, 1264, 1254])).
% 0.81/0.84 tff(1308,plain,
% 0.81/0.84 (c2_1(a681)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[229, 1307])).
% 0.81/0.84 tff(1309,plain,
% 0.81/0.84 (~c0_1(a681)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[207, 1307])).
% 0.81/0.84 tff(1310,plain,
% 0.81/0.84 (c3_1(a681)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[218, 1307])).
% 0.81/0.84 tff(1311,plain,
% 0.81/0.84 (~c1_1(a681)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[236, 99, 1308, 1310, 1309, 22])).
% 0.81/0.84 tff(1312,plain,
% 0.81/0.84 (hskp11),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[253, 99, 1308, 1310, 1309, 247, 1311])).
% 0.81/0.84 tff(1313,plain,
% 0.81/0.84 (~c2_1(a683)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[281, 1312])).
% 0.81/0.84 tff(1314,plain,
% 0.81/0.84 (c0_1(a683)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[264, 1312])).
% 0.81/0.84 tff(1315,plain,
% 0.81/0.84 (c3_1(a683)),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[275, 1312])).
% 0.81/0.84 tff(1316,plain,
% 0.81/0.84 ($false),
% 0.81/0.84 inference(unit_resolution,[status(thm)],[498, 1315, 1314, 1244, 1310, 1313, 1309, 865, 864, 861, 1308])).
% 0.81/0.84 % SZS output end Proof
%------------------------------------------------------------------------------