TSTP Solution File: SYN450-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN450-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 23:55:30 EDT 2022
% Result : Unsatisfiable 0.90s 0.85s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN450-1 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 03:51:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.90/0.85 % SZS status Unsatisfiable
% 0.90/0.85 % SZS output start Proof
% 0.90/0.85 tff(c3_1_type, type, (
% 0.90/0.85 c3_1: $i > $o)).
% 0.90/0.85 tff(a643_type, type, (
% 0.90/0.85 a643: $i)).
% 0.90/0.85 tff(c2_1_type, type, (
% 0.90/0.85 c2_1: $i > $o)).
% 0.90/0.85 tff(a675_type, type, (
% 0.90/0.85 a675: $i)).
% 0.90/0.85 tff(hskp17_type, type, (
% 0.90/0.85 hskp17: $o)).
% 0.90/0.85 tff(c0_1_type, type, (
% 0.90/0.85 c0_1: $i > $o)).
% 0.90/0.85 tff(a647_type, type, (
% 0.90/0.85 a647: $i)).
% 0.90/0.85 tff(hskp5_type, type, (
% 0.90/0.85 hskp5: $o)).
% 0.90/0.85 tff(c1_1_type, type, (
% 0.90/0.85 c1_1: $i > $o)).
% 0.90/0.85 tff(hskp2_type, type, (
% 0.90/0.85 hskp2: $o)).
% 0.90/0.85 tff(a665_type, type, (
% 0.90/0.85 a665: $i)).
% 0.90/0.85 tff(ndr1_0_type, type, (
% 0.90/0.85 ndr1_0: $o)).
% 0.90/0.85 tff(hskp14_type, type, (
% 0.90/0.85 hskp14: $o)).
% 0.90/0.85 tff(hskp1_type, type, (
% 0.90/0.85 hskp1: $o)).
% 0.90/0.85 tff(hskp28_type, type, (
% 0.90/0.85 hskp28: $o)).
% 0.90/0.85 tff(a651_type, type, (
% 0.90/0.85 a651: $i)).
% 0.90/0.85 tff(hskp7_type, type, (
% 0.90/0.85 hskp7: $o)).
% 0.90/0.85 tff(a641_type, type, (
% 0.90/0.85 a641: $i)).
% 0.90/0.85 tff(hskp0_type, type, (
% 0.90/0.85 hskp0: $o)).
% 0.90/0.85 tff(a642_type, type, (
% 0.90/0.85 a642: $i)).
% 0.90/0.85 tff(a648_type, type, (
% 0.90/0.85 a648: $i)).
% 0.90/0.85 tff(hskp6_type, type, (
% 0.90/0.85 hskp6: $o)).
% 0.90/0.85 tff(a698_type, type, (
% 0.90/0.85 a698: $i)).
% 0.90/0.85 tff(hskp24_type, type, (
% 0.90/0.85 hskp24: $o)).
% 0.90/0.85 tff(hskp20_type, type, (
% 0.90/0.85 hskp20: $o)).
% 0.90/0.85 tff(a686_type, type, (
% 0.90/0.85 a686: $i)).
% 0.90/0.85 tff(a695_type, type, (
% 0.90/0.85 a695: $i)).
% 0.90/0.85 tff(a676_type, type, (
% 0.90/0.85 a676: $i)).
% 0.90/0.85 tff(hskp18_type, type, (
% 0.90/0.85 hskp18: $o)).
% 0.90/0.85 tff(hskp23_type, type, (
% 0.90/0.85 hskp23: $o)).
% 0.90/0.85 tff(a660_type, type, (
% 0.90/0.85 a660: $i)).
% 0.90/0.85 tff(hskp12_type, type, (
% 0.90/0.85 hskp12: $o)).
% 0.90/0.85 tff(a657_type, type, (
% 0.90/0.85 a657: $i)).
% 0.90/0.85 tff(hskp11_type, type, (
% 0.90/0.85 hskp11: $o)).
% 0.90/0.85 tff(a693_type, type, (
% 0.90/0.85 a693: $i)).
% 0.90/0.85 tff(hskp22_type, type, (
% 0.90/0.85 hskp22: $o)).
% 0.90/0.85 tff(hskp4_type, type, (
% 0.90/0.85 hskp4: $o)).
% 0.90/0.85 tff(a671_type, type, (
% 0.90/0.85 a671: $i)).
% 0.90/0.85 tff(a646_type, type, (
% 0.90/0.85 a646: $i)).
% 0.90/0.85 tff(a710_type, type, (
% 0.90/0.85 a710: $i)).
% 0.90/0.85 tff(hskp25_type, type, (
% 0.90/0.85 hskp25: $o)).
% 0.90/0.85 tff(a655_type, type, (
% 0.90/0.85 a655: $i)).
% 0.90/0.85 tff(hskp27_type, type, (
% 0.90/0.85 hskp27: $o)).
% 0.90/0.85 tff(a645_type, type, (
% 0.90/0.85 a645: $i)).
% 0.90/0.85 tff(hskp3_type, type, (
% 0.90/0.85 hskp3: $o)).
% 0.90/0.85 tff(a640_type, type, (
% 0.90/0.85 a640: $i)).
% 0.90/0.85 tff(hskp26_type, type, (
% 0.90/0.85 hskp26: $o)).
% 0.90/0.85 tff(a652_type, type, (
% 0.90/0.85 a652: $i)).
% 0.90/0.85 tff(hskp8_type, type, (
% 0.90/0.85 hskp8: $o)).
% 0.90/0.85 tff(a672_type, type, (
% 0.90/0.85 a672: $i)).
% 0.90/0.85 tff(hskp16_type, type, (
% 0.90/0.85 hskp16: $o)).
% 0.90/0.85 tff(a682_type, type, (
% 0.90/0.85 a682: $i)).
% 0.90/0.85 tff(hskp19_type, type, (
% 0.90/0.85 hskp19: $o)).
% 0.90/0.85 tff(1,assumption,(~hskp17), introduced(assumption)).
% 0.90/0.85 tff(2,assumption,(~hskp5), introduced(assumption)).
% 0.90/0.85 tff(3,plain,
% 0.90/0.85 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(4,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[3])).
% 0.90/0.85 tff(5,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(6,plain,
% 0.90/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | 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) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(7,plain,
% 0.90/0.85 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[6])).
% 0.90/0.85 tff(8,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 0.90/0.85 tff(9,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.90/0.85 tff(10,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.90/0.85 tff(11,plain,(
% 0.90/0.85 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.85 inference(skolemize,[status(sab)],[10])).
% 0.90/0.85 tff(12,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.90/0.85 tff(13,plain,
% 0.90/0.85 (^[U: $i] : refl((hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(14,plain,
% 0.90/0.85 (![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[13])).
% 0.90/0.85 tff(15,plain,
% 0.90/0.85 (![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(16,plain,
% 0.90/0.85 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp17))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp7) <=> ((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp7))), rewrite(((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp7) <=> (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp7) <=> (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(17,plain,
% 0.90/0.85 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp7) <=> ![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[16])).
% 0.90/0.85 tff(18,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 0.90/0.85 tff(19,plain,
% 0.90/0.85 (![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.90/0.85 tff(20,plain,
% 0.90/0.85 (![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.90/0.85 tff(21,plain,(
% 0.90/0.85 ![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.90/0.85 inference(skolemize,[status(sab)],[20])).
% 0.90/0.85 tff(22,plain,
% 0.90/0.85 (![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.90/0.85 tff(23,assumption,(~hskp0), introduced(assumption)).
% 0.90/0.85 tff(24,assumption,(~hskp2), introduced(assumption)).
% 0.90/0.85 tff(25,plain,
% 0.90/0.85 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(26,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[25])).
% 0.90/0.85 tff(27,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(28,plain,
% 0.90/0.85 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_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) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(29,plain,
% 0.90/0.85 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[28])).
% 0.90/0.85 tff(30,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause157')).
% 0.90/0.85 tff(31,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.90/0.85 tff(32,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.90/0.85 tff(33,plain,(
% 0.90/0.85 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.90/0.85 inference(skolemize,[status(sab)],[32])).
% 0.90/0.85 tff(34,plain,
% 0.90/0.85 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.90/0.85 tff(35,plain,
% 0.90/0.85 (^[U: $i] : refl((hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(36,plain,
% 0.90/0.85 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[35])).
% 0.90/0.85 tff(37,plain,
% 0.90/0.85 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(38,plain,
% 0.90/0.85 (^[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)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp2) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp2))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp2) <=> (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp2) <=> (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.90/0.85 inference(bind,[status(th)],[])).
% 0.90/0.85 tff(39,plain,
% 0.90/0.85 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp2) <=> ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.85 inference(quant_intro,[status(thm)],[38])).
% 0.90/0.85 tff(40,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 0.90/0.85 tff(41,plain,
% 0.90/0.85 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.90/0.85 tff(42,plain,
% 0.90/0.85 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.90/0.85 tff(43,plain,(
% 0.90/0.85 ![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.85 inference(skolemize,[status(sab)],[42])).
% 0.90/0.85 tff(44,plain,
% 0.90/0.85 (![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.90/0.85 tff(45,assumption,(hskp14), introduced(assumption)).
% 0.90/0.85 tff(46,plain,
% 0.90/0.85 (((~hskp14) | (~c1_1(a665))) <=> ((~hskp14) | (~c1_1(a665)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(47,plain,
% 0.90/0.85 (((~c1_1(a665)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a665)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(48,axiom,((~c1_1(a665)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 0.90/0.85 tff(49,plain,
% 0.90/0.85 ((~hskp14) | (~c1_1(a665))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.90/0.85 tff(50,plain,
% 0.90/0.85 ((~hskp14) | (~c1_1(a665))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[49, 46])).
% 0.90/0.85 tff(51,plain,
% 0.90/0.85 (~c1_1(a665)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[50, 45])).
% 0.90/0.85 tff(52,plain,
% 0.90/0.85 (((~hskp14) | (~c0_1(a665))) <=> ((~hskp14) | (~c0_1(a665)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(53,plain,
% 0.90/0.85 (((~c0_1(a665)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a665)))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(54,axiom,((~c0_1(a665)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 0.90/0.85 tff(55,plain,
% 0.90/0.85 ((~hskp14) | (~c0_1(a665))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.90/0.85 tff(56,plain,
% 0.90/0.85 ((~hskp14) | (~c0_1(a665))),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.90/0.85 tff(57,plain,
% 0.90/0.85 (~c0_1(a665)),
% 0.90/0.85 inference(unit_resolution,[status(thm)],[56, 45])).
% 0.90/0.85 tff(58,plain,
% 0.90/0.85 (((~hskp14) | c2_1(a665)) <=> ((~hskp14) | c2_1(a665))),
% 0.90/0.85 inference(rewrite,[status(thm)],[])).
% 0.90/0.85 tff(59,axiom,((~hskp14) | c2_1(a665)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.90/0.85 tff(60,plain,
% 0.90/0.85 ((~hskp14) | c2_1(a665)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.90/0.85 tff(61,plain,
% 0.90/0.85 ((~hskp14) | c2_1(a665)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[60, 58])).
% 0.90/0.85 tff(62,plain,
% 0.90/0.85 ((~hskp14) | c2_1(a665)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[61, 58])).
% 0.90/0.85 tff(63,plain,
% 0.90/0.85 ((~hskp14) | c2_1(a665)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.90/0.85 tff(64,plain,
% 0.90/0.85 ((~hskp14) | c2_1(a665)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[63, 58])).
% 0.90/0.85 tff(65,plain,
% 0.90/0.85 ((~hskp14) | c2_1(a665)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[64, 58])).
% 0.90/0.85 tff(66,plain,
% 0.90/0.85 ((~hskp14) | c2_1(a665)),
% 0.90/0.85 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.90/0.85 tff(67,plain,
% 0.90/0.85 ((~hskp14) | c2_1(a665)),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[66, 58])).
% 0.95/0.85 tff(68,plain,
% 0.95/0.85 (c2_1(a665)),
% 0.95/0.85 inference(unit_resolution,[status(thm)],[67, 45])).
% 0.95/0.85 tff(69,assumption,(~ndr1_0), introduced(assumption)).
% 0.95/0.85 tff(70,plain,
% 0.95/0.85 ((ndr1_0 | (~hskp0)) <=> (ndr1_0 | (~hskp0))),
% 0.95/0.85 inference(rewrite,[status(thm)],[])).
% 0.95/0.85 tff(71,plain,
% 0.95/0.85 (((~hskp0) | ndr1_0) <=> (ndr1_0 | (~hskp0))),
% 0.95/0.85 inference(rewrite,[status(thm)],[])).
% 0.95/0.85 tff(72,axiom,((~hskp0) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause30')).
% 0.95/0.85 tff(73,plain,
% 0.95/0.85 (ndr1_0 | (~hskp0)),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.95/0.85 tff(74,plain,
% 0.95/0.85 (ndr1_0 | (~hskp0)),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[73, 70])).
% 0.95/0.85 tff(75,plain,
% 0.95/0.85 (~hskp0),
% 0.95/0.85 inference(unit_resolution,[status(thm)],[74, 69])).
% 0.95/0.85 tff(76,plain,
% 0.95/0.85 ((ndr1_0 | (~hskp24)) <=> (ndr1_0 | (~hskp24))),
% 0.95/0.85 inference(rewrite,[status(thm)],[])).
% 0.95/0.85 tff(77,plain,
% 0.95/0.85 (((~hskp24) | ndr1_0) <=> (ndr1_0 | (~hskp24))),
% 0.95/0.85 inference(rewrite,[status(thm)],[])).
% 0.95/0.85 tff(78,axiom,((~hskp24) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause6')).
% 0.95/0.85 tff(79,plain,
% 0.95/0.85 (ndr1_0 | (~hskp24)),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.95/0.85 tff(80,plain,
% 0.95/0.85 (ndr1_0 | (~hskp24)),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[79, 76])).
% 0.95/0.85 tff(81,plain,
% 0.95/0.85 (~hskp24),
% 0.95/0.85 inference(unit_resolution,[status(thm)],[80, 69])).
% 0.95/0.85 tff(82,plain,
% 0.95/0.85 ((ndr1_0 | (~hskp20)) <=> (ndr1_0 | (~hskp20))),
% 0.95/0.85 inference(rewrite,[status(thm)],[])).
% 0.95/0.85 tff(83,plain,
% 0.95/0.85 (((~hskp20) | ndr1_0) <=> (ndr1_0 | (~hskp20))),
% 0.95/0.85 inference(rewrite,[status(thm)],[])).
% 0.95/0.85 tff(84,axiom,((~hskp20) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause10')).
% 0.95/0.85 tff(85,plain,
% 0.95/0.85 (ndr1_0 | (~hskp20)),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.95/0.85 tff(86,plain,
% 0.95/0.85 (ndr1_0 | (~hskp20)),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[85, 82])).
% 0.95/0.85 tff(87,plain,
% 0.95/0.85 (~hskp20),
% 0.95/0.85 inference(unit_resolution,[status(thm)],[86, 69])).
% 0.95/0.85 tff(88,plain,
% 0.95/0.85 ((hskp24 | hskp20 | hskp0) <=> (hskp24 | hskp20 | hskp0)),
% 0.95/0.85 inference(rewrite,[status(thm)],[])).
% 0.95/0.85 tff(89,plain,
% 0.95/0.85 (((hskp20 | hskp24) | hskp0) <=> (hskp24 | hskp20 | hskp0)),
% 0.95/0.85 inference(rewrite,[status(thm)],[])).
% 0.95/0.85 tff(90,axiom,((hskp20 | hskp24) | hskp0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause35')).
% 0.95/0.85 tff(91,plain,
% 0.95/0.85 (hskp24 | hskp20 | hskp0),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.95/0.85 tff(92,plain,
% 0.95/0.85 (hskp24 | hskp20 | hskp0),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[91, 88])).
% 0.95/0.85 tff(93,plain,
% 0.95/0.85 (hskp24 | hskp20 | hskp0),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.95/0.85 tff(94,plain,
% 0.95/0.85 (hskp24 | hskp20 | hskp0),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[93, 88])).
% 0.95/0.85 tff(95,plain,
% 0.95/0.85 (hskp24 | hskp20 | hskp0),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[94, 88])).
% 0.95/0.85 tff(96,plain,
% 0.95/0.85 (hskp24 | hskp20 | hskp0),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.95/0.85 tff(97,plain,
% 0.95/0.85 (hskp24 | hskp20 | hskp0),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[96, 88])).
% 0.95/0.85 tff(98,plain,
% 0.95/0.85 (hskp24 | hskp20 | hskp0),
% 0.95/0.85 inference(modus_ponens,[status(thm)],[97, 88])).
% 0.95/0.85 tff(99,plain,
% 0.95/0.85 ($false),
% 0.95/0.85 inference(unit_resolution,[status(thm)],[98, 87, 81, 23])).
% 0.95/0.85 tff(100,plain,(ndr1_0 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.95/0.85 tff(101,plain,
% 0.95/0.85 ($false),
% 0.95/0.85 inference(unit_resolution,[status(thm)],[100, 75, 69])).
% 0.95/0.85 tff(102,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.95/0.85 tff(103,plain,
% 0.95/0.85 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)))),
% 0.95/0.85 inference(rewrite,[status(thm)],[])).
% 0.95/0.85 tff(104,plain,
% 0.95/0.85 ((hskp6 | hskp2 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | (~c2_1(a665))) <=> (hskp6 | hskp2 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)))),
% 0.95/0.85 inference(rewrite,[status(thm)],[])).
% 0.95/0.85 tff(105,plain,
% 0.95/0.85 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | (~c2_1(a665)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665))))),
% 0.95/0.86 inference(monotonicity,[status(thm)],[104])).
% 0.95/0.86 tff(106,plain,
% 0.95/0.86 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | (~c2_1(a665)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)))),
% 0.95/0.86 inference(transitivity,[status(thm)],[105, 103])).
% 0.95/0.86 tff(107,plain,
% 0.95/0.86 ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | (~c2_1(a665)))),
% 0.95/0.86 inference(quant_inst,[status(thm)],[])).
% 0.95/0.86 tff(108,plain,
% 0.95/0.86 ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.95/0.86 tff(109,plain,
% 0.95/0.86 (hskp6),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[108, 102, 24, 68, 57, 51, 44])).
% 0.95/0.86 tff(110,plain,
% 0.95/0.86 (((~hskp6) | (~c3_1(a648))) <=> ((~hskp6) | (~c3_1(a648)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(111,plain,
% 0.95/0.86 (((~c3_1(a648)) | (~hskp6)) <=> ((~hskp6) | (~c3_1(a648)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(112,axiom,((~c3_1(a648)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 0.95/0.86 tff(113,plain,
% 0.95/0.86 ((~hskp6) | (~c3_1(a648))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.95/0.86 tff(114,plain,
% 0.95/0.86 ((~hskp6) | (~c3_1(a648))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[113, 110])).
% 0.95/0.86 tff(115,plain,
% 0.95/0.86 (~c3_1(a648)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[114, 109])).
% 0.95/0.86 tff(116,plain,
% 0.95/0.86 (((~hskp6) | (~c2_1(a648))) <=> ((~hskp6) | (~c2_1(a648)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(117,plain,
% 0.95/0.86 (((~c2_1(a648)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a648)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(118,axiom,((~c2_1(a648)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 0.95/0.86 tff(119,plain,
% 0.95/0.86 ((~hskp6) | (~c2_1(a648))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.95/0.86 tff(120,plain,
% 0.95/0.86 ((~hskp6) | (~c2_1(a648))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[119, 116])).
% 0.95/0.86 tff(121,plain,
% 0.95/0.86 (~c2_1(a648)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[120, 109])).
% 0.95/0.86 tff(122,plain,
% 0.95/0.86 (^[U: $i] : refl((hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(123,plain,
% 0.95/0.86 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[122])).
% 0.95/0.86 tff(124,plain,
% 0.95/0.86 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(125,plain,
% 0.95/0.86 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp2))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) <=> (hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp0) <=> ((hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp0))), rewrite(((hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U)) | hskp0) <=> (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp0) <=> (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(126,plain,
% 0.95/0.86 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp0) <=> ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[125])).
% 0.95/0.86 tff(127,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp2) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.95/0.86 tff(128,plain,
% 0.95/0.86 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.95/0.86 tff(129,plain,
% 0.95/0.86 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.95/0.86 tff(130,plain,(
% 0.95/0.86 ![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.95/0.86 inference(skolemize,[status(sab)],[129])).
% 0.95/0.86 tff(131,plain,
% 0.95/0.86 (![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.95/0.86 tff(132,plain,
% 0.95/0.86 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | c3_1(a665))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | c3_1(a665))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(133,plain,
% 0.95/0.86 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | c3_1(a665)) <=> (hskp2 | hskp0 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | c3_1(a665))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(134,plain,
% 0.95/0.86 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | c3_1(a665))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | c3_1(a665)))),
% 0.95/0.86 inference(monotonicity,[status(thm)],[133])).
% 0.95/0.86 tff(135,plain,
% 0.95/0.86 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | c3_1(a665))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | c3_1(a665))),
% 0.95/0.86 inference(transitivity,[status(thm)],[134, 132])).
% 0.95/0.86 tff(136,plain,
% 0.95/0.86 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a665) | c0_1(a665) | c3_1(a665))),
% 0.95/0.86 inference(quant_inst,[status(thm)],[])).
% 0.95/0.86 tff(137,plain,
% 0.95/0.86 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | c3_1(a665)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.95/0.86 tff(138,plain,
% 0.95/0.86 (c3_1(a665)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[137, 102, 24, 23, 57, 51, 131])).
% 0.95/0.86 tff(139,plain,
% 0.95/0.86 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(140,plain,
% 0.95/0.86 ((hskp17 | hskp7 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665))) <=> (hskp17 | hskp7 | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(141,plain,
% 0.95/0.86 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665))))),
% 0.95/0.86 inference(monotonicity,[status(thm)],[140])).
% 0.95/0.86 tff(142,plain,
% 0.95/0.86 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.95/0.86 inference(transitivity,[status(thm)],[141, 139])).
% 0.95/0.86 tff(143,plain,
% 0.95/0.86 ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)))),
% 0.95/0.86 inference(quant_inst,[status(thm)],[])).
% 0.95/0.86 tff(144,plain,
% 0.95/0.86 ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.95/0.86 tff(145,plain,
% 0.95/0.86 (hskp7 | (~c3_1(a665))),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[144, 102, 1, 68, 51, 22])).
% 0.95/0.86 tff(146,plain,
% 0.95/0.86 (hskp7),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[145, 138])).
% 0.95/0.86 tff(147,plain,
% 0.95/0.86 (((~hskp7) | (~c1_1(a651))) <=> ((~hskp7) | (~c1_1(a651)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(148,plain,
% 0.95/0.86 (((~c1_1(a651)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a651)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(149,axiom,((~c1_1(a651)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.95/0.86 tff(150,plain,
% 0.95/0.86 ((~hskp7) | (~c1_1(a651))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.95/0.86 tff(151,plain,
% 0.95/0.86 ((~hskp7) | (~c1_1(a651))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[150, 147])).
% 0.95/0.86 tff(152,plain,
% 0.95/0.86 (~c1_1(a651)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[151, 146])).
% 0.95/0.86 tff(153,plain,
% 0.95/0.86 (((~hskp7) | (~c0_1(a651))) <=> ((~hskp7) | (~c0_1(a651)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(154,plain,
% 0.95/0.86 (((~c0_1(a651)) | (~hskp7)) <=> ((~hskp7) | (~c0_1(a651)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(155,axiom,((~c0_1(a651)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.95/0.86 tff(156,plain,
% 0.95/0.86 ((~hskp7) | (~c0_1(a651))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.95/0.86 tff(157,plain,
% 0.95/0.86 ((~hskp7) | (~c0_1(a651))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[156, 153])).
% 0.95/0.86 tff(158,plain,
% 0.95/0.86 (~c0_1(a651)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[157, 146])).
% 0.95/0.86 tff(159,plain,
% 0.95/0.86 (((~hskp7) | c3_1(a651)) <=> ((~hskp7) | c3_1(a651))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(160,axiom,((~hskp7) | c3_1(a651)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.95/0.86 tff(161,plain,
% 0.95/0.86 ((~hskp7) | c3_1(a651)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.95/0.86 tff(162,plain,
% 0.95/0.86 ((~hskp7) | c3_1(a651)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[161, 159])).
% 0.95/0.86 tff(163,plain,
% 0.95/0.86 ((~hskp7) | c3_1(a651)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[162, 159])).
% 0.95/0.86 tff(164,plain,
% 0.95/0.86 ((~hskp7) | c3_1(a651)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.95/0.86 tff(165,plain,
% 0.95/0.86 ((~hskp7) | c3_1(a651)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[164, 159])).
% 0.95/0.86 tff(166,plain,
% 0.95/0.86 ((~hskp7) | c3_1(a651)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[165, 159])).
% 0.95/0.86 tff(167,plain,
% 0.95/0.86 ((~hskp7) | c3_1(a651)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.95/0.86 tff(168,plain,
% 0.95/0.86 ((~hskp7) | c3_1(a651)),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[167, 159])).
% 0.95/0.86 tff(169,plain,
% 0.95/0.86 (c3_1(a651)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[168, 146])).
% 0.95/0.86 tff(170,plain,
% 0.95/0.86 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a651) | c1_1(a651) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c1_1(a648)) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a651) | c1_1(a651) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c1_1(a648)) | (~c3_1(a651)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(171,plain,
% 0.95/0.86 ((hskp2 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c1_1(a648)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651))) <=> (hskp2 | c0_1(a651) | c1_1(a651) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c1_1(a648)) | (~c3_1(a651)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(172,plain,
% 0.95/0.86 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c1_1(a648)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a651) | c1_1(a651) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c1_1(a648)) | (~c3_1(a651))))),
% 0.95/0.86 inference(monotonicity,[status(thm)],[171])).
% 0.95/0.86 tff(173,plain,
% 0.95/0.86 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c1_1(a648)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a651) | c1_1(a651) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c1_1(a648)) | (~c3_1(a651)))),
% 0.95/0.86 inference(transitivity,[status(thm)],[172, 170])).
% 0.95/0.86 tff(174,plain,
% 0.95/0.86 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c1_1(a648)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))),
% 0.95/0.86 inference(quant_inst,[status(thm)],[])).
% 0.95/0.86 tff(175,plain,
% 0.95/0.86 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a651) | c1_1(a651) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c1_1(a648)) | (~c3_1(a651))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.95/0.86 tff(176,plain,
% 0.95/0.86 (~c1_1(a648)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[175, 102, 24, 169, 158, 152, 121, 115, 34])).
% 0.95/0.86 tff(177,plain,
% 0.95/0.86 (^[V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(178,plain,
% 0.95/0.86 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[177])).
% 0.95/0.86 tff(179,plain,
% 0.95/0.86 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(180,plain,
% 0.95/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(181,plain,
% 0.95/0.86 (![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[180])).
% 0.95/0.86 tff(182,axiom,(![V: $i, U: $i] : (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c2_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 0.95/0.86 tff(183,plain,
% 0.95/0.86 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.95/0.86 tff(184,plain,
% 0.95/0.86 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.95/0.86 tff(185,plain,(
% 0.95/0.86 ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.95/0.86 inference(skolemize,[status(sab)],[184])).
% 0.95/0.86 tff(186,plain,
% 0.95/0.86 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.95/0.86 tff(187,plain,
% 0.95/0.86 (^[U: $i] : refl((hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(188,plain,
% 0.95/0.86 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[187])).
% 0.95/0.86 tff(189,plain,
% 0.95/0.86 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(190,plain,
% 0.95/0.86 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp5) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp5))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U))) | hskp5) <=> (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp5) <=> (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(191,plain,
% 0.95/0.86 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp5) <=> ![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[190])).
% 0.95/0.86 tff(192,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp20) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.95/0.86 tff(193,plain,
% 0.95/0.86 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.95/0.86 tff(194,plain,
% 0.95/0.86 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.95/0.86 tff(195,plain,(
% 0.95/0.86 ![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/0.86 inference(skolemize,[status(sab)],[194])).
% 0.95/0.86 tff(196,plain,
% 0.95/0.86 (![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.95/0.86 tff(197,plain,
% 0.95/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(198,plain,
% 0.95/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[197])).
% 0.95/0.86 tff(199,plain,
% 0.95/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(200,plain,
% 0.95/0.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(201,plain,
% 0.95/0.86 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[200])).
% 0.95/0.86 tff(202,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.95/0.86 tff(203,plain,
% 0.95/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.95/0.86 tff(204,plain,
% 0.95/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.95/0.86 tff(205,plain,(
% 0.95/0.86 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.95/0.86 inference(skolemize,[status(sab)],[204])).
% 0.95/0.86 tff(206,plain,
% 0.95/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[205, 198])).
% 0.95/0.86 tff(207,assumption,(~hskp20), introduced(assumption)).
% 0.95/0.86 tff(208,plain,
% 0.95/0.86 ((hskp20 | hskp18 | hskp2) <=> (hskp20 | hskp18 | hskp2)),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(209,plain,
% 0.95/0.86 (((hskp18 | hskp2) | hskp20) <=> (hskp20 | hskp18 | hskp2)),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(210,axiom,((hskp18 | hskp2) | hskp20), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause32')).
% 0.95/0.86 tff(211,plain,
% 0.95/0.86 (hskp20 | hskp18 | hskp2),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.95/0.86 tff(212,plain,
% 0.95/0.86 (hskp20 | hskp18 | hskp2),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[211, 208])).
% 0.95/0.86 tff(213,plain,
% 0.95/0.86 (hskp20 | hskp18 | hskp2),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[212, 208])).
% 0.95/0.86 tff(214,plain,
% 0.95/0.86 (hskp20 | hskp18 | hskp2),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[213, 208])).
% 0.95/0.86 tff(215,plain,
% 0.95/0.86 (hskp20 | hskp18 | hskp2),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[214, 208])).
% 0.95/0.86 tff(216,plain,
% 0.95/0.86 (hskp20 | hskp18 | hskp2),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.95/0.86 tff(217,plain,
% 0.95/0.86 (hskp20 | hskp18 | hskp2),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[216, 208])).
% 0.95/0.86 tff(218,plain,
% 0.95/0.86 (hskp20 | hskp18 | hskp2),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[217, 208])).
% 0.95/0.86 tff(219,plain,
% 0.95/0.86 (hskp18),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[218, 207, 24])).
% 0.95/0.86 tff(220,plain,
% 0.95/0.86 (((~hskp18) | (~c2_1(a676))) <=> ((~hskp18) | (~c2_1(a676)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(221,plain,
% 0.95/0.86 (((~c2_1(a676)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a676)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(222,axiom,((~c2_1(a676)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.95/0.86 tff(223,plain,
% 0.95/0.86 ((~hskp18) | (~c2_1(a676))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.95/0.86 tff(224,plain,
% 0.95/0.86 ((~hskp18) | (~c2_1(a676))),
% 0.95/0.86 inference(modus_ponens,[status(thm)],[223, 220])).
% 0.95/0.86 tff(225,plain,
% 0.95/0.86 (~c2_1(a676)),
% 0.95/0.86 inference(unit_resolution,[status(thm)],[224, 219])).
% 0.95/0.86 tff(226,plain,
% 0.95/0.86 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))))),
% 0.95/0.86 inference(bind,[status(th)],[])).
% 0.95/0.86 tff(227,plain,
% 0.95/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.95/0.86 inference(quant_intro,[status(thm)],[226])).
% 0.95/0.86 tff(228,plain,
% 0.95/0.86 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.95/0.86 inference(rewrite,[status(thm)],[])).
% 0.95/0.86 tff(229,plain,
% 0.95/0.86 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))))),
% 0.95/0.87 inference(bind,[status(th)],[])).
% 0.95/0.87 tff(230,plain,
% 0.95/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.95/0.87 inference(quant_intro,[status(thm)],[229])).
% 0.95/0.87 tff(231,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c1_1(W))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.95/0.87 tff(232,plain,
% 0.95/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.95/0.87 tff(233,plain,
% 0.95/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.95/0.87 tff(234,plain,(
% 0.95/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.95/0.87 inference(skolemize,[status(sab)],[233])).
% 0.95/0.87 tff(235,plain,
% 0.95/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.95/0.87 tff(236,assumption,(~c3_1(a647)), introduced(assumption)).
% 0.95/0.87 tff(237,plain,
% 0.95/0.87 (hskp24),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[98, 207, 23])).
% 0.95/0.87 tff(238,plain,
% 0.95/0.87 (((~hskp24) | (~c2_1(a698))) <=> ((~hskp24) | (~c2_1(a698)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(239,plain,
% 0.95/0.87 (((~c2_1(a698)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a698)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(240,axiom,((~c2_1(a698)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 0.95/0.87 tff(241,plain,
% 0.95/0.87 ((~hskp24) | (~c2_1(a698))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.95/0.87 tff(242,plain,
% 0.95/0.87 ((~hskp24) | (~c2_1(a698))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[241, 238])).
% 0.95/0.87 tff(243,plain,
% 0.95/0.87 (~c2_1(a698)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[242, 237])).
% 0.95/0.87 tff(244,plain,
% 0.95/0.87 (((~hskp24) | c1_1(a698)) <=> ((~hskp24) | c1_1(a698))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(245,axiom,((~hskp24) | c1_1(a698)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 0.95/0.87 tff(246,plain,
% 0.95/0.87 ((~hskp24) | c1_1(a698)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.95/0.87 tff(247,plain,
% 0.95/0.87 ((~hskp24) | c1_1(a698)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[246, 244])).
% 0.95/0.87 tff(248,plain,
% 0.95/0.87 ((~hskp24) | c1_1(a698)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[247, 244])).
% 0.95/0.87 tff(249,plain,
% 0.95/0.87 ((~hskp24) | c1_1(a698)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.95/0.87 tff(250,plain,
% 0.95/0.87 ((~hskp24) | c1_1(a698)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[249, 244])).
% 0.95/0.87 tff(251,plain,
% 0.95/0.87 ((~hskp24) | c1_1(a698)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[250, 244])).
% 0.95/0.87 tff(252,plain,
% 0.95/0.87 ((~hskp24) | c1_1(a698)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[251, 244])).
% 0.95/0.87 tff(253,plain,
% 0.95/0.87 ((~hskp24) | c1_1(a698)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[252, 244])).
% 0.95/0.87 tff(254,plain,
% 0.95/0.87 (c1_1(a698)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[253, 237])).
% 0.95/0.87 tff(255,plain,
% 0.95/0.87 (((~hskp24) | (~c0_1(a698))) <=> ((~hskp24) | (~c0_1(a698)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(256,plain,
% 0.95/0.87 (((~c0_1(a698)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a698)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(257,axiom,((~c0_1(a698)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 0.95/0.87 tff(258,plain,
% 0.95/0.87 ((~hskp24) | (~c0_1(a698))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.95/0.87 tff(259,plain,
% 0.95/0.87 ((~hskp24) | (~c0_1(a698))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[258, 255])).
% 0.95/0.87 tff(260,plain,
% 0.95/0.87 (~c0_1(a698)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[259, 237])).
% 0.95/0.87 tff(261,assumption,(~c0_1(a647)), introduced(assumption)).
% 0.95/0.87 tff(262,plain,
% 0.95/0.87 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(263,plain,
% 0.95/0.87 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a647) | c0_1(a647) | c3_1(a647)) <=> (hskp2 | hskp0 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(264,plain,
% 0.95/0.87 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a647) | c0_1(a647) | c3_1(a647))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0)))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[263])).
% 0.95/0.87 tff(265,plain,
% 0.95/0.87 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a647) | c0_1(a647) | c3_1(a647))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0))),
% 0.95/0.87 inference(transitivity,[status(thm)],[264, 262])).
% 0.95/0.87 tff(266,plain,
% 0.95/0.87 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a647) | c0_1(a647) | c3_1(a647))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(267,plain,
% 0.95/0.87 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.95/0.87 tff(268,plain,
% 0.95/0.87 (c1_1(a647) | c0_1(a647)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[267, 102, 24, 23, 236, 131])).
% 0.95/0.87 tff(269,plain,
% 0.95/0.87 (c1_1(a647)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[268, 261])).
% 0.95/0.87 tff(270,assumption,(c1_1(a647)), introduced(assumption)).
% 0.95/0.87 tff(271,assumption,(c3_1(a698)), introduced(assumption)).
% 0.95/0.87 tff(272,plain,
% 0.95/0.87 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.95/0.87 inference(bind,[status(th)],[])).
% 0.95/0.87 tff(273,plain,
% 0.95/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(quant_intro,[status(thm)],[272])).
% 0.95/0.87 tff(274,plain,
% 0.95/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(275,plain,
% 0.95/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.95/0.87 inference(bind,[status(th)],[])).
% 0.95/0.87 tff(276,plain,
% 0.95/0.87 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(quant_intro,[status(thm)],[275])).
% 0.95/0.87 tff(277,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 0.95/0.87 tff(278,plain,
% 0.95/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.95/0.87 tff(279,plain,
% 0.95/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[278, 274])).
% 0.95/0.87 tff(280,plain,(
% 0.95/0.87 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(skolemize,[status(sab)],[279])).
% 0.95/0.87 tff(281,plain,
% 0.95/0.87 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[280, 273])).
% 0.95/0.87 tff(282,assumption,(~c2_1(a698)), introduced(assumption)).
% 0.95/0.87 tff(283,assumption,(c1_1(a698)), introduced(assumption)).
% 0.95/0.87 tff(284,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(285,plain,
% 0.95/0.87 ((hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (hskp6 | c2_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(286,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[285])).
% 0.95/0.87 tff(287,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[286, 284])).
% 0.95/0.87 tff(288,plain,
% 0.95/0.87 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(289,plain,
% 0.95/0.87 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.95/0.87 tff(290,plain,
% 0.95/0.87 (hskp6 | c0_1(a647) | (~c1_1(a647)) | (~c3_1(a698))),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[289, 102, 283, 282, 236, 281])).
% 0.95/0.87 tff(291,plain,
% 0.95/0.87 (hskp6),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[290, 271, 261, 270])).
% 0.95/0.87 tff(292,plain,
% 0.95/0.87 (~c3_1(a648)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[114, 291])).
% 0.95/0.87 tff(293,plain,
% 0.95/0.87 (~c2_1(a648)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[120, 291])).
% 0.95/0.87 tff(294,plain,
% 0.95/0.87 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.95/0.87 inference(bind,[status(th)],[])).
% 0.95/0.87 tff(295,plain,
% 0.95/0.87 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(quant_intro,[status(thm)],[294])).
% 0.95/0.87 tff(296,plain,
% 0.95/0.87 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(297,plain,
% 0.95/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.95/0.87 inference(bind,[status(th)],[])).
% 0.95/0.87 tff(298,plain,
% 0.95/0.87 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(quant_intro,[status(thm)],[297])).
% 0.95/0.87 tff(299,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 0.95/0.87 tff(300,plain,
% 0.95/0.87 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.95/0.87 tff(301,plain,
% 0.95/0.87 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[300, 296])).
% 0.95/0.87 tff(302,plain,(
% 0.95/0.87 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(skolemize,[status(sab)],[301])).
% 0.95/0.87 tff(303,plain,
% 0.95/0.87 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[302, 295])).
% 0.95/0.87 tff(304,assumption,(~c0_1(a698)), introduced(assumption)).
% 0.95/0.87 tff(305,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(306,plain,
% 0.95/0.87 ((hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (hskp11 | c0_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(307,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[306])).
% 0.95/0.87 tff(308,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[307, 305])).
% 0.95/0.87 tff(309,plain,
% 0.95/0.87 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(310,plain,
% 0.95/0.87 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a698) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a698)) | (~c3_1(a698))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.95/0.87 tff(311,plain,
% 0.95/0.87 (hskp11 | c0_1(a647) | (~c1_1(a647)) | (~c3_1(a698))),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[310, 102, 283, 304, 236, 303])).
% 0.95/0.87 tff(312,plain,
% 0.95/0.87 (hskp11),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[311, 271, 261, 270])).
% 0.95/0.87 tff(313,plain,
% 0.95/0.87 (((~hskp11) | (~c3_1(a657))) <=> ((~hskp11) | (~c3_1(a657)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(314,plain,
% 0.95/0.87 (((~c3_1(a657)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a657)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(315,axiom,((~c3_1(a657)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.95/0.87 tff(316,plain,
% 0.95/0.87 ((~hskp11) | (~c3_1(a657))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.95/0.87 tff(317,plain,
% 0.95/0.87 ((~hskp11) | (~c3_1(a657))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[316, 313])).
% 0.95/0.87 tff(318,plain,
% 0.95/0.87 (~c3_1(a657)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[317, 312])).
% 0.95/0.87 tff(319,plain,
% 0.95/0.87 (((~hskp6) | c0_1(a648)) <=> ((~hskp6) | c0_1(a648))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(320,axiom,((~hskp6) | c0_1(a648)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.95/0.87 tff(321,plain,
% 0.95/0.87 ((~hskp6) | c0_1(a648)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.95/0.87 tff(322,plain,
% 0.95/0.87 ((~hskp6) | c0_1(a648)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[321, 319])).
% 0.95/0.87 tff(323,plain,
% 0.95/0.87 ((~hskp6) | c0_1(a648)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[322, 319])).
% 0.95/0.87 tff(324,plain,
% 0.95/0.87 ((~hskp6) | c0_1(a648)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[323, 319])).
% 0.95/0.87 tff(325,plain,
% 0.95/0.87 ((~hskp6) | c0_1(a648)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[324, 319])).
% 0.95/0.87 tff(326,plain,
% 0.95/0.87 ((~hskp6) | c0_1(a648)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[325, 319])).
% 0.95/0.87 tff(327,plain,
% 0.95/0.87 ((~hskp6) | c0_1(a648)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[326, 319])).
% 0.95/0.87 tff(328,plain,
% 0.95/0.87 ((~hskp6) | c0_1(a648)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[327, 319])).
% 0.95/0.87 tff(329,plain,
% 0.95/0.87 (c0_1(a648)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[328, 291])).
% 0.95/0.87 tff(330,plain,
% 0.95/0.87 (((~hskp11) | c2_1(a657)) <=> ((~hskp11) | c2_1(a657))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(331,axiom,((~hskp11) | c2_1(a657)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 0.95/0.87 tff(332,plain,
% 0.95/0.87 ((~hskp11) | c2_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.95/0.87 tff(333,plain,
% 0.95/0.87 ((~hskp11) | c2_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[332, 330])).
% 0.95/0.87 tff(334,plain,
% 0.95/0.87 ((~hskp11) | c2_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[333, 330])).
% 0.95/0.87 tff(335,plain,
% 0.95/0.87 ((~hskp11) | c2_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[334, 330])).
% 0.95/0.87 tff(336,plain,
% 0.95/0.87 ((~hskp11) | c2_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[335, 330])).
% 0.95/0.87 tff(337,plain,
% 0.95/0.87 ((~hskp11) | c2_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[336, 330])).
% 0.95/0.87 tff(338,plain,
% 0.95/0.87 ((~hskp11) | c2_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[337, 330])).
% 0.95/0.87 tff(339,plain,
% 0.95/0.87 ((~hskp11) | c2_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[338, 330])).
% 0.95/0.87 tff(340,plain,
% 0.95/0.87 (c2_1(a657)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[339, 312])).
% 0.95/0.87 tff(341,plain,
% 0.95/0.87 (((~hskp11) | c0_1(a657)) <=> ((~hskp11) | c0_1(a657))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(342,axiom,((~hskp11) | c0_1(a657)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.95/0.87 tff(343,plain,
% 0.95/0.87 ((~hskp11) | c0_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.95/0.87 tff(344,plain,
% 0.95/0.87 ((~hskp11) | c0_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[343, 341])).
% 0.95/0.87 tff(345,plain,
% 0.95/0.87 ((~hskp11) | c0_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[344, 341])).
% 0.95/0.87 tff(346,plain,
% 0.95/0.87 ((~hskp11) | c0_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[345, 341])).
% 0.95/0.87 tff(347,plain,
% 0.95/0.87 ((~hskp11) | c0_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[346, 341])).
% 0.95/0.87 tff(348,plain,
% 0.95/0.87 ((~hskp11) | c0_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[347, 341])).
% 0.95/0.87 tff(349,plain,
% 0.95/0.87 ((~hskp11) | c0_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[348, 341])).
% 0.95/0.87 tff(350,plain,
% 0.95/0.87 ((~hskp11) | c0_1(a657)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[349, 341])).
% 0.95/0.87 tff(351,plain,
% 0.95/0.87 (c0_1(a657)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[350, 312])).
% 0.95/0.87 tff(352,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a657) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a657) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(353,plain,
% 0.95/0.87 (((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648))) <=> (c3_1(a657) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(354,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a657) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657))))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[353])).
% 0.95/0.87 tff(355,plain,
% 0.95/0.87 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a657) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))),
% 0.95/0.87 inference(transitivity,[status(thm)],[354, 352])).
% 0.95/0.87 tff(356,plain,
% 0.95/0.87 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648)))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(357,plain,
% 0.95/0.87 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a657) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657))),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.95/0.87 tff(358,plain,
% 0.95/0.87 ($false),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[357, 102, 351, 340, 329, 318, 293, 292, 186])).
% 0.95/0.87 tff(359,plain,((~c3_1(a698)) | c0_1(a647) | (~c1_1(a647)) | (~c1_1(a698)) | c0_1(a698) | c3_1(a647) | c2_1(a698)), inference(lemma,lemma(discharge,[]))).
% 0.95/0.87 tff(360,plain,
% 0.95/0.87 (~c3_1(a698)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[359, 261, 269, 254, 260, 236, 243])).
% 0.95/0.87 tff(361,assumption,(~c3_1(a698)), introduced(assumption)).
% 0.95/0.87 tff(362,assumption,(hskp7), introduced(assumption)).
% 0.95/0.87 tff(363,plain,
% 0.95/0.87 (~c0_1(a651)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[157, 362])).
% 0.95/0.87 tff(364,plain,
% 0.95/0.87 (~c1_1(a651)),
% 0.95/0.87 inference(unit_resolution,[status(thm)],[151, 362])).
% 0.95/0.87 tff(365,assumption,(~c1_1(a651)), introduced(assumption)).
% 0.95/0.87 tff(366,assumption,(~c0_1(a651)), introduced(assumption)).
% 0.95/0.87 tff(367,plain,
% 0.95/0.87 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c3_1(a651) | c0_1(a651) | c1_1(a651) | (~ndr1_0))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c3_1(a651) | c0_1(a651) | c1_1(a651) | (~ndr1_0))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(368,plain,
% 0.95/0.87 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | c3_1(a651)) <=> (hskp2 | hskp0 | c3_1(a651) | c0_1(a651) | c1_1(a651) | (~ndr1_0))),
% 0.95/0.87 inference(rewrite,[status(thm)],[])).
% 0.95/0.87 tff(369,plain,
% 0.95/0.87 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | c3_1(a651))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c3_1(a651) | c0_1(a651) | c1_1(a651) | (~ndr1_0)))),
% 0.95/0.87 inference(monotonicity,[status(thm)],[368])).
% 0.95/0.87 tff(370,plain,
% 0.95/0.87 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | c3_1(a651))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c3_1(a651) | c0_1(a651) | c1_1(a651) | (~ndr1_0))),
% 0.95/0.87 inference(transitivity,[status(thm)],[369, 367])).
% 0.95/0.87 tff(371,plain,
% 0.95/0.87 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | c3_1(a651))),
% 0.95/0.87 inference(quant_inst,[status(thm)],[])).
% 0.95/0.87 tff(372,plain,
% 0.95/0.87 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c3_1(a651) | c0_1(a651) | c1_1(a651) | (~ndr1_0)),
% 0.95/0.87 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.95/0.88 tff(373,plain,
% 0.95/0.88 (c3_1(a651) | c0_1(a651)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[372, 102, 24, 23, 365, 131])).
% 0.95/0.88 tff(374,plain,
% 0.95/0.88 (c3_1(a651)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[373, 366])).
% 0.95/0.88 tff(375,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a698) | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a698)) | c3_1(a698))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a698) | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a698)) | c3_1(a698))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(376,plain,
% 0.95/0.88 ((hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651))) <=> (hskp2 | c2_1(a698) | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a698)) | c3_1(a698))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(377,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a698) | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a698)) | c3_1(a698)))),
% 0.95/0.88 inference(monotonicity,[status(thm)],[376])).
% 0.95/0.88 tff(378,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a698) | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a698)) | c3_1(a698))),
% 0.95/0.88 inference(transitivity,[status(thm)],[377, 375])).
% 0.95/0.88 tff(379,plain,
% 0.95/0.88 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(380,plain,
% 0.95/0.88 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a698) | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c1_1(a698)) | c3_1(a698)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.95/0.88 tff(381,plain,
% 0.95/0.88 ($false),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[380, 102, 24, 283, 374, 282, 366, 365, 34, 361])).
% 0.95/0.88 tff(382,plain,(c0_1(a651) | hskp2 | (~c1_1(a698)) | c2_1(a698) | c1_1(a651) | c3_1(a698) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.95/0.88 tff(383,plain,
% 0.95/0.88 ($false),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[382, 364, 363, 283, 282, 24, 361, 23])).
% 0.95/0.88 tff(384,plain,((~hskp7) | (~c1_1(a698)) | c2_1(a698) | hskp2 | c3_1(a698) | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.95/0.88 tff(385,plain,
% 0.95/0.88 (~hskp7),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[384, 360, 243, 24, 254, 23])).
% 0.95/0.88 tff(386,assumption,(hskp1), introduced(assumption)).
% 0.95/0.88 tff(387,plain,
% 0.95/0.88 (((~hskp1) | (~c1_1(a642))) <=> ((~hskp1) | (~c1_1(a642)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(388,plain,
% 0.95/0.88 (((~c1_1(a642)) | (~hskp1)) <=> ((~hskp1) | (~c1_1(a642)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(389,axiom,((~c1_1(a642)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.95/0.88 tff(390,plain,
% 0.95/0.88 ((~hskp1) | (~c1_1(a642))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.95/0.88 tff(391,plain,
% 0.95/0.88 ((~hskp1) | (~c1_1(a642))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[390, 387])).
% 0.95/0.88 tff(392,plain,
% 0.95/0.88 (~c1_1(a642)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[391, 386])).
% 0.95/0.88 tff(393,assumption,(~hskp7), introduced(assumption)).
% 0.95/0.88 tff(394,plain,
% 0.95/0.88 (((~hskp1) | c0_1(a642)) <=> ((~hskp1) | c0_1(a642))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(395,axiom,((~hskp1) | c0_1(a642)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.95/0.88 tff(396,plain,
% 0.95/0.88 ((~hskp1) | c0_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.95/0.88 tff(397,plain,
% 0.95/0.88 ((~hskp1) | c0_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[396, 394])).
% 0.95/0.88 tff(398,plain,
% 0.95/0.88 ((~hskp1) | c0_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[397, 394])).
% 0.95/0.88 tff(399,plain,
% 0.95/0.88 ((~hskp1) | c0_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[398, 394])).
% 0.95/0.88 tff(400,plain,
% 0.95/0.88 ((~hskp1) | c0_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[399, 394])).
% 0.95/0.88 tff(401,plain,
% 0.95/0.88 ((~hskp1) | c0_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[400, 394])).
% 0.95/0.88 tff(402,plain,
% 0.95/0.88 ((~hskp1) | c0_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[401, 394])).
% 0.95/0.88 tff(403,plain,
% 0.95/0.88 ((~hskp1) | c0_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[402, 394])).
% 0.95/0.88 tff(404,plain,
% 0.95/0.88 (c0_1(a642)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[403, 386])).
% 0.95/0.88 tff(405,plain,
% 0.95/0.88 (((~hskp1) | c3_1(a642)) <=> ((~hskp1) | c3_1(a642))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(406,axiom,((~hskp1) | c3_1(a642)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.95/0.88 tff(407,plain,
% 0.95/0.88 ((~hskp1) | c3_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.95/0.88 tff(408,plain,
% 0.95/0.88 ((~hskp1) | c3_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[407, 405])).
% 0.95/0.88 tff(409,plain,
% 0.95/0.88 ((~hskp1) | c3_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[408, 405])).
% 0.95/0.88 tff(410,plain,
% 0.95/0.88 ((~hskp1) | c3_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[409, 405])).
% 0.95/0.88 tff(411,plain,
% 0.95/0.88 ((~hskp1) | c3_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[410, 405])).
% 0.95/0.88 tff(412,plain,
% 0.95/0.88 ((~hskp1) | c3_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[411, 405])).
% 0.95/0.88 tff(413,plain,
% 0.95/0.88 ((~hskp1) | c3_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[412, 405])).
% 0.95/0.88 tff(414,plain,
% 0.95/0.88 ((~hskp1) | c3_1(a642)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[413, 405])).
% 0.95/0.88 tff(415,plain,
% 0.95/0.88 (c3_1(a642)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[414, 386])).
% 0.95/0.88 tff(416,assumption,(~c1_1(a642)), introduced(assumption)).
% 0.95/0.88 tff(417,assumption,(c3_1(a642)), introduced(assumption)).
% 0.95/0.88 tff(418,plain,
% 0.95/0.88 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(419,plain,
% 0.95/0.88 ((hskp17 | hskp7 | (~ndr1_0) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642))) <=> (hskp17 | hskp7 | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(420,plain,
% 0.95/0.88 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642))))),
% 0.95/0.88 inference(monotonicity,[status(thm)],[419])).
% 0.95/0.88 tff(421,plain,
% 0.95/0.88 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)))),
% 0.95/0.88 inference(transitivity,[status(thm)],[420, 418])).
% 0.95/0.88 tff(422,plain,
% 0.95/0.88 ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(423,plain,
% 0.95/0.88 ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.95/0.88 tff(424,plain,
% 0.95/0.88 (hskp7 | (~c2_1(a642))),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[423, 102, 1, 417, 416, 22])).
% 0.95/0.88 tff(425,plain,
% 0.95/0.88 (~c2_1(a642)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[424, 393])).
% 0.95/0.88 tff(426,plain,
% 0.95/0.88 (^[U: $i] : refl((hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.95/0.88 inference(bind,[status(th)],[])).
% 0.95/0.88 tff(427,plain,
% 0.95/0.88 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.88 inference(quant_intro,[status(thm)],[426])).
% 0.95/0.88 tff(428,plain,
% 0.95/0.88 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(429,plain,
% 0.95/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp22) <=> ((hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp22))), rewrite(((hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp22) <=> (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp22) <=> (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.95/0.88 inference(bind,[status(th)],[])).
% 0.95/0.88 tff(430,plain,
% 0.95/0.88 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp22) <=> ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.88 inference(quant_intro,[status(thm)],[429])).
% 0.95/0.88 tff(431,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp20) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 0.95/0.88 tff(432,plain,
% 0.95/0.88 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.95/0.88 tff(433,plain,
% 0.95/0.88 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[432, 428])).
% 0.95/0.88 tff(434,plain,(
% 0.95/0.88 ![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.88 inference(skolemize,[status(sab)],[433])).
% 0.95/0.88 tff(435,plain,
% 0.95/0.88 (![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[434, 427])).
% 0.95/0.88 tff(436,assumption,(c0_1(a642)), introduced(assumption)).
% 0.95/0.88 tff(437,plain,
% 0.95/0.88 (((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp20 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(438,plain,
% 0.95/0.88 ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp22 | hskp20 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(439,plain,
% 0.95/0.88 ((~![U: $i] : (hskp22 | hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp22 | hskp20 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.95/0.88 tff(440,plain,
% 0.95/0.88 (hskp22 | c2_1(a642)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[439, 102, 207, 436, 417, 435])).
% 0.95/0.88 tff(441,plain,
% 0.95/0.88 (hskp22),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[440, 425])).
% 0.95/0.88 tff(442,plain,
% 0.95/0.88 (((~hskp22) | (~c0_1(a693))) <=> ((~hskp22) | (~c0_1(a693)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(443,plain,
% 0.95/0.88 (((~c0_1(a693)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a693)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(444,axiom,((~c0_1(a693)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.95/0.88 tff(445,plain,
% 0.95/0.88 ((~hskp22) | (~c0_1(a693))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.95/0.88 tff(446,plain,
% 0.95/0.88 ((~hskp22) | (~c0_1(a693))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[445, 442])).
% 0.95/0.88 tff(447,plain,
% 0.95/0.88 (~c0_1(a693)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[446, 441])).
% 0.95/0.88 tff(448,plain,
% 0.95/0.88 (((~hskp22) | c2_1(a693)) <=> ((~hskp22) | c2_1(a693))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(449,axiom,((~hskp22) | c2_1(a693)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 0.95/0.88 tff(450,plain,
% 0.95/0.88 ((~hskp22) | c2_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.95/0.88 tff(451,plain,
% 0.95/0.88 ((~hskp22) | c2_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[450, 448])).
% 0.95/0.88 tff(452,plain,
% 0.95/0.88 ((~hskp22) | c2_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[451, 448])).
% 0.95/0.88 tff(453,plain,
% 0.95/0.88 ((~hskp22) | c2_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[452, 448])).
% 0.95/0.88 tff(454,plain,
% 0.95/0.88 ((~hskp22) | c2_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[453, 448])).
% 0.95/0.88 tff(455,plain,
% 0.95/0.88 ((~hskp22) | c2_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[454, 448])).
% 0.95/0.88 tff(456,plain,
% 0.95/0.88 ((~hskp22) | c2_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[455, 448])).
% 0.95/0.88 tff(457,plain,
% 0.95/0.88 ((~hskp22) | c2_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[456, 448])).
% 0.95/0.88 tff(458,plain,
% 0.95/0.88 (c2_1(a693)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[457, 441])).
% 0.95/0.88 tff(459,plain,
% 0.95/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a693) | c0_1(a647) | c3_1(a647) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c1_1(a647)) | (~c1_1(a693)) | (~c2_1(a693)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a693) | c0_1(a647) | c3_1(a647) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c1_1(a647)) | (~c1_1(a693)) | (~c2_1(a693)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(460,plain,
% 0.95/0.88 (((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (c0_1(a693) | c0_1(a647) | c3_1(a647) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c1_1(a647)) | (~c1_1(a693)) | (~c2_1(a693)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(461,plain,
% 0.95/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a693) | c0_1(a647) | c3_1(a647) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c1_1(a647)) | (~c1_1(a693)) | (~c2_1(a693))))),
% 0.95/0.88 inference(monotonicity,[status(thm)],[460])).
% 0.95/0.88 tff(462,plain,
% 0.95/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a693) | c0_1(a647) | c3_1(a647) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c1_1(a647)) | (~c1_1(a693)) | (~c2_1(a693)))),
% 0.95/0.88 inference(transitivity,[status(thm)],[461, 459])).
% 0.95/0.88 tff(463,plain,
% 0.95/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a693) | (~c2_1(a693)) | (~c1_1(a693)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(464,plain,
% 0.95/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a693) | c0_1(a647) | c3_1(a647) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c1_1(a647)) | (~c1_1(a693)) | (~c2_1(a693))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.95/0.88 tff(465,plain,
% 0.95/0.88 (~c1_1(a693)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[464, 102, 458, 270, 436, 447, 261, 236, 416, 235, 425])).
% 0.95/0.88 tff(466,plain,
% 0.95/0.88 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 0.95/0.88 inference(bind,[status(th)],[])).
% 0.95/0.88 tff(467,plain,
% 0.95/0.88 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.95/0.88 inference(quant_intro,[status(thm)],[466])).
% 0.95/0.88 tff(468,plain,
% 0.95/0.88 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(469,plain,
% 0.95/0.88 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_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) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_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) | (~c3_1(U)) | (~c0_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)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 0.95/0.88 inference(bind,[status(th)],[])).
% 0.95/0.88 tff(470,plain,
% 0.95/0.88 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.95/0.88 inference(quant_intro,[status(thm)],[469])).
% 0.95/0.88 tff(471,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.95/0.88 tff(472,plain,
% 0.95/0.88 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.95/0.88 tff(473,plain,
% 0.95/0.88 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[472, 468])).
% 0.95/0.88 tff(474,plain,(
% 0.95/0.88 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.95/0.88 inference(skolemize,[status(sab)],[473])).
% 0.95/0.88 tff(475,plain,
% 0.95/0.88 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[474, 467])).
% 0.95/0.88 tff(476,plain,
% 0.95/0.88 (((~hskp22) | c3_1(a693)) <=> ((~hskp22) | c3_1(a693))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(477,axiom,((~hskp22) | c3_1(a693)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 0.95/0.88 tff(478,plain,
% 0.95/0.88 ((~hskp22) | c3_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.95/0.88 tff(479,plain,
% 0.95/0.88 ((~hskp22) | c3_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[478, 476])).
% 0.95/0.88 tff(480,plain,
% 0.95/0.88 ((~hskp22) | c3_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[479, 476])).
% 0.95/0.88 tff(481,plain,
% 0.95/0.88 ((~hskp22) | c3_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[480, 476])).
% 0.95/0.88 tff(482,plain,
% 0.95/0.88 ((~hskp22) | c3_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[481, 476])).
% 0.95/0.88 tff(483,plain,
% 0.95/0.88 ((~hskp22) | c3_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[482, 476])).
% 0.95/0.88 tff(484,plain,
% 0.95/0.88 ((~hskp22) | c3_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[483, 476])).
% 0.95/0.88 tff(485,plain,
% 0.95/0.88 ((~hskp22) | c3_1(a693)),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[484, 476])).
% 0.95/0.88 tff(486,plain,
% 0.95/0.88 (c3_1(a693)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[485, 441])).
% 0.95/0.88 tff(487,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a693) | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c1_1(a693) | (~c3_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a693) | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c1_1(a693) | (~c3_1(a693)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(488,plain,
% 0.95/0.88 ((hskp7 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c0_1(a693) | c1_1(a693) | (~c3_1(a693))) <=> (hskp7 | c0_1(a693) | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c1_1(a693) | (~c3_1(a693)))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(489,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c0_1(a693) | c1_1(a693) | (~c3_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a693) | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c1_1(a693) | (~c3_1(a693))))),
% 0.95/0.88 inference(monotonicity,[status(thm)],[488])).
% 0.95/0.88 tff(490,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c0_1(a693) | c1_1(a693) | (~c3_1(a693)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a693) | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c1_1(a693) | (~c3_1(a693)))),
% 0.95/0.88 inference(transitivity,[status(thm)],[489, 487])).
% 0.95/0.88 tff(491,plain,
% 0.95/0.88 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c0_1(a693) | c1_1(a693) | (~c3_1(a693)))),
% 0.95/0.88 inference(quant_inst,[status(thm)],[])).
% 0.95/0.88 tff(492,plain,
% 0.95/0.88 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a693) | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)) | c1_1(a693) | (~c3_1(a693))),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[491, 490])).
% 0.95/0.88 tff(493,plain,
% 0.95/0.88 ($false),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[492, 102, 393, 486, 436, 417, 447, 475, 425, 465])).
% 0.95/0.88 tff(494,plain,(hskp7 | (~c0_1(a642)) | (~c3_1(a642)) | (~c1_1(a647)) | c0_1(a647) | c3_1(a647) | c1_1(a642) | hskp20 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.95/0.88 tff(495,plain,
% 0.95/0.88 ($false),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[494, 415, 404, 393, 270, 261, 236, 392, 207, 1])).
% 0.95/0.88 tff(496,plain,((~hskp1) | hskp7 | (~c1_1(a647)) | c0_1(a647) | c3_1(a647) | hskp20 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.95/0.88 tff(497,plain,
% 0.95/0.88 (~hskp1),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[496, 385, 269, 261, 236, 207, 1])).
% 0.95/0.88 tff(498,plain,
% 0.95/0.88 ((hskp17 | hskp14 | hskp1) <=> (hskp17 | hskp14 | hskp1)),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(499,plain,
% 0.95/0.88 (((hskp1 | hskp14) | hskp17) <=> (hskp17 | hskp14 | hskp1)),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(500,axiom,((hskp1 | hskp14) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 0.95/0.88 tff(501,plain,
% 0.95/0.88 (hskp17 | hskp14 | hskp1),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.95/0.88 tff(502,plain,
% 0.95/0.88 (hskp17 | hskp14 | hskp1),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[501, 498])).
% 0.95/0.88 tff(503,plain,
% 0.95/0.88 (hskp17 | hskp14 | hskp1),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[502, 498])).
% 0.95/0.88 tff(504,plain,
% 0.95/0.88 (hskp17 | hskp14 | hskp1),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[503, 498])).
% 0.95/0.88 tff(505,plain,
% 0.95/0.88 (hskp17 | hskp14 | hskp1),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[504, 498])).
% 0.95/0.88 tff(506,plain,
% 0.95/0.88 (hskp17 | hskp14 | hskp1),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[505, 498])).
% 0.95/0.88 tff(507,plain,
% 0.95/0.88 (hskp17 | hskp14 | hskp1),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[506, 498])).
% 0.95/0.88 tff(508,plain,
% 0.95/0.88 (hskp17 | hskp14 | hskp1),
% 0.95/0.88 inference(modus_ponens,[status(thm)],[507, 498])).
% 0.95/0.88 tff(509,plain,
% 0.95/0.88 (hskp14),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[508, 497, 1])).
% 0.95/0.88 tff(510,plain,
% 0.95/0.88 (~c0_1(a665)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[56, 509])).
% 0.95/0.88 tff(511,plain,
% 0.95/0.88 (~c1_1(a665)),
% 0.95/0.88 inference(unit_resolution,[status(thm)],[50, 509])).
% 0.95/0.88 tff(512,assumption,(~c1_1(a665)), introduced(assumption)).
% 0.95/0.88 tff(513,assumption,(~c0_1(a665)), introduced(assumption)).
% 0.95/0.88 tff(514,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a698) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a698)) | c3_1(a698))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a698) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a698)) | c3_1(a698))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(515,plain,
% 0.95/0.88 ((hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665))) <=> (hskp2 | c2_1(a698) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a698)) | c3_1(a698))),
% 0.95/0.88 inference(rewrite,[status(thm)],[])).
% 0.95/0.88 tff(516,plain,
% 0.95/0.88 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a698) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a698)) | c3_1(a698)))),
% 0.95/0.89 inference(monotonicity,[status(thm)],[515])).
% 0.95/0.89 tff(517,plain,
% 0.95/0.89 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a698) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a698)) | c3_1(a698))),
% 0.95/0.89 inference(transitivity,[status(thm)],[516, 514])).
% 0.95/0.89 tff(518,plain,
% 0.95/0.89 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a698) | c3_1(a698) | (~c1_1(a698)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665)))),
% 0.95/0.89 inference(quant_inst,[status(thm)],[])).
% 0.95/0.89 tff(519,plain,
% 0.95/0.89 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a698) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a698)) | c3_1(a698)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.95/0.89 tff(520,plain,
% 0.95/0.89 (c1_1(a665) | (~c3_1(a665))),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[519, 102, 24, 283, 282, 513, 34, 361])).
% 0.95/0.89 tff(521,plain,
% 0.95/0.89 (~c3_1(a665)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[520, 512])).
% 0.95/0.89 tff(522,plain,
% 0.95/0.89 (c1_1(a665) | c3_1(a665)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[137, 102, 24, 23, 513, 131])).
% 0.95/0.89 tff(523,plain,
% 0.95/0.89 ($false),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[522, 521, 512])).
% 0.95/0.89 tff(524,plain,(c1_1(a665) | hskp2 | hskp0 | c0_1(a665) | (~c1_1(a698)) | c2_1(a698) | c3_1(a698)), inference(lemma,lemma(discharge,[]))).
% 0.95/0.89 tff(525,plain,
% 0.95/0.89 ($false),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[524, 511, 510, 23, 360, 254, 243, 24])).
% 0.95/0.89 tff(526,plain,(c0_1(a647) | hskp0 | hskp2 | hskp17 | c3_1(a647) | hskp20), inference(lemma,lemma(discharge,[]))).
% 0.95/0.89 tff(527,plain,
% 0.95/0.89 (c0_1(a647)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[526, 236, 24, 1, 23, 207])).
% 0.95/0.89 tff(528,plain,
% 0.95/0.89 (((~hskp5) | (~c0_1(a647))) <=> ((~hskp5) | (~c0_1(a647)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(529,plain,
% 0.95/0.89 (((~c0_1(a647)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a647)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(530,axiom,((~c0_1(a647)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.95/0.89 tff(531,plain,
% 0.95/0.89 ((~hskp5) | (~c0_1(a647))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.95/0.89 tff(532,plain,
% 0.95/0.89 ((~hskp5) | (~c0_1(a647))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[531, 528])).
% 0.95/0.89 tff(533,plain,
% 0.95/0.89 (~hskp5),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[532, 527])).
% 0.95/0.89 tff(534,plain,
% 0.95/0.89 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | c2_1(a647))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | c2_1(a647))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(535,plain,
% 0.95/0.89 ((hskp20 | hskp5 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c0_1(a647))) <=> (hskp20 | hskp5 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | c2_1(a647))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(536,plain,
% 0.95/0.89 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | c2_1(a647)))),
% 0.95/0.89 inference(monotonicity,[status(thm)],[535])).
% 0.95/0.89 tff(537,plain,
% 0.95/0.89 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | c2_1(a647))),
% 0.95/0.89 inference(transitivity,[status(thm)],[536, 534])).
% 0.95/0.89 tff(538,plain,
% 0.95/0.89 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c0_1(a647)))),
% 0.95/0.89 inference(quant_inst,[status(thm)],[])).
% 0.95/0.89 tff(539,plain,
% 0.95/0.89 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | c2_1(a647)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[538, 537])).
% 0.95/0.89 tff(540,plain,
% 0.95/0.89 (hskp5 | (~c0_1(a647)) | c2_1(a647)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[539, 102, 207, 236, 196])).
% 0.95/0.89 tff(541,plain,
% 0.95/0.89 (c2_1(a647)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[540, 533, 527])).
% 0.95/0.89 tff(542,plain,
% 0.95/0.89 (^[U: $i] : refl((hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))),
% 0.95/0.89 inference(bind,[status(th)],[])).
% 0.95/0.89 tff(543,plain,
% 0.95/0.89 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(quant_intro,[status(thm)],[542])).
% 0.95/0.89 tff(544,plain,
% 0.95/0.89 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(545,plain,
% 0.95/0.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp20) <=> ((hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20))), rewrite(((hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp20) <=> (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))))),
% 0.95/0.89 inference(bind,[status(th)],[])).
% 0.95/0.89 tff(546,plain,
% 0.95/0.89 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp20) <=> ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(quant_intro,[status(thm)],[545])).
% 0.95/0.89 tff(547,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 0.95/0.89 tff(548,plain,
% 0.95/0.89 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[547, 546])).
% 0.95/0.89 tff(549,plain,
% 0.95/0.89 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[548, 544])).
% 0.95/0.89 tff(550,plain,(
% 0.95/0.89 ![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(skolemize,[status(sab)],[549])).
% 0.95/0.89 tff(551,plain,
% 0.95/0.89 (![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[550, 543])).
% 0.95/0.89 tff(552,plain,
% 0.95/0.89 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp12 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp12 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(553,plain,
% 0.95/0.89 ((hskp20 | hskp12 | (~ndr1_0) | c3_1(a647) | (~c2_1(a647)) | (~c0_1(a647))) <=> (hskp20 | hskp12 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(554,plain,
% 0.95/0.89 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a647) | (~c2_1(a647)) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp12 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647))))),
% 0.95/0.89 inference(monotonicity,[status(thm)],[553])).
% 0.95/0.89 tff(555,plain,
% 0.95/0.89 (((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a647) | (~c2_1(a647)) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp12 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))),
% 0.95/0.89 inference(transitivity,[status(thm)],[554, 552])).
% 0.95/0.89 tff(556,plain,
% 0.95/0.89 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp12 | (~ndr1_0) | c3_1(a647) | (~c2_1(a647)) | (~c0_1(a647)))),
% 0.95/0.89 inference(quant_inst,[status(thm)],[])).
% 0.95/0.89 tff(557,plain,
% 0.95/0.89 ((~![U: $i] : (hskp20 | hskp12 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp12 | (~c0_1(a647)) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.95/0.89 tff(558,plain,
% 0.95/0.89 (hskp12 | (~c0_1(a647)) | (~c2_1(a647))),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[557, 102, 207, 236, 551])).
% 0.95/0.89 tff(559,plain,
% 0.95/0.89 (hskp12),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[558, 541, 527])).
% 0.95/0.89 tff(560,plain,
% 0.95/0.89 (((~hskp12) | (~c2_1(a660))) <=> ((~hskp12) | (~c2_1(a660)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(561,plain,
% 0.95/0.89 (((~c2_1(a660)) | (~hskp12)) <=> ((~hskp12) | (~c2_1(a660)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(562,axiom,((~c2_1(a660)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.95/0.89 tff(563,plain,
% 0.95/0.89 ((~hskp12) | (~c2_1(a660))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[562, 561])).
% 0.95/0.89 tff(564,plain,
% 0.95/0.89 ((~hskp12) | (~c2_1(a660))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[563, 560])).
% 0.95/0.89 tff(565,plain,
% 0.95/0.89 (~c2_1(a660)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[564, 559])).
% 0.95/0.89 tff(566,plain,
% 0.95/0.89 (((~hskp12) | (~c1_1(a660))) <=> ((~hskp12) | (~c1_1(a660)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(567,plain,
% 0.95/0.89 (((~c1_1(a660)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a660)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(568,axiom,((~c1_1(a660)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.95/0.89 tff(569,plain,
% 0.95/0.89 ((~hskp12) | (~c1_1(a660))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.95/0.89 tff(570,plain,
% 0.95/0.89 ((~hskp12) | (~c1_1(a660))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[569, 566])).
% 0.95/0.89 tff(571,plain,
% 0.95/0.89 (~c1_1(a660)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[570, 559])).
% 0.95/0.89 tff(572,plain,
% 0.95/0.89 (((~hskp18) | c0_1(a676)) <=> ((~hskp18) | c0_1(a676))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(573,axiom,((~hskp18) | c0_1(a676)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.95/0.89 tff(574,plain,
% 0.95/0.89 ((~hskp18) | c0_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[573, 572])).
% 0.95/0.89 tff(575,plain,
% 0.95/0.89 ((~hskp18) | c0_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[574, 572])).
% 0.95/0.89 tff(576,plain,
% 0.95/0.89 ((~hskp18) | c0_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[575, 572])).
% 0.95/0.89 tff(577,plain,
% 0.95/0.89 ((~hskp18) | c0_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[576, 572])).
% 0.95/0.89 tff(578,plain,
% 0.95/0.89 ((~hskp18) | c0_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[577, 572])).
% 0.95/0.89 tff(579,plain,
% 0.95/0.89 ((~hskp18) | c0_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[578, 572])).
% 0.95/0.89 tff(580,plain,
% 0.95/0.89 ((~hskp18) | c0_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[579, 572])).
% 0.95/0.89 tff(581,plain,
% 0.95/0.89 ((~hskp18) | c0_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[580, 572])).
% 0.95/0.89 tff(582,plain,
% 0.95/0.89 (c0_1(a676)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[581, 219])).
% 0.95/0.89 tff(583,plain,
% 0.95/0.89 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(584,plain,
% 0.95/0.89 ((hskp20 | hskp5 | (~ndr1_0) | c2_1(a676) | c3_1(a676) | (~c0_1(a676))) <=> (hskp20 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(585,plain,
% 0.95/0.89 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a676) | c3_1(a676) | (~c0_1(a676)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676)))),
% 0.95/0.89 inference(monotonicity,[status(thm)],[584])).
% 0.95/0.89 tff(586,plain,
% 0.95/0.89 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a676) | c3_1(a676) | (~c0_1(a676)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676))),
% 0.95/0.89 inference(transitivity,[status(thm)],[585, 583])).
% 0.95/0.89 tff(587,plain,
% 0.95/0.89 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a676) | c3_1(a676) | (~c0_1(a676)))),
% 0.95/0.89 inference(quant_inst,[status(thm)],[])).
% 0.95/0.89 tff(588,plain,
% 0.95/0.89 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[587, 586])).
% 0.95/0.89 tff(589,plain,
% 0.95/0.89 (hskp5 | c3_1(a676)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[588, 102, 207, 582, 225, 196])).
% 0.95/0.89 tff(590,plain,
% 0.95/0.89 (c3_1(a676)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[589, 533])).
% 0.95/0.89 tff(591,plain,
% 0.95/0.89 (^[U: $i] : refl((hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.95/0.89 inference(bind,[status(th)],[])).
% 0.95/0.89 tff(592,plain,
% 0.95/0.89 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(quant_intro,[status(thm)],[591])).
% 0.95/0.89 tff(593,plain,
% 0.95/0.89 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(594,plain,
% 0.95/0.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp23) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp23) <=> (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.95/0.89 inference(bind,[status(th)],[])).
% 0.95/0.89 tff(595,plain,
% 0.95/0.89 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp23) <=> ![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(quant_intro,[status(thm)],[594])).
% 0.95/0.89 tff(596,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 0.95/0.89 tff(597,plain,
% 0.95/0.89 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.95/0.89 tff(598,plain,
% 0.95/0.89 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[597, 593])).
% 0.95/0.89 tff(599,plain,(
% 0.95/0.89 ![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(skolemize,[status(sab)],[598])).
% 0.95/0.89 tff(600,plain,
% 0.95/0.89 (![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[599, 592])).
% 0.95/0.89 tff(601,plain,
% 0.95/0.89 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | (~c3_1(a676)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | (~c3_1(a676)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(602,plain,
% 0.95/0.89 ((hskp23 | hskp5 | (~ndr1_0) | c2_1(a676) | (~c3_1(a676)) | (~c0_1(a676))) <=> (hskp23 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | (~c3_1(a676)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(603,plain,
% 0.95/0.89 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a676) | (~c3_1(a676)) | (~c0_1(a676)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | (~c3_1(a676))))),
% 0.95/0.89 inference(monotonicity,[status(thm)],[602])).
% 0.95/0.89 tff(604,plain,
% 0.95/0.89 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a676) | (~c3_1(a676)) | (~c0_1(a676)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | (~c3_1(a676)))),
% 0.95/0.89 inference(transitivity,[status(thm)],[603, 601])).
% 0.95/0.89 tff(605,plain,
% 0.95/0.89 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a676) | (~c3_1(a676)) | (~c0_1(a676)))),
% 0.95/0.89 inference(quant_inst,[status(thm)],[])).
% 0.95/0.89 tff(606,plain,
% 0.95/0.89 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | (~c3_1(a676))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.95/0.89 tff(607,plain,
% 0.95/0.89 (hskp23 | hskp5 | (~c3_1(a676))),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[606, 102, 582, 225, 600])).
% 0.95/0.89 tff(608,plain,
% 0.95/0.89 (hskp23),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[607, 590, 533])).
% 0.95/0.89 tff(609,plain,
% 0.95/0.89 (((~hskp23) | (~c3_1(a695))) <=> ((~hskp23) | (~c3_1(a695)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(610,plain,
% 0.95/0.89 (((~c3_1(a695)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a695)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(611,axiom,((~c3_1(a695)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 0.95/0.89 tff(612,plain,
% 0.95/0.89 ((~hskp23) | (~c3_1(a695))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[611, 610])).
% 0.95/0.89 tff(613,plain,
% 0.95/0.89 ((~hskp23) | (~c3_1(a695))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[612, 609])).
% 0.95/0.89 tff(614,plain,
% 0.95/0.89 (~c3_1(a695)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[613, 608])).
% 0.95/0.89 tff(615,plain,
% 0.95/0.89 (((~hskp23) | (~c0_1(a695))) <=> ((~hskp23) | (~c0_1(a695)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(616,plain,
% 0.95/0.89 (((~c0_1(a695)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a695)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(617,axiom,((~c0_1(a695)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 0.95/0.89 tff(618,plain,
% 0.95/0.89 ((~hskp23) | (~c0_1(a695))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[617, 616])).
% 0.95/0.89 tff(619,plain,
% 0.95/0.89 ((~hskp23) | (~c0_1(a695))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[618, 615])).
% 0.95/0.89 tff(620,plain,
% 0.95/0.89 (~c0_1(a695)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[619, 608])).
% 0.95/0.89 tff(621,plain,
% 0.95/0.89 (((~hskp12) | c0_1(a660)) <=> ((~hskp12) | c0_1(a660))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(622,axiom,((~hskp12) | c0_1(a660)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.95/0.89 tff(623,plain,
% 0.95/0.89 ((~hskp12) | c0_1(a660)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[622, 621])).
% 0.95/0.89 tff(624,plain,
% 0.95/0.89 ((~hskp12) | c0_1(a660)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[623, 621])).
% 0.95/0.89 tff(625,plain,
% 0.95/0.89 ((~hskp12) | c0_1(a660)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[624, 621])).
% 0.95/0.89 tff(626,plain,
% 0.95/0.89 ((~hskp12) | c0_1(a660)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[625, 621])).
% 0.95/0.89 tff(627,plain,
% 0.95/0.89 ((~hskp12) | c0_1(a660)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[626, 621])).
% 0.95/0.89 tff(628,plain,
% 0.95/0.89 ((~hskp12) | c0_1(a660)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[627, 621])).
% 0.95/0.89 tff(629,plain,
% 0.95/0.89 ((~hskp12) | c0_1(a660)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[628, 621])).
% 0.95/0.89 tff(630,plain,
% 0.95/0.89 ((~hskp12) | c0_1(a660)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[629, 621])).
% 0.95/0.89 tff(631,plain,
% 0.95/0.89 (c0_1(a660)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[630, 559])).
% 0.95/0.89 tff(632,plain,
% 0.95/0.89 (((~hskp23) | c2_1(a695)) <=> ((~hskp23) | c2_1(a695))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(633,axiom,((~hskp23) | c2_1(a695)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause50')).
% 0.95/0.89 tff(634,plain,
% 0.95/0.89 ((~hskp23) | c2_1(a695)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[633, 632])).
% 0.95/0.89 tff(635,plain,
% 0.95/0.89 ((~hskp23) | c2_1(a695)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[634, 632])).
% 0.95/0.89 tff(636,plain,
% 0.95/0.89 ((~hskp23) | c2_1(a695)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[635, 632])).
% 0.95/0.89 tff(637,plain,
% 0.95/0.89 ((~hskp23) | c2_1(a695)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[636, 632])).
% 0.95/0.89 tff(638,plain,
% 0.95/0.89 ((~hskp23) | c2_1(a695)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[637, 632])).
% 0.95/0.89 tff(639,plain,
% 0.95/0.89 ((~hskp23) | c2_1(a695)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[638, 632])).
% 0.95/0.89 tff(640,plain,
% 0.95/0.89 ((~hskp23) | c2_1(a695)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[639, 632])).
% 0.95/0.89 tff(641,plain,
% 0.95/0.89 ((~hskp23) | c2_1(a695)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[640, 632])).
% 0.95/0.89 tff(642,plain,
% 0.95/0.89 (c2_1(a695)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[641, 608])).
% 0.95/0.89 tff(643,plain,
% 0.95/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a695) | c3_1(a695) | c1_1(a660) | c2_1(a660) | (~ndr1_0) | (~c0_1(a660)) | (~c2_1(a695)) | (~c1_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a695) | c3_1(a695) | c1_1(a660) | c2_1(a660) | (~ndr1_0) | (~c0_1(a660)) | (~c2_1(a695)) | (~c1_1(a695)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(644,plain,
% 0.95/0.89 (((~ndr1_0) | c2_1(a660) | c1_1(a660) | (~c0_1(a660)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695))) <=> (c0_1(a695) | c3_1(a695) | c1_1(a660) | c2_1(a660) | (~ndr1_0) | (~c0_1(a660)) | (~c2_1(a695)) | (~c1_1(a695)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(645,plain,
% 0.95/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a660) | c1_1(a660) | (~c0_1(a660)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a695) | c3_1(a695) | c1_1(a660) | c2_1(a660) | (~ndr1_0) | (~c0_1(a660)) | (~c2_1(a695)) | (~c1_1(a695))))),
% 0.95/0.89 inference(monotonicity,[status(thm)],[644])).
% 0.95/0.89 tff(646,plain,
% 0.95/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a660) | c1_1(a660) | (~c0_1(a660)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a695) | c3_1(a695) | c1_1(a660) | c2_1(a660) | (~ndr1_0) | (~c0_1(a660)) | (~c2_1(a695)) | (~c1_1(a695)))),
% 0.95/0.89 inference(transitivity,[status(thm)],[645, 643])).
% 0.95/0.89 tff(647,plain,
% 0.95/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a660) | c1_1(a660) | (~c0_1(a660)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))),
% 0.95/0.89 inference(quant_inst,[status(thm)],[])).
% 0.95/0.89 tff(648,plain,
% 0.95/0.89 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a695) | c3_1(a695) | c1_1(a660) | c2_1(a660) | (~ndr1_0) | (~c0_1(a660)) | (~c2_1(a695)) | (~c1_1(a695))),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[647, 646])).
% 0.95/0.89 tff(649,plain,
% 0.95/0.89 (~c1_1(a695)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[648, 102, 642, 631, 620, 614, 571, 565, 235])).
% 0.95/0.89 tff(650,plain,
% 0.95/0.89 (((~hskp18) | c1_1(a676)) <=> ((~hskp18) | c1_1(a676))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(651,axiom,((~hskp18) | c1_1(a676)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 0.95/0.89 tff(652,plain,
% 0.95/0.89 ((~hskp18) | c1_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[651, 650])).
% 0.95/0.89 tff(653,plain,
% 0.95/0.89 ((~hskp18) | c1_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[652, 650])).
% 0.95/0.89 tff(654,plain,
% 0.95/0.89 ((~hskp18) | c1_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[653, 650])).
% 0.95/0.89 tff(655,plain,
% 0.95/0.89 ((~hskp18) | c1_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[654, 650])).
% 0.95/0.89 tff(656,plain,
% 0.95/0.89 ((~hskp18) | c1_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[655, 650])).
% 0.95/0.89 tff(657,plain,
% 0.95/0.89 ((~hskp18) | c1_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[656, 650])).
% 0.95/0.89 tff(658,plain,
% 0.95/0.89 ((~hskp18) | c1_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[657, 650])).
% 0.95/0.89 tff(659,plain,
% 0.95/0.89 ((~hskp18) | c1_1(a676)),
% 0.95/0.89 inference(modus_ponens,[status(thm)],[658, 650])).
% 0.95/0.89 tff(660,plain,
% 0.95/0.89 (c1_1(a676)),
% 0.95/0.89 inference(unit_resolution,[status(thm)],[659, 219])).
% 0.95/0.89 tff(661,plain,
% 0.95/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a695) | (~c2_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a695) | (~c2_1(a695)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(662,plain,
% 0.95/0.89 (((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)) | c3_1(a695) | c1_1(a695) | c0_1(a695)) <=> (c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a695) | (~c2_1(a695)))),
% 0.95/0.89 inference(rewrite,[status(thm)],[])).
% 0.95/0.89 tff(663,plain,
% 0.95/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)) | c3_1(a695) | c1_1(a695) | c0_1(a695))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a695) | (~c2_1(a695))))),
% 0.95/0.90 inference(monotonicity,[status(thm)],[662])).
% 0.95/0.90 tff(664,plain,
% 0.95/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)) | c3_1(a695) | c1_1(a695) | c0_1(a695))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a695) | (~c2_1(a695)))),
% 0.95/0.90 inference(transitivity,[status(thm)],[663, 661])).
% 0.95/0.90 tff(665,plain,
% 0.95/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)) | c3_1(a695) | c1_1(a695) | c0_1(a695))),
% 0.95/0.90 inference(quant_inst,[status(thm)],[])).
% 0.95/0.90 tff(666,plain,
% 0.95/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a695) | (~c2_1(a695))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[665, 664])).
% 0.95/0.90 tff(667,plain,
% 0.95/0.90 ($false),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[666, 102, 642, 582, 660, 620, 614, 225, 206, 649])).
% 0.95/0.90 tff(668,plain,(c3_1(a647) | hskp20 | hskp2 | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.95/0.90 tff(669,plain,
% 0.95/0.90 (c3_1(a647)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[668, 207, 24, 1, 23])).
% 0.95/0.90 tff(670,plain,
% 0.95/0.90 (((~hskp5) | (~c3_1(a647))) <=> ((~hskp5) | (~c3_1(a647)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(671,plain,
% 0.95/0.90 (((~c3_1(a647)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a647)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(672,axiom,((~c3_1(a647)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.95/0.90 tff(673,plain,
% 0.95/0.90 ((~hskp5) | (~c3_1(a647))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[672, 671])).
% 0.95/0.90 tff(674,plain,
% 0.95/0.90 ((~hskp5) | (~c3_1(a647))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[673, 670])).
% 0.95/0.90 tff(675,plain,
% 0.95/0.90 (~hskp5),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[674, 669])).
% 0.95/0.90 tff(676,plain,
% 0.95/0.90 (c3_1(a676)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[589, 675])).
% 0.95/0.90 tff(677,plain,
% 0.95/0.90 (hskp23),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[607, 676, 675])).
% 0.95/0.90 tff(678,plain,
% 0.95/0.90 (~c3_1(a695)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[613, 677])).
% 0.95/0.90 tff(679,plain,
% 0.95/0.90 (~c0_1(a695)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[619, 677])).
% 0.95/0.90 tff(680,plain,
% 0.95/0.90 (c2_1(a695)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[641, 677])).
% 0.95/0.90 tff(681,plain,
% 0.95/0.90 (c1_1(a695)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[666, 102, 680, 582, 660, 679, 678, 225, 206])).
% 0.95/0.90 tff(682,plain,
% 0.95/0.90 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c3_1(a676)) | (~c1_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c3_1(a676)) | (~c1_1(a695)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(683,plain,
% 0.95/0.90 ((hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695))) <=> (hskp6 | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c3_1(a676)) | (~c1_1(a695)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(684,plain,
% 0.95/0.90 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c3_1(a676)) | (~c1_1(a695))))),
% 0.95/0.90 inference(monotonicity,[status(thm)],[683])).
% 0.95/0.90 tff(685,plain,
% 0.95/0.90 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c3_1(a676)) | (~c1_1(a695)))),
% 0.95/0.90 inference(transitivity,[status(thm)],[684, 682])).
% 0.95/0.90 tff(686,plain,
% 0.95/0.90 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))),
% 0.95/0.90 inference(quant_inst,[status(thm)],[])).
% 0.95/0.90 tff(687,plain,
% 0.95/0.90 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a695) | c3_1(a695) | c2_1(a676) | (~ndr1_0) | (~c1_1(a676)) | (~c3_1(a676)) | (~c1_1(a695))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[686, 685])).
% 0.95/0.90 tff(688,plain,
% 0.95/0.90 (hskp6),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[687, 102, 660, 679, 678, 225, 281, 676, 681])).
% 0.95/0.90 tff(689,plain,
% 0.95/0.90 (~c3_1(a648)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[114, 688])).
% 0.95/0.90 tff(690,plain,
% 0.95/0.90 (~c2_1(a648)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[120, 688])).
% 0.95/0.90 tff(691,plain,
% 0.95/0.90 (c0_1(a648)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[328, 688])).
% 0.95/0.90 tff(692,plain,
% 0.95/0.90 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(693,plain,
% 0.95/0.90 ((hskp20 | hskp5 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c0_1(a648))) <=> (hskp20 | hskp5 | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(694,plain,
% 0.95/0.90 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c0_1(a648)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648))))),
% 0.95/0.90 inference(monotonicity,[status(thm)],[693])).
% 0.95/0.90 tff(695,plain,
% 0.95/0.90 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c0_1(a648)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)))),
% 0.95/0.90 inference(transitivity,[status(thm)],[694, 692])).
% 0.95/0.90 tff(696,plain,
% 0.95/0.90 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a648) | c3_1(a648) | (~c0_1(a648)))),
% 0.95/0.90 inference(quant_inst,[status(thm)],[])).
% 0.95/0.90 tff(697,plain,
% 0.95/0.90 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[696, 695])).
% 0.95/0.90 tff(698,plain,
% 0.95/0.90 ($false),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[697, 102, 207, 675, 691, 690, 689, 196])).
% 0.95/0.90 tff(699,plain,(hskp20 | hskp2 | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.95/0.90 tff(700,plain,
% 0.95/0.90 (hskp20),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[699, 1, 24, 23])).
% 0.95/0.90 tff(701,plain,
% 0.95/0.90 (((~hskp20) | (~c3_1(a686))) <=> ((~hskp20) | (~c3_1(a686)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(702,plain,
% 0.95/0.90 (((~c3_1(a686)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a686)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(703,axiom,((~c3_1(a686)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.95/0.90 tff(704,plain,
% 0.95/0.90 ((~hskp20) | (~c3_1(a686))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[703, 702])).
% 0.95/0.90 tff(705,plain,
% 0.95/0.90 ((~hskp20) | (~c3_1(a686))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[704, 701])).
% 0.95/0.90 tff(706,plain,
% 0.95/0.90 (~c3_1(a686)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[705, 700])).
% 0.95/0.90 tff(707,plain,
% 0.95/0.90 (c0_1(a648)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[328, 109])).
% 0.95/0.90 tff(708,plain,
% 0.95/0.90 (((~hskp20) | c2_1(a686)) <=> ((~hskp20) | c2_1(a686))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(709,axiom,((~hskp20) | c2_1(a686)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.95/0.90 tff(710,plain,
% 0.95/0.90 ((~hskp20) | c2_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[709, 708])).
% 0.95/0.90 tff(711,plain,
% 0.95/0.90 ((~hskp20) | c2_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[710, 708])).
% 0.95/0.90 tff(712,plain,
% 0.95/0.90 ((~hskp20) | c2_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[711, 708])).
% 0.95/0.90 tff(713,plain,
% 0.95/0.90 ((~hskp20) | c2_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[712, 708])).
% 0.95/0.90 tff(714,plain,
% 0.95/0.90 ((~hskp20) | c2_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[713, 708])).
% 0.95/0.90 tff(715,plain,
% 0.95/0.90 ((~hskp20) | c2_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[714, 708])).
% 0.95/0.90 tff(716,plain,
% 0.95/0.90 ((~hskp20) | c2_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[715, 708])).
% 0.95/0.90 tff(717,plain,
% 0.95/0.90 ((~hskp20) | c2_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[716, 708])).
% 0.95/0.90 tff(718,plain,
% 0.95/0.90 (c2_1(a686)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[717, 700])).
% 0.95/0.90 tff(719,plain,
% 0.95/0.90 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a686) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a686) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(720,plain,
% 0.95/0.90 (((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648))) <=> (c3_1(a686) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(721,plain,
% 0.95/0.90 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a686) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686))))),
% 0.95/0.90 inference(monotonicity,[status(thm)],[720])).
% 0.95/0.90 tff(722,plain,
% 0.95/0.90 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a686) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.95/0.90 inference(transitivity,[status(thm)],[721, 719])).
% 0.95/0.90 tff(723,plain,
% 0.95/0.90 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a648) | c2_1(a648) | (~c0_1(a648)))),
% 0.95/0.90 inference(quant_inst,[status(thm)],[])).
% 0.95/0.90 tff(724,plain,
% 0.95/0.90 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a686) | c2_1(a648) | c3_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[723, 722])).
% 0.95/0.90 tff(725,plain,
% 0.95/0.90 (~c0_1(a686)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[724, 102, 718, 707, 706, 121, 115, 186])).
% 0.95/0.90 tff(726,plain,
% 0.95/0.90 (((~hskp20) | c1_1(a686)) <=> ((~hskp20) | c1_1(a686))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(727,axiom,((~hskp20) | c1_1(a686)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.95/0.90 tff(728,plain,
% 0.95/0.90 ((~hskp20) | c1_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[727, 726])).
% 0.95/0.90 tff(729,plain,
% 0.95/0.90 ((~hskp20) | c1_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[728, 726])).
% 0.95/0.90 tff(730,plain,
% 0.95/0.90 ((~hskp20) | c1_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[729, 726])).
% 0.95/0.90 tff(731,plain,
% 0.95/0.90 ((~hskp20) | c1_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[730, 726])).
% 0.95/0.90 tff(732,plain,
% 0.95/0.90 ((~hskp20) | c1_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[731, 726])).
% 0.95/0.90 tff(733,plain,
% 0.95/0.90 ((~hskp20) | c1_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[732, 726])).
% 0.95/0.90 tff(734,plain,
% 0.95/0.90 ((~hskp20) | c1_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[733, 726])).
% 0.95/0.90 tff(735,plain,
% 0.95/0.90 ((~hskp20) | c1_1(a686)),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[734, 726])).
% 0.95/0.90 tff(736,plain,
% 0.95/0.90 (c1_1(a686)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[735, 700])).
% 0.95/0.90 tff(737,plain,
% 0.95/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a686) | c2_1(a648) | (~ndr1_0) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a686) | c2_1(a648) | (~ndr1_0) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(738,plain,
% 0.95/0.90 (((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686))) <=> (c3_1(a686) | c2_1(a648) | (~ndr1_0) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(739,plain,
% 0.95/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a686) | c2_1(a648) | (~ndr1_0) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686))))),
% 0.95/0.90 inference(monotonicity,[status(thm)],[738])).
% 0.95/0.90 tff(740,plain,
% 0.95/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a686) | c2_1(a648) | (~ndr1_0) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.95/0.90 inference(transitivity,[status(thm)],[739, 737])).
% 0.95/0.90 tff(741,plain,
% 0.95/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))),
% 0.95/0.90 inference(quant_inst,[status(thm)],[])).
% 0.95/0.90 tff(742,plain,
% 0.95/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a686) | c2_1(a648) | (~ndr1_0) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[741, 740])).
% 0.95/0.90 tff(743,plain,
% 0.95/0.90 ($false),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[742, 102, 736, 718, 707, 706, 121, 235, 725, 176])).
% 0.95/0.90 tff(744,plain,((~hskp14) | hskp2 | hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.95/0.90 tff(745,plain,
% 0.95/0.90 (~hskp14),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[744, 1, 24, 23])).
% 0.95/0.90 tff(746,plain,
% 0.95/0.90 ((hskp24 | hskp17 | hskp14) <=> (hskp24 | hskp17 | hskp14)),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(747,plain,
% 0.95/0.90 (((hskp24 | hskp14) | hskp17) <=> (hskp24 | hskp17 | hskp14)),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(748,plain,
% 0.95/0.90 ((hskp24 | hskp14) <=> (hskp24 | hskp14)),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(749,plain,
% 0.95/0.90 (((hskp24 | hskp14) | hskp17) <=> ((hskp24 | hskp14) | hskp17)),
% 0.95/0.90 inference(monotonicity,[status(thm)],[748])).
% 0.95/0.90 tff(750,plain,
% 0.95/0.90 (((hskp24 | hskp14) | hskp17) <=> (hskp24 | hskp17 | hskp14)),
% 0.95/0.90 inference(transitivity,[status(thm)],[749, 747])).
% 0.95/0.90 tff(751,axiom,((hskp24 | hskp14) | hskp17), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause36')).
% 0.95/0.90 tff(752,plain,
% 0.95/0.90 (hskp24 | hskp17 | hskp14),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[751, 750])).
% 0.95/0.90 tff(753,plain,
% 0.95/0.90 (hskp24 | hskp17 | hskp14),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[752, 746])).
% 0.95/0.90 tff(754,plain,
% 0.95/0.90 (hskp24 | hskp17 | hskp14),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[753, 746])).
% 0.95/0.90 tff(755,plain,
% 0.95/0.90 (hskp24 | hskp17 | hskp14),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[754, 746])).
% 0.95/0.90 tff(756,plain,
% 0.95/0.90 (hskp24 | hskp17 | hskp14),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[755, 746])).
% 0.95/0.90 tff(757,plain,
% 0.95/0.90 (hskp24 | hskp17 | hskp14),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[756, 746])).
% 0.95/0.90 tff(758,plain,
% 0.95/0.90 (hskp24 | hskp17 | hskp14),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[757, 746])).
% 0.95/0.90 tff(759,plain,
% 0.95/0.90 (hskp24 | hskp17 | hskp14),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[758, 746])).
% 0.95/0.90 tff(760,plain,
% 0.95/0.90 (hskp24),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[759, 745, 1])).
% 0.95/0.90 tff(761,plain,
% 0.95/0.90 (c1_1(a698)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[253, 760])).
% 0.95/0.90 tff(762,plain,
% 0.95/0.90 (~c2_1(a698)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[242, 760])).
% 0.95/0.90 tff(763,plain,
% 0.95/0.90 (hskp1),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[508, 745, 1])).
% 0.95/0.90 tff(764,plain,
% 0.95/0.90 (~c1_1(a642)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[391, 763])).
% 0.95/0.90 tff(765,plain,
% 0.95/0.90 (c3_1(a642)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[414, 763])).
% 0.95/0.90 tff(766,plain,
% 0.95/0.90 (hskp7 | (~c2_1(a642))),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[423, 102, 1, 765, 764, 22])).
% 0.95/0.90 tff(767,plain,
% 0.95/0.90 (~c2_1(a642)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[766, 393])).
% 0.95/0.90 tff(768,plain,
% 0.95/0.90 (c0_1(a642)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[403, 763])).
% 0.95/0.90 tff(769,plain,
% 0.95/0.90 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(770,plain,
% 0.95/0.90 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.95/0.90 inference(quant_inst,[status(thm)],[])).
% 0.95/0.90 tff(771,plain,
% 0.95/0.90 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | (~ndr1_0) | c2_1(a642) | (~c3_1(a642)) | (~c0_1(a642))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[770, 769])).
% 0.95/0.90 tff(772,plain,
% 0.95/0.90 (hskp23 | hskp5 | c2_1(a642)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[771, 102, 768, 765, 600])).
% 0.95/0.90 tff(773,plain,
% 0.95/0.90 (hskp23),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[772, 767, 2])).
% 0.95/0.90 tff(774,plain,
% 0.95/0.90 (~c3_1(a695)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[613, 773])).
% 0.95/0.90 tff(775,plain,
% 0.95/0.90 (~c0_1(a695)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[619, 773])).
% 0.95/0.90 tff(776,plain,
% 0.95/0.90 (c2_1(a695)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[641, 773])).
% 0.95/0.90 tff(777,plain,
% 0.95/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a695) | c3_1(a695) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a695) | c3_1(a695) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(778,plain,
% 0.95/0.90 (((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695))) <=> (c0_1(a695) | c3_1(a695) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(779,plain,
% 0.95/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a695) | c3_1(a695) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a695)) | (~c1_1(a695))))),
% 0.95/0.90 inference(monotonicity,[status(thm)],[778])).
% 0.95/0.90 tff(780,plain,
% 0.95/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a695) | c3_1(a695) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)))),
% 0.95/0.90 inference(transitivity,[status(thm)],[779, 777])).
% 0.95/0.90 tff(781,plain,
% 0.95/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a695) | (~c2_1(a695)) | (~c1_1(a695)) | c3_1(a695) | c0_1(a695) | (~c1_1(a695)))),
% 0.95/0.90 inference(quant_inst,[status(thm)],[])).
% 0.95/0.90 tff(782,plain,
% 0.95/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a695) | c3_1(a695) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a695)) | (~c1_1(a695))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[781, 780])).
% 0.95/0.90 tff(783,plain,
% 0.95/0.90 (~c1_1(a695)),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[782, 102, 776, 768, 775, 774, 764, 235, 767])).
% 0.95/0.90 tff(784,plain,
% 0.95/0.90 (^[U: $i] : refl((hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.95/0.90 inference(bind,[status(th)],[])).
% 0.95/0.90 tff(785,plain,
% 0.95/0.90 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.90 inference(quant_intro,[status(thm)],[784])).
% 0.95/0.90 tff(786,plain,
% 0.95/0.90 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(787,plain,
% 0.95/0.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp17) <=> ((hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp17))), rewrite(((hskp28 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp17) <=> (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp17) <=> (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.95/0.90 inference(bind,[status(th)],[])).
% 0.95/0.90 tff(788,plain,
% 0.95/0.90 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp17) <=> ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.90 inference(quant_intro,[status(thm)],[787])).
% 0.95/0.90 tff(789,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp28) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.95/0.90 tff(790,plain,
% 0.95/0.90 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.95/0.90 tff(791,plain,
% 0.95/0.90 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[790, 786])).
% 0.95/0.90 tff(792,plain,(
% 0.95/0.90 ![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.90 inference(skolemize,[status(sab)],[791])).
% 0.95/0.90 tff(793,plain,
% 0.95/0.90 (![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[792, 785])).
% 0.95/0.90 tff(794,assumption,(~hskp28), introduced(assumption)).
% 0.95/0.90 tff(795,plain,
% 0.95/0.90 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp17 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(796,plain,
% 0.95/0.90 ((hskp28 | hskp17 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642))) <=> (hskp28 | hskp17 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(797,plain,
% 0.95/0.90 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642))))),
% 0.95/0.90 inference(monotonicity,[status(thm)],[796])).
% 0.95/0.90 tff(798,plain,
% 0.95/0.90 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp17 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.95/0.90 inference(transitivity,[status(thm)],[797, 795])).
% 0.95/0.90 tff(799,plain,
% 0.95/0.90 ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.95/0.90 inference(quant_inst,[status(thm)],[])).
% 0.95/0.90 tff(800,plain,
% 0.95/0.90 ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp17 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642))),
% 0.95/0.90 inference(modus_ponens,[status(thm)],[799, 798])).
% 0.95/0.90 tff(801,plain,
% 0.95/0.90 ($false),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[800, 102, 794, 1, 404, 415, 392, 793])).
% 0.95/0.90 tff(802,plain,((~hskp1) | hskp28 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.95/0.90 tff(803,plain,
% 0.95/0.90 (hskp28),
% 0.95/0.90 inference(unit_resolution,[status(thm)],[802, 763, 1])).
% 0.95/0.90 tff(804,plain,
% 0.95/0.90 (((~hskp28) | c2_1(a671)) <=> ((~hskp28) | c2_1(a671))),
% 0.95/0.90 inference(rewrite,[status(thm)],[])).
% 0.95/0.90 tff(805,axiom,((~hskp28) | c2_1(a671)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 0.95/0.91 tff(806,plain,
% 0.95/0.91 ((~hskp28) | c2_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[805, 804])).
% 0.95/0.91 tff(807,plain,
% 0.95/0.91 ((~hskp28) | c2_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[806, 804])).
% 0.95/0.91 tff(808,plain,
% 0.95/0.91 ((~hskp28) | c2_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[807, 804])).
% 0.95/0.91 tff(809,plain,
% 0.95/0.91 ((~hskp28) | c2_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[808, 804])).
% 0.95/0.91 tff(810,plain,
% 0.95/0.91 ((~hskp28) | c2_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[809, 804])).
% 0.95/0.91 tff(811,plain,
% 0.95/0.91 ((~hskp28) | c2_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[810, 804])).
% 0.95/0.91 tff(812,plain,
% 0.95/0.91 ((~hskp28) | c2_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[811, 804])).
% 0.95/0.91 tff(813,plain,
% 0.95/0.91 ((~hskp28) | c2_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[812, 804])).
% 0.95/0.91 tff(814,plain,
% 0.95/0.91 (c2_1(a671)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[813, 803])).
% 0.95/0.91 tff(815,plain,
% 0.95/0.91 (((~hskp28) | c1_1(a671)) <=> ((~hskp28) | c1_1(a671))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(816,axiom,((~hskp28) | c1_1(a671)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 0.95/0.91 tff(817,plain,
% 0.95/0.91 ((~hskp28) | c1_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.95/0.91 tff(818,plain,
% 0.95/0.91 ((~hskp28) | c1_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[817, 815])).
% 0.95/0.91 tff(819,plain,
% 0.95/0.91 ((~hskp28) | c1_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[818, 815])).
% 0.95/0.91 tff(820,plain,
% 0.95/0.91 ((~hskp28) | c1_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[819, 815])).
% 0.95/0.91 tff(821,plain,
% 0.95/0.91 ((~hskp28) | c1_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[820, 815])).
% 0.95/0.91 tff(822,plain,
% 0.95/0.91 ((~hskp28) | c1_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[821, 815])).
% 0.95/0.91 tff(823,plain,
% 0.95/0.91 ((~hskp28) | c1_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[822, 815])).
% 0.95/0.91 tff(824,plain,
% 0.95/0.91 ((~hskp28) | c1_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[823, 815])).
% 0.95/0.91 tff(825,plain,
% 0.95/0.91 (c1_1(a671)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[824, 803])).
% 0.95/0.91 tff(826,plain,
% 0.95/0.91 (((~hskp28) | c0_1(a671)) <=> ((~hskp28) | c0_1(a671))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(827,axiom,((~hskp28) | c0_1(a671)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.95/0.91 tff(828,plain,
% 0.95/0.91 ((~hskp28) | c0_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[827, 826])).
% 0.95/0.91 tff(829,plain,
% 0.95/0.91 ((~hskp28) | c0_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[828, 826])).
% 0.95/0.91 tff(830,plain,
% 0.95/0.91 ((~hskp28) | c0_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[829, 826])).
% 0.95/0.91 tff(831,plain,
% 0.95/0.91 ((~hskp28) | c0_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[830, 826])).
% 0.95/0.91 tff(832,plain,
% 0.95/0.91 ((~hskp28) | c0_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[831, 826])).
% 0.95/0.91 tff(833,plain,
% 0.95/0.91 ((~hskp28) | c0_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[832, 826])).
% 0.95/0.91 tff(834,plain,
% 0.95/0.91 ((~hskp28) | c0_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[833, 826])).
% 0.95/0.91 tff(835,plain,
% 0.95/0.91 ((~hskp28) | c0_1(a671)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[834, 826])).
% 0.95/0.91 tff(836,plain,
% 0.95/0.91 (c0_1(a671)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[835, 803])).
% 0.95/0.91 tff(837,assumption,(hskp4), introduced(assumption)).
% 0.95/0.91 tff(838,plain,
% 0.95/0.91 (((~hskp4) | (~c3_1(a646))) <=> ((~hskp4) | (~c3_1(a646)))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(839,plain,
% 0.95/0.91 (((~c3_1(a646)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a646)))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(840,axiom,((~c3_1(a646)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.95/0.91 tff(841,plain,
% 0.95/0.91 ((~hskp4) | (~c3_1(a646))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[840, 839])).
% 0.95/0.91 tff(842,plain,
% 0.95/0.91 ((~hskp4) | (~c3_1(a646))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[841, 838])).
% 0.95/0.91 tff(843,plain,
% 0.95/0.91 (~c3_1(a646)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[842, 837])).
% 0.95/0.91 tff(844,plain,
% 0.95/0.91 (((~hskp4) | (~c1_1(a646))) <=> ((~hskp4) | (~c1_1(a646)))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(845,plain,
% 0.95/0.91 (((~c1_1(a646)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a646)))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(846,axiom,((~c1_1(a646)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.95/0.91 tff(847,plain,
% 0.95/0.91 ((~hskp4) | (~c1_1(a646))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[846, 845])).
% 0.95/0.91 tff(848,plain,
% 0.95/0.91 ((~hskp4) | (~c1_1(a646))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[847, 844])).
% 0.95/0.91 tff(849,plain,
% 0.95/0.91 (~c1_1(a646)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[848, 837])).
% 0.95/0.91 tff(850,plain,
% 0.95/0.91 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | c0_1(a646))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | c0_1(a646))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(851,plain,
% 0.95/0.91 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a646) | c0_1(a646) | c3_1(a646)) <=> (hskp2 | hskp0 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | c0_1(a646))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(852,plain,
% 0.95/0.91 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a646) | c0_1(a646) | c3_1(a646))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | c0_1(a646)))),
% 0.95/0.91 inference(monotonicity,[status(thm)],[851])).
% 0.95/0.91 tff(853,plain,
% 0.95/0.91 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a646) | c0_1(a646) | c3_1(a646))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | c0_1(a646))),
% 0.95/0.91 inference(transitivity,[status(thm)],[852, 850])).
% 0.95/0.91 tff(854,plain,
% 0.95/0.91 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a646) | c0_1(a646) | c3_1(a646))),
% 0.95/0.91 inference(quant_inst,[status(thm)],[])).
% 0.95/0.91 tff(855,plain,
% 0.95/0.91 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | c0_1(a646)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.95/0.91 tff(856,plain,
% 0.95/0.91 (c0_1(a646)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[855, 102, 24, 23, 849, 843, 131])).
% 0.95/0.91 tff(857,plain,
% 0.95/0.91 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.95/0.91 inference(bind,[status(th)],[])).
% 0.95/0.91 tff(858,plain,
% 0.95/0.91 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.95/0.91 inference(quant_intro,[status(thm)],[857])).
% 0.95/0.91 tff(859,plain,
% 0.95/0.91 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(860,plain,
% 0.95/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp7) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp7))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.95/0.91 inference(bind,[status(th)],[])).
% 0.95/0.91 tff(861,plain,
% 0.95/0.91 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.95/0.91 inference(quant_intro,[status(thm)],[860])).
% 0.95/0.91 tff(862,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 0.95/0.91 tff(863,plain,
% 0.95/0.91 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[862, 861])).
% 0.95/0.91 tff(864,plain,
% 0.95/0.91 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[863, 859])).
% 0.95/0.91 tff(865,plain,(
% 0.95/0.91 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.95/0.91 inference(skolemize,[status(sab)],[864])).
% 0.95/0.91 tff(866,plain,
% 0.95/0.91 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[865, 858])).
% 0.95/0.91 tff(867,assumption,(c2_1(a671)), introduced(assumption)).
% 0.95/0.91 tff(868,assumption,(c1_1(a671)), introduced(assumption)).
% 0.95/0.91 tff(869,assumption,(c0_1(a671)), introduced(assumption)).
% 0.95/0.91 tff(870,plain,
% 0.95/0.91 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | (~c0_1(a646)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | (~c0_1(a646)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(871,plain,
% 0.95/0.91 ((hskp7 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c3_1(a646) | c1_1(a646) | (~c0_1(a646))) <=> (hskp7 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | (~c0_1(a646)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(872,plain,
% 0.95/0.91 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c3_1(a646) | c1_1(a646) | (~c0_1(a646)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | (~c0_1(a646)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 0.95/0.91 inference(monotonicity,[status(thm)],[871])).
% 0.95/0.91 tff(873,plain,
% 0.95/0.91 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c3_1(a646) | c1_1(a646) | (~c0_1(a646)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | (~c0_1(a646)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.95/0.91 inference(transitivity,[status(thm)],[872, 870])).
% 0.95/0.91 tff(874,plain,
% 0.95/0.91 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp7 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c3_1(a646) | c1_1(a646) | (~c0_1(a646)))),
% 0.95/0.91 inference(quant_inst,[status(thm)],[])).
% 0.95/0.91 tff(875,plain,
% 0.95/0.91 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp7 | c1_1(a646) | c3_1(a646) | (~ndr1_0) | (~c0_1(a646)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[874, 873])).
% 0.95/0.91 tff(876,plain,
% 0.95/0.91 ($false),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[875, 102, 393, 869, 868, 867, 849, 843, 866, 856])).
% 0.95/0.91 tff(877,plain,((~hskp4) | hskp7 | (~c0_1(a671)) | (~c1_1(a671)) | (~c2_1(a671)) | hskp2 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.95/0.91 tff(878,plain,
% 0.95/0.91 (~hskp4),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[877, 393, 836, 825, 814, 24, 23])).
% 0.95/0.91 tff(879,plain,
% 0.95/0.91 (^[U: $i] : refl((hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.95/0.91 inference(bind,[status(th)],[])).
% 0.95/0.91 tff(880,plain,
% 0.95/0.91 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.91 inference(quant_intro,[status(thm)],[879])).
% 0.95/0.91 tff(881,plain,
% 0.95/0.91 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(882,plain,
% 0.95/0.91 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp18))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp4) <=> ((hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4))), rewrite(((hskp18 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp4) <=> (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.95/0.91 inference(bind,[status(th)],[])).
% 0.95/0.91 tff(883,plain,
% 0.95/0.91 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp4) <=> ![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.91 inference(quant_intro,[status(thm)],[882])).
% 0.95/0.91 tff(884,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp18) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 0.95/0.91 tff(885,plain,
% 0.95/0.91 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[884, 883])).
% 0.95/0.91 tff(886,plain,
% 0.95/0.91 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[885, 881])).
% 0.95/0.91 tff(887,plain,(
% 0.95/0.91 ![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.91 inference(skolemize,[status(sab)],[886])).
% 0.95/0.91 tff(888,plain,
% 0.95/0.91 (![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[887, 880])).
% 0.95/0.91 tff(889,plain,
% 0.95/0.91 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp4 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp18 | hskp4 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(890,plain,
% 0.95/0.91 ((hskp18 | hskp4 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642))) <=> (hskp18 | hskp4 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(891,plain,
% 0.95/0.91 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp4 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642))))),
% 0.95/0.91 inference(monotonicity,[status(thm)],[890])).
% 0.95/0.91 tff(892,plain,
% 0.95/0.91 (((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))) <=> ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp18 | hskp4 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.95/0.91 inference(transitivity,[status(thm)],[891, 889])).
% 0.95/0.91 tff(893,plain,
% 0.95/0.91 ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp18 | hskp4 | (~ndr1_0) | c1_1(a642) | (~c3_1(a642)) | (~c0_1(a642)))),
% 0.95/0.91 inference(quant_inst,[status(thm)],[])).
% 0.95/0.91 tff(894,plain,
% 0.95/0.91 ((~![U: $i] : (hskp18 | hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp18 | hskp4 | c1_1(a642) | (~ndr1_0) | (~c3_1(a642)) | (~c0_1(a642))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[893, 892])).
% 0.95/0.91 tff(895,plain,
% 0.95/0.91 (hskp18 | hskp4),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[894, 102, 768, 765, 764, 888])).
% 0.95/0.91 tff(896,plain,
% 0.95/0.91 (hskp18),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[895, 878])).
% 0.95/0.91 tff(897,plain,
% 0.95/0.91 (~c2_1(a676)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[224, 896])).
% 0.95/0.91 tff(898,plain,
% 0.95/0.91 (c1_1(a676)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[659, 896])).
% 0.95/0.91 tff(899,plain,
% 0.95/0.91 (c0_1(a676)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[581, 896])).
% 0.95/0.91 tff(900,plain,
% 0.95/0.91 ($false),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[666, 102, 776, 899, 898, 775, 774, 897, 206, 783])).
% 0.95/0.91 tff(901,plain,(hskp7 | hskp5 | hskp2 | hskp0 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.95/0.91 tff(902,plain,
% 0.95/0.91 (hskp7),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[901, 2, 24, 23, 1])).
% 0.95/0.91 tff(903,plain,
% 0.95/0.91 (c3_1(a698)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[384, 902, 762, 24, 761, 23])).
% 0.95/0.91 tff(904,assumption,(hskp23), introduced(assumption)).
% 0.95/0.91 tff(905,plain,
% 0.95/0.91 (~c3_1(a695)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[613, 904])).
% 0.95/0.91 tff(906,plain,
% 0.95/0.91 (~c0_1(a695)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[619, 904])).
% 0.95/0.91 tff(907,plain,
% 0.95/0.91 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(908,plain,
% 0.95/0.91 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a695) | c0_1(a695) | c3_1(a695)) <=> (hskp2 | hskp0 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(909,plain,
% 0.95/0.91 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a695) | c0_1(a695) | c3_1(a695))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695)))),
% 0.95/0.91 inference(monotonicity,[status(thm)],[908])).
% 0.95/0.91 tff(910,plain,
% 0.95/0.91 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a695) | c0_1(a695) | c3_1(a695))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695))),
% 0.95/0.91 inference(transitivity,[status(thm)],[909, 907])).
% 0.95/0.91 tff(911,plain,
% 0.95/0.91 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a695) | c0_1(a695) | c3_1(a695))),
% 0.95/0.91 inference(quant_inst,[status(thm)],[])).
% 0.95/0.91 tff(912,plain,
% 0.95/0.91 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695)),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[911, 910])).
% 0.95/0.91 tff(913,plain,
% 0.95/0.91 (c1_1(a695)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[912, 102, 24, 23, 906, 905, 131])).
% 0.95/0.91 tff(914,plain,
% 0.95/0.91 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_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)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 0.95/0.91 inference(bind,[status(th)],[])).
% 0.95/0.91 tff(915,plain,
% 0.95/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.95/0.91 inference(quant_intro,[status(thm)],[914])).
% 0.95/0.91 tff(916,plain,
% 0.95/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(917,plain,
% 0.95/0.91 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 0.95/0.91 inference(bind,[status(th)],[])).
% 0.95/0.91 tff(918,plain,
% 0.95/0.91 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.95/0.91 inference(quant_intro,[status(thm)],[917])).
% 0.95/0.91 tff(919,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c1_1(W))) | (~c2_1(W))) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 0.95/0.91 tff(920,plain,
% 0.95/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[919, 918])).
% 0.95/0.91 tff(921,plain,
% 0.95/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[920, 916])).
% 0.95/0.91 tff(922,plain,(
% 0.95/0.91 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.95/0.91 inference(skolemize,[status(sab)],[921])).
% 0.95/0.91 tff(923,plain,
% 0.95/0.91 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[922, 915])).
% 0.95/0.91 tff(924,plain,
% 0.95/0.91 (c2_1(a695)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[641, 904])).
% 0.95/0.91 tff(925,plain,
% 0.95/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a695) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a695) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(926,plain,
% 0.95/0.91 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695))) <=> (c0_1(a695) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.95/0.91 inference(rewrite,[status(thm)],[])).
% 0.95/0.91 tff(927,plain,
% 0.95/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a695) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 0.95/0.91 inference(monotonicity,[status(thm)],[926])).
% 0.95/0.91 tff(928,plain,
% 0.95/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a695) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.95/0.91 inference(transitivity,[status(thm)],[927, 925])).
% 0.95/0.91 tff(929,plain,
% 0.95/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 0.95/0.91 inference(quant_inst,[status(thm)],[])).
% 0.95/0.91 tff(930,plain,
% 0.95/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a695) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 0.95/0.91 inference(modus_ponens,[status(thm)],[929, 928])).
% 0.95/0.91 tff(931,plain,
% 0.95/0.91 ((~c2_1(a642)) | (~c1_1(a695))),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[930, 102, 869, 868, 867, 924, 417, 906, 416, 923])).
% 0.95/0.91 tff(932,plain,
% 0.95/0.91 (~c2_1(a642)),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[931, 913])).
% 0.95/0.91 tff(933,plain,
% 0.95/0.91 ($false),
% 0.95/0.91 inference(unit_resolution,[status(thm)],[782, 102, 924, 436, 906, 905, 416, 235, 932, 913])).
% 0.95/0.91 tff(934,plain,((~hskp23) | (~c0_1(a642)) | c1_1(a642) | (~c0_1(a671)) | (~c1_1(a671)) | (~c2_1(a671)) | (~c3_1(a642)) | hskp2 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.95/0.92 tff(935,plain,
% 0.95/0.92 (~hskp23),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[934, 768, 764, 836, 825, 814, 765, 24, 23])).
% 0.95/0.92 tff(936,plain,
% 0.95/0.92 (^[U: $i] : refl((hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.95/0.92 inference(bind,[status(th)],[])).
% 0.95/0.92 tff(937,plain,
% 0.95/0.92 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/0.92 inference(quant_intro,[status(thm)],[936])).
% 0.95/0.92 tff(938,plain,
% 0.95/0.92 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(939,plain,
% 0.95/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) <=> (hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp25) <=> ((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp25))), rewrite(((hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp25) <=> (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.95/0.92 inference(bind,[status(th)],[])).
% 0.95/0.92 tff(940,plain,
% 0.95/0.92 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp25) <=> ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/0.92 inference(quant_intro,[status(thm)],[939])).
% 0.95/0.92 tff(941,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp23) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 0.95/0.92 tff(942,plain,
% 0.95/0.92 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[941, 940])).
% 0.95/0.92 tff(943,plain,
% 0.95/0.92 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[942, 938])).
% 0.95/0.92 tff(944,plain,(
% 0.95/0.92 ![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/0.92 inference(skolemize,[status(sab)],[943])).
% 0.95/0.92 tff(945,plain,
% 0.95/0.92 (![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[944, 937])).
% 0.95/0.92 tff(946,plain,
% 0.95/0.92 (((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(947,plain,
% 0.95/0.92 ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 0.95/0.92 inference(quant_inst,[status(thm)],[])).
% 0.95/0.92 tff(948,plain,
% 0.95/0.92 ((~![U: $i] : (hskp25 | hskp23 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp23 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[947, 946])).
% 0.95/0.92 tff(949,plain,
% 0.95/0.92 (hskp25 | hskp23),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[948, 102, 836, 825, 814, 945])).
% 0.95/0.92 tff(950,plain,
% 0.95/0.92 (hskp25),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[949, 935])).
% 0.95/0.92 tff(951,plain,
% 0.95/0.92 (((~hskp25) | (~c3_1(a710))) <=> ((~hskp25) | (~c3_1(a710)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(952,plain,
% 0.95/0.92 (((~c3_1(a710)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a710)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(953,axiom,((~c3_1(a710)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.95/0.92 tff(954,plain,
% 0.95/0.92 ((~hskp25) | (~c3_1(a710))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[953, 952])).
% 0.95/0.92 tff(955,plain,
% 0.95/0.92 ((~hskp25) | (~c3_1(a710))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[954, 951])).
% 0.95/0.92 tff(956,plain,
% 0.95/0.92 (~c3_1(a710)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[955, 950])).
% 0.95/0.92 tff(957,plain,
% 0.95/0.92 (((~hskp25) | (~c0_1(a710))) <=> ((~hskp25) | (~c0_1(a710)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(958,plain,
% 0.95/0.92 (((~c0_1(a710)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a710)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(959,axiom,((~c0_1(a710)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.95/0.92 tff(960,plain,
% 0.95/0.92 ((~hskp25) | (~c0_1(a710))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[959, 958])).
% 0.95/0.92 tff(961,plain,
% 0.95/0.92 ((~hskp25) | (~c0_1(a710))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[960, 957])).
% 0.95/0.92 tff(962,plain,
% 0.95/0.92 (~c0_1(a710)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[961, 950])).
% 0.95/0.92 tff(963,plain,
% 0.95/0.92 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c0_1(a710) | c3_1(a710) | (~ndr1_0) | c1_1(a710))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a710) | c3_1(a710) | (~ndr1_0) | c1_1(a710))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(964,plain,
% 0.95/0.92 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a710) | c0_1(a710) | c3_1(a710)) <=> (hskp2 | hskp0 | c0_1(a710) | c3_1(a710) | (~ndr1_0) | c1_1(a710))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(965,plain,
% 0.95/0.92 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a710) | c0_1(a710) | c3_1(a710))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c0_1(a710) | c3_1(a710) | (~ndr1_0) | c1_1(a710)))),
% 0.95/0.92 inference(monotonicity,[status(thm)],[964])).
% 0.95/0.92 tff(966,plain,
% 0.95/0.92 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a710) | c0_1(a710) | c3_1(a710))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a710) | c3_1(a710) | (~ndr1_0) | c1_1(a710))),
% 0.95/0.92 inference(transitivity,[status(thm)],[965, 963])).
% 0.95/0.92 tff(967,plain,
% 0.95/0.92 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a710) | c0_1(a710) | c3_1(a710))),
% 0.95/0.92 inference(quant_inst,[status(thm)],[])).
% 0.95/0.92 tff(968,plain,
% 0.95/0.92 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c0_1(a710) | c3_1(a710) | (~ndr1_0) | c1_1(a710)),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[967, 966])).
% 0.95/0.92 tff(969,plain,
% 0.95/0.92 (c1_1(a710)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[968, 102, 24, 23, 962, 956, 131])).
% 0.95/0.92 tff(970,plain,
% 0.95/0.92 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a710) | c3_1(a710) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a710) | c3_1(a710) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(971,plain,
% 0.95/0.92 ((hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710))) <=> (hskp6 | c0_1(a710) | c3_1(a710) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(972,plain,
% 0.95/0.92 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a710) | c3_1(a710) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710))))),
% 0.95/0.92 inference(monotonicity,[status(thm)],[971])).
% 0.95/0.92 tff(973,plain,
% 0.95/0.92 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a710) | c3_1(a710) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))),
% 0.95/0.92 inference(transitivity,[status(thm)],[972, 970])).
% 0.95/0.92 tff(974,plain,
% 0.95/0.92 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710)))),
% 0.95/0.92 inference(quant_inst,[status(thm)],[])).
% 0.95/0.92 tff(975,plain,
% 0.95/0.92 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a710) | c3_1(a710) | c2_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[974, 973])).
% 0.95/0.92 tff(976,plain,
% 0.95/0.92 (hskp6 | (~c3_1(a698))),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[975, 102, 761, 962, 956, 762, 281, 969])).
% 0.95/0.92 tff(977,plain,
% 0.95/0.92 (hskp6),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[976, 903])).
% 0.95/0.92 tff(978,plain,
% 0.95/0.92 (~c3_1(a648)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[114, 977])).
% 0.95/0.92 tff(979,plain,
% 0.95/0.92 (~c2_1(a648)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[120, 977])).
% 0.95/0.92 tff(980,plain,
% 0.95/0.92 (~c1_1(a651)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[151, 902])).
% 0.95/0.92 tff(981,plain,
% 0.95/0.92 (~c0_1(a651)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[157, 902])).
% 0.95/0.92 tff(982,plain,
% 0.95/0.92 (c3_1(a651)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[168, 902])).
% 0.95/0.92 tff(983,plain,
% 0.95/0.92 (~c1_1(a648)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[175, 102, 24, 982, 981, 980, 979, 978, 34])).
% 0.95/0.92 tff(984,plain,
% 0.95/0.92 (c2_1(a642)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[772, 2, 935])).
% 0.95/0.92 tff(985,plain,
% 0.95/0.92 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))))),
% 0.95/0.92 inference(bind,[status(th)],[])).
% 0.95/0.92 tff(986,plain,
% 0.95/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.95/0.92 inference(quant_intro,[status(thm)],[985])).
% 0.95/0.92 tff(987,plain,
% 0.95/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(988,plain,
% 0.95/0.92 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))))),
% 0.95/0.92 inference(bind,[status(th)],[])).
% 0.95/0.92 tff(989,plain,
% 0.95/0.92 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_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)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.95/0.92 inference(quant_intro,[status(thm)],[988])).
% 0.95/0.92 tff(990,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c0_1(W))) | c3_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 0.95/0.92 tff(991,plain,
% 0.95/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[990, 989])).
% 0.95/0.92 tff(992,plain,
% 0.95/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[991, 987])).
% 0.95/0.92 tff(993,plain,(
% 0.95/0.92 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.95/0.92 inference(skolemize,[status(sab)],[992])).
% 0.95/0.92 tff(994,plain,
% 0.95/0.92 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[993, 986])).
% 0.95/0.92 tff(995,plain,
% 0.95/0.92 (~c0_1(a698)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[259, 760])).
% 0.95/0.92 tff(996,plain,
% 0.95/0.92 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a710) | c3_1(a710) | c0_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a710) | c3_1(a710) | c0_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(997,plain,
% 0.95/0.92 ((hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710))) <=> (hskp11 | c0_1(a710) | c3_1(a710) | c0_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(998,plain,
% 0.95/0.92 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a710) | c3_1(a710) | c0_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710))))),
% 0.95/0.92 inference(monotonicity,[status(thm)],[997])).
% 0.95/0.92 tff(999,plain,
% 0.95/0.92 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a710) | c3_1(a710) | c0_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710)))),
% 0.95/0.92 inference(transitivity,[status(thm)],[998, 996])).
% 0.95/0.92 tff(1000,plain,
% 0.95/0.92 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)) | c3_1(a710) | c0_1(a710) | (~c1_1(a710)))),
% 0.95/0.92 inference(quant_inst,[status(thm)],[])).
% 0.95/0.92 tff(1001,plain,
% 0.95/0.92 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a710) | c3_1(a710) | c0_1(a698) | (~ndr1_0) | (~c1_1(a698)) | (~c3_1(a698)) | (~c1_1(a710))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[1000, 999])).
% 0.95/0.92 tff(1002,plain,
% 0.95/0.92 (hskp11 | (~c3_1(a698))),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[1001, 102, 761, 962, 956, 995, 303, 969])).
% 0.95/0.92 tff(1003,plain,
% 0.95/0.92 (hskp11),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[1002, 903])).
% 0.95/0.92 tff(1004,plain,
% 0.95/0.92 (~c3_1(a657)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[317, 1003])).
% 0.95/0.92 tff(1005,plain,
% 0.95/0.92 (c0_1(a648)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[328, 977])).
% 0.95/0.92 tff(1006,plain,
% 0.95/0.92 (c2_1(a657)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[339, 1003])).
% 0.95/0.92 tff(1007,plain,
% 0.95/0.92 (c0_1(a657)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[350, 1003])).
% 0.95/0.92 tff(1008,plain,
% 0.95/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a657) | c3_1(a648) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c0_1(a642)) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a657) | c3_1(a648) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c0_1(a642)) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(1009,plain,
% 0.95/0.92 (((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c1_1(a642) | (~c2_1(a642)) | (~c0_1(a642)) | c3_1(a648) | c1_1(a648) | (~c0_1(a648))) <=> (c3_1(a657) | c3_1(a648) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c0_1(a642)) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(1010,plain,
% 0.95/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c1_1(a642) | (~c2_1(a642)) | (~c0_1(a642)) | c3_1(a648) | c1_1(a648) | (~c0_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c3_1(a657) | c3_1(a648) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c0_1(a642)) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657))))),
% 0.95/0.92 inference(monotonicity,[status(thm)],[1009])).
% 0.95/0.92 tff(1011,plain,
% 0.95/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c1_1(a642) | (~c2_1(a642)) | (~c0_1(a642)) | c3_1(a648) | c1_1(a648) | (~c0_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a657) | c3_1(a648) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c0_1(a642)) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657)))),
% 0.95/0.92 inference(transitivity,[status(thm)],[1010, 1008])).
% 0.95/0.92 tff(1012,plain,
% 0.95/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a657) | (~c2_1(a657)) | (~c0_1(a657)) | c1_1(a642) | (~c2_1(a642)) | (~c0_1(a642)) | c3_1(a648) | c1_1(a648) | (~c0_1(a648)))),
% 0.95/0.92 inference(quant_inst,[status(thm)],[])).
% 0.95/0.92 tff(1013,plain,
% 0.95/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c3_1(a657) | c3_1(a648) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c0_1(a642)) | c1_1(a648) | (~c0_1(a648)) | (~c2_1(a657)) | (~c0_1(a657))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 0.95/0.92 tff(1014,plain,
% 0.95/0.92 ($false),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[1013, 102, 1007, 1006, 1005, 768, 1004, 978, 764, 994, 984, 983])).
% 0.95/0.92 tff(1015,plain,(hskp5 | hskp2 | hskp0 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.95/0.92 tff(1016,plain,
% 0.95/0.92 (hskp5),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[1015, 1, 23, 24])).
% 0.95/0.92 tff(1017,plain,
% 0.95/0.92 (~c0_1(a647)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[532, 1016])).
% 0.95/0.92 tff(1018,plain,
% 0.95/0.92 (~c3_1(a647)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[674, 1016])).
% 0.95/0.92 tff(1019,plain,
% 0.95/0.92 (~c3_1(a698)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[359, 269, 761, 261, 995, 236, 762])).
% 0.95/0.92 tff(1020,plain,
% 0.95/0.92 (~hskp7),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[384, 1019, 762, 24, 761, 23])).
% 0.95/0.92 tff(1021,plain,
% 0.95/0.92 (~c2_1(a642)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[766, 1020])).
% 0.95/0.92 tff(1022,assumption,(~c2_1(a642)), introduced(assumption)).
% 0.95/0.92 tff(1023,assumption,(~c0_1(a686)), introduced(assumption)).
% 0.95/0.92 tff(1024,assumption,(~c3_1(a686)), introduced(assumption)).
% 0.95/0.92 tff(1025,assumption,(c2_1(a686)), introduced(assumption)).
% 0.95/0.92 tff(1026,assumption,(c1_1(a686)), introduced(assumption)).
% 0.95/0.92 tff(1027,plain,
% 0.95/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a686) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a686) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(1028,plain,
% 0.95/0.92 (((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686))) <=> (c3_1(a686) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.95/0.92 inference(rewrite,[status(thm)],[])).
% 0.95/0.92 tff(1029,plain,
% 0.95/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c3_1(a686) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686))))),
% 0.95/0.92 inference(monotonicity,[status(thm)],[1028])).
% 0.95/0.92 tff(1030,plain,
% 0.95/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a686) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 0.95/0.92 inference(transitivity,[status(thm)],[1029, 1027])).
% 0.95/0.92 tff(1031,plain,
% 0.95/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))),
% 0.95/0.92 inference(quant_inst,[status(thm)],[])).
% 0.95/0.92 tff(1032,plain,
% 0.95/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c3_1(a686) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686))),
% 0.95/0.92 inference(modus_ponens,[status(thm)],[1031, 1030])).
% 0.95/0.92 tff(1033,plain,
% 0.95/0.92 ($false),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[1032, 102, 1026, 1025, 436, 1024, 416, 235, 1023, 1022])).
% 0.95/0.92 tff(1034,plain,(c0_1(a686) | (~c1_1(a686)) | (~c2_1(a686)) | (~c0_1(a642)) | c3_1(a686) | c1_1(a642) | c2_1(a642)), inference(lemma,lemma(discharge,[]))).
% 0.95/0.92 tff(1035,plain,
% 0.95/0.92 (c0_1(a686)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[1034, 1021, 718, 768, 706, 764, 736])).
% 0.95/0.92 tff(1036,plain,
% 0.95/0.92 (~hskp4),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[877, 1020, 836, 825, 814, 24, 23])).
% 0.95/0.92 tff(1037,plain,
% 0.95/0.92 (hskp18),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[895, 1036])).
% 0.95/0.92 tff(1038,plain,
% 0.95/0.92 (~c2_1(a676)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[224, 1037])).
% 0.95/0.92 tff(1039,plain,
% 0.95/0.92 (c0_1(a676)),
% 0.95/0.92 inference(unit_resolution,[status(thm)],[581, 1037])).
% 0.95/0.92 tff(1040,assumption,(~c3_1(a676)), introduced(assumption)).
% 0.95/0.93 tff(1041,assumption,(c0_1(a686)), introduced(assumption)).
% 0.95/0.93 tff(1042,assumption,(~c2_1(a676)), introduced(assumption)).
% 0.95/0.93 tff(1043,assumption,(c0_1(a676)), introduced(assumption)).
% 0.95/0.93 tff(1044,plain,
% 0.95/0.93 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a686) | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676) | (~c2_1(a686)) | (~c0_1(a686)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a686) | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1045,plain,
% 0.95/0.93 (((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a676) | c2_1(a676) | (~c0_1(a676))) <=> (c3_1(a686) | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1046,plain,
% 0.95/0.93 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a676) | c2_1(a676) | (~c0_1(a676)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c3_1(a686) | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676) | (~c2_1(a686)) | (~c0_1(a686))))),
% 0.95/0.93 inference(monotonicity,[status(thm)],[1045])).
% 0.95/0.93 tff(1047,plain,
% 0.95/0.93 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a676) | c2_1(a676) | (~c0_1(a676)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a686) | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676) | (~c2_1(a686)) | (~c0_1(a686)))),
% 0.95/0.93 inference(transitivity,[status(thm)],[1046, 1044])).
% 0.95/0.93 tff(1048,plain,
% 0.95/0.93 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a676) | c2_1(a676) | (~c0_1(a676)))),
% 0.95/0.93 inference(quant_inst,[status(thm)],[])).
% 0.95/0.93 tff(1049,plain,
% 0.95/0.93 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c3_1(a686) | c2_1(a676) | (~ndr1_0) | (~c0_1(a676)) | c3_1(a676) | (~c2_1(a686)) | (~c0_1(a686))),
% 0.95/0.93 inference(modus_ponens,[status(thm)],[1048, 1047])).
% 0.95/0.93 tff(1050,plain,
% 0.95/0.93 ($false),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[1049, 102, 1025, 1043, 1024, 1042, 186, 1041, 1040])).
% 0.95/0.93 tff(1051,plain,(c3_1(a676) | (~c2_1(a686)) | (~c0_1(a676)) | c3_1(a686) | c2_1(a676) | (~c0_1(a686))), inference(lemma,lemma(discharge,[]))).
% 0.95/0.93 tff(1052,plain,
% 0.95/0.93 (c3_1(a676)),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[1051, 1039, 718, 706, 1038, 1035])).
% 0.95/0.93 tff(1053,plain,
% 0.95/0.93 (c1_1(a676)),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[659, 1037])).
% 0.95/0.93 tff(1054,plain,
% 0.95/0.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a676) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a676)) | (~c3_1(a676)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a676) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a676)) | (~c3_1(a676)))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1055,plain,
% 0.95/0.93 ((hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (hskp6 | c2_1(a676) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a676)) | (~c3_1(a676)))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1056,plain,
% 0.95/0.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c2_1(a676) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a676)) | (~c3_1(a676))))),
% 0.95/0.93 inference(monotonicity,[status(thm)],[1055])).
% 0.95/0.93 tff(1057,plain,
% 0.95/0.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a676) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a676)) | (~c3_1(a676)))),
% 0.95/0.93 inference(transitivity,[status(thm)],[1056, 1054])).
% 0.95/0.93 tff(1058,plain,
% 0.95/0.93 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c3_1(a676)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 0.95/0.93 inference(quant_inst,[status(thm)],[])).
% 0.95/0.93 tff(1059,plain,
% 0.95/0.93 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c2_1(a676) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c1_1(a676)) | (~c3_1(a676))),
% 0.95/0.93 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 0.95/0.93 tff(1060,plain,
% 0.95/0.93 (hskp6 | (~c3_1(a676))),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[1059, 102, 1053, 269, 1038, 261, 236, 281])).
% 0.95/0.93 tff(1061,plain,
% 0.95/0.93 (hskp6),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[1060, 1052])).
% 0.95/0.93 tff(1062,plain,
% 0.95/0.93 (~c3_1(a648)),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[114, 1061])).
% 0.95/0.93 tff(1063,plain,
% 0.95/0.93 (~c2_1(a648)),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[120, 1061])).
% 0.95/0.93 tff(1064,plain,
% 0.95/0.93 (c0_1(a648)),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[328, 1061])).
% 0.95/0.93 tff(1065,plain,
% 0.95/0.93 ($false),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[724, 102, 718, 1064, 706, 1063, 1062, 186, 1035])).
% 0.95/0.93 tff(1066,plain,(c0_1(a647) | c3_1(a647) | hskp2 | hskp0 | hskp17), inference(lemma,lemma(discharge,[]))).
% 0.95/0.93 tff(1067,plain,
% 0.95/0.93 ($false),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[1066, 1018, 1017, 24, 23, 1])).
% 0.95/0.93 tff(1068,plain,(hskp17 | hskp2 | hskp0), inference(lemma,lemma(discharge,[]))).
% 0.95/0.93 tff(1069,plain,
% 0.95/0.93 (hskp17),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[1068, 24, 23])).
% 0.95/0.93 tff(1070,plain,
% 0.95/0.93 (((~hskp17) | (~c1_1(a675))) <=> ((~hskp17) | (~c1_1(a675)))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1071,plain,
% 0.95/0.93 (((~c1_1(a675)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a675)))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1072,axiom,((~c1_1(a675)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 0.95/0.93 tff(1073,plain,
% 0.95/0.93 ((~hskp17) | (~c1_1(a675))),
% 0.95/0.93 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 0.95/0.93 tff(1074,plain,
% 0.95/0.93 ((~hskp17) | (~c1_1(a675))),
% 0.95/0.93 inference(modus_ponens,[status(thm)],[1073, 1070])).
% 0.95/0.93 tff(1075,plain,
% 0.95/0.93 (~c1_1(a675)),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[1074, 1069])).
% 0.95/0.93 tff(1076,plain,
% 0.95/0.93 (((~hskp17) | (~c3_1(a675))) <=> ((~hskp17) | (~c3_1(a675)))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1077,plain,
% 0.95/0.93 (((~c3_1(a675)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a675)))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1078,axiom,((~c3_1(a675)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 0.95/0.93 tff(1079,plain,
% 0.95/0.93 ((~hskp17) | (~c3_1(a675))),
% 0.95/0.93 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 0.95/0.93 tff(1080,plain,
% 0.95/0.93 ((~hskp17) | (~c3_1(a675))),
% 0.95/0.93 inference(modus_ponens,[status(thm)],[1079, 1076])).
% 0.95/0.93 tff(1081,plain,
% 0.95/0.93 (~c3_1(a675)),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[1080, 1069])).
% 0.95/0.93 tff(1082,assumption,(~c3_1(a675)), introduced(assumption)).
% 0.95/0.93 tff(1083,assumption,(~c1_1(a675)), introduced(assumption)).
% 0.95/0.93 tff(1084,plain,
% 0.95/0.93 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | c0_1(a675))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | c0_1(a675))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1085,plain,
% 0.95/0.93 ((hskp2 | hskp0 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | c3_1(a675)) <=> (hskp2 | hskp0 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | c0_1(a675))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1086,plain,
% 0.95/0.93 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | c3_1(a675))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | c0_1(a675)))),
% 0.95/0.93 inference(monotonicity,[status(thm)],[1085])).
% 0.95/0.93 tff(1087,plain,
% 0.95/0.93 (((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | c3_1(a675))) <=> ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | c0_1(a675))),
% 0.95/0.93 inference(transitivity,[status(thm)],[1086, 1084])).
% 0.95/0.93 tff(1088,plain,
% 0.95/0.93 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | (hskp2 | hskp0 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | c3_1(a675))),
% 0.95/0.93 inference(quant_inst,[status(thm)],[])).
% 0.95/0.93 tff(1089,plain,
% 0.95/0.93 ((~![U: $i] : (hskp2 | hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | c3_1(U))) | hskp2 | hskp0 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | c0_1(a675)),
% 0.95/0.93 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 0.95/0.93 tff(1090,plain,
% 0.95/0.93 (c3_1(a675) | c0_1(a675)),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[1089, 102, 24, 23, 1083, 131])).
% 0.95/0.93 tff(1091,plain,
% 0.95/0.93 (c0_1(a675)),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[1090, 1082])).
% 0.95/0.93 tff(1092,plain,
% 0.95/0.93 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))))),
% 0.95/0.93 inference(bind,[status(th)],[])).
% 0.95/0.93 tff(1093,plain,
% 0.95/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.95/0.93 inference(quant_intro,[status(thm)],[1092])).
% 0.95/0.93 tff(1094,plain,
% 0.95/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1095,plain,
% 0.95/0.93 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))))),
% 0.95/0.93 inference(bind,[status(th)],[])).
% 0.95/0.93 tff(1096,plain,
% 0.95/0.93 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.95/0.93 inference(quant_intro,[status(thm)],[1095])).
% 0.95/0.93 tff(1097,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 0.95/0.93 tff(1098,plain,
% 0.95/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.95/0.93 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 0.95/0.93 tff(1099,plain,
% 0.95/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.95/0.93 inference(modus_ponens,[status(thm)],[1098, 1094])).
% 0.95/0.93 tff(1100,plain,(
% 0.95/0.93 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.95/0.93 inference(skolemize,[status(sab)],[1099])).
% 0.95/0.93 tff(1101,plain,
% 0.95/0.93 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))),
% 0.95/0.93 inference(modus_ponens,[status(thm)],[1100, 1093])).
% 0.95/0.93 tff(1102,plain,
% 0.95/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a698) | c2_1(a676) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)) | (~c1_1(a698)) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a698) | c2_1(a676) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1103,plain,
% 0.95/0.93 (((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698))) <=> (c0_1(a698) | c2_1(a676) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1104,plain,
% 0.95/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | (c0_1(a698) | c2_1(a676) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)) | (~c1_1(a698)) | (~c3_1(a698))))),
% 0.95/0.93 inference(monotonicity,[status(thm)],[1103])).
% 0.95/0.93 tff(1105,plain,
% 0.95/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a698) | c2_1(a676) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.95/0.93 inference(transitivity,[status(thm)],[1104, 1102])).
% 0.95/0.93 tff(1106,plain,
% 0.95/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a698) | (~c1_1(a698)) | (~c3_1(a698)))),
% 0.95/0.93 inference(quant_inst,[status(thm)],[])).
% 0.95/0.93 tff(1107,plain,
% 0.95/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)) | (~c3_1(W)))) | c0_1(a698) | c2_1(a676) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)) | (~c1_1(a698)) | (~c3_1(a698))),
% 0.95/0.93 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 0.95/0.93 tff(1108,plain,
% 0.95/0.93 (~c3_1(a698)),
% 0.95/0.93 inference(unit_resolution,[status(thm)],[1107, 102, 254, 582, 660, 260, 225, 1083, 1082, 1101, 1091])).
% 0.95/0.93 tff(1109,plain,
% 0.95/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675)))),
% 0.95/0.93 inference(rewrite,[status(thm)],[])).
% 0.95/0.93 tff(1110,plain,
% 0.95/0.93 (((~ndr1_0) | c3_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c1_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675))) <=> (c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(1111,plain,
% 1.03/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c1_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | (c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675))))),
% 1.03/0.93 inference(monotonicity,[status(thm)],[1110])).
% 1.03/0.93 tff(1112,plain,
% 1.03/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c1_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675)))),
% 1.03/0.93 inference(transitivity,[status(thm)],[1111, 1109])).
% 1.03/0.93 tff(1113,plain,
% 1.03/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | ((~ndr1_0) | c3_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c1_1(a675) | (~c2_1(a675)) | (~c0_1(a675)) | c3_1(a675) | c1_1(a675) | (~c0_1(a675)))),
% 1.03/0.93 inference(quant_inst,[status(thm)],[])).
% 1.03/0.93 tff(1114,plain,
% 1.03/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c3_1(W) | c1_1(W) | (~c0_1(W)))) | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 1.03/0.93 tff(1115,plain,
% 1.03/0.93 (~c2_1(a675)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[1114, 102, 1083, 1082, 994, 1091])).
% 1.03/0.93 tff(1116,plain,
% 1.03/0.93 (((~hskp17) | c2_1(a675)) <=> ((~hskp17) | c2_1(a675))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(1117,axiom,((~hskp17) | c2_1(a675)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.03/0.93 tff(1118,plain,
% 1.03/0.93 ((~hskp17) | c2_1(a675)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1117, 1116])).
% 1.03/0.93 tff(1119,plain,
% 1.03/0.93 ((~hskp17) | c2_1(a675)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1118, 1116])).
% 1.03/0.93 tff(1120,plain,
% 1.03/0.93 ((~hskp17) | c2_1(a675)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1119, 1116])).
% 1.03/0.93 tff(1121,plain,
% 1.03/0.93 ((~hskp17) | c2_1(a675)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1120, 1116])).
% 1.03/0.93 tff(1122,plain,
% 1.03/0.93 ((~hskp17) | c2_1(a675)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1121, 1116])).
% 1.03/0.93 tff(1123,plain,
% 1.03/0.93 ((~hskp17) | c2_1(a675)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1122, 1116])).
% 1.03/0.93 tff(1124,plain,
% 1.03/0.93 ((~hskp17) | c2_1(a675)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1123, 1116])).
% 1.03/0.93 tff(1125,plain,
% 1.03/0.93 ((~hskp17) | c2_1(a675)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1124, 1116])).
% 1.03/0.93 tff(1126,plain,
% 1.03/0.93 (~hskp17),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[1125, 1115])).
% 1.03/0.93 tff(1127,plain,
% 1.03/0.93 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(1128,plain,
% 1.03/0.93 ((hskp20 | hskp5 | (~ndr1_0) | c2_1(a675) | c3_1(a675) | (~c0_1(a675))) <=> (hskp20 | hskp5 | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(1129,plain,
% 1.03/0.93 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a675) | c3_1(a675) | (~c0_1(a675)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675))))),
% 1.03/0.93 inference(monotonicity,[status(thm)],[1128])).
% 1.03/0.93 tff(1130,plain,
% 1.03/0.93 (((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a675) | c3_1(a675) | (~c0_1(a675)))) <=> ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)))),
% 1.03/0.93 inference(transitivity,[status(thm)],[1129, 1127])).
% 1.03/0.93 tff(1131,plain,
% 1.03/0.93 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | (hskp20 | hskp5 | (~ndr1_0) | c2_1(a675) | c3_1(a675) | (~c0_1(a675)))),
% 1.03/0.93 inference(quant_inst,[status(thm)],[])).
% 1.03/0.93 tff(1132,plain,
% 1.03/0.93 ((~![U: $i] : (hskp20 | hskp5 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c0_1(U)))) | hskp20 | hskp5 | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675))),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 1.03/0.93 tff(1133,plain,
% 1.03/0.93 (hskp20 | hskp5 | c2_1(a675)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[1132, 102, 1082, 196, 1091])).
% 1.03/0.93 tff(1134,plain,
% 1.03/0.93 (hskp5),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[1133, 207, 1115])).
% 1.03/0.93 tff(1135,plain,
% 1.03/0.93 (~c3_1(a647)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[674, 1134])).
% 1.03/0.93 tff(1136,plain,
% 1.03/0.93 (~c0_1(a647)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[532, 1134])).
% 1.03/0.93 tff(1137,plain,
% 1.03/0.93 (((~hskp5) | c1_1(a647)) <=> ((~hskp5) | c1_1(a647))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(1138,axiom,((~hskp5) | c1_1(a647)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.03/0.93 tff(1139,plain,
% 1.03/0.93 ((~hskp5) | c1_1(a647)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1138, 1137])).
% 1.03/0.93 tff(1140,plain,
% 1.03/0.93 ((~hskp5) | c1_1(a647)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1139, 1137])).
% 1.03/0.93 tff(1141,plain,
% 1.03/0.93 ((~hskp5) | c1_1(a647)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1140, 1137])).
% 1.03/0.93 tff(1142,plain,
% 1.03/0.93 ((~hskp5) | c1_1(a647)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1141, 1137])).
% 1.03/0.93 tff(1143,plain,
% 1.03/0.93 ((~hskp5) | c1_1(a647)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1142, 1137])).
% 1.03/0.93 tff(1144,plain,
% 1.03/0.93 ((~hskp5) | c1_1(a647)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1143, 1137])).
% 1.03/0.93 tff(1145,plain,
% 1.03/0.93 ((~hskp5) | c1_1(a647)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1144, 1137])).
% 1.03/0.93 tff(1146,plain,
% 1.03/0.93 ((~hskp5) | c1_1(a647)),
% 1.03/0.93 inference(modus_ponens,[status(thm)],[1145, 1137])).
% 1.03/0.93 tff(1147,plain,
% 1.03/0.93 (c1_1(a647)),
% 1.03/0.93 inference(unit_resolution,[status(thm)],[1146, 1134])).
% 1.03/0.93 tff(1148,plain,
% 1.03/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a675) | c1_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)) | (~c1_1(a647)) | (~c0_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a675) | c1_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)) | (~c1_1(a647)) | (~c0_1(a675)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(1149,plain,
% 1.03/0.93 (((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a647) | (~c2_1(a647)) | (~c1_1(a647)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (c2_1(a675) | c1_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)) | (~c1_1(a647)) | (~c0_1(a675)))),
% 1.03/0.93 inference(rewrite,[status(thm)],[])).
% 1.03/0.93 tff(1150,plain,
% 1.03/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a647) | (~c2_1(a647)) | (~c1_1(a647)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a675) | c1_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)) | (~c1_1(a647)) | (~c0_1(a675))))),
% 1.03/0.93 inference(monotonicity,[status(thm)],[1149])).
% 1.03/0.93 tff(1151,plain,
% 1.03/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a647) | (~c2_1(a647)) | (~c1_1(a647)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a675) | c1_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)) | (~c1_1(a647)) | (~c0_1(a675)))),
% 1.03/0.94 inference(transitivity,[status(thm)],[1150, 1148])).
% 1.03/0.94 tff(1152,plain,
% 1.03/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a647) | (~c2_1(a647)) | (~c1_1(a647)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(1153,plain,
% 1.03/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a675) | c1_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)) | (~c1_1(a647)) | (~c0_1(a675))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 1.03/0.94 tff(1154,plain,
% 1.03/0.94 (~c2_1(a647)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1153, 102, 1115, 1147, 1083, 1136, 1135, 235, 1091])).
% 1.03/0.94 tff(1155,assumption,(~c2_1(a647)), introduced(assumption)).
% 1.03/0.94 tff(1156,plain,
% 1.03/0.94 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W)))),
% 1.03/0.94 inference(bind,[status(th)],[])).
% 1.03/0.94 tff(1157,plain,
% 1.03/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.03/0.94 inference(quant_intro,[status(thm)],[1156])).
% 1.03/0.94 tff(1158,plain,
% 1.03/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1159,plain,
% 1.03/0.94 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W) | c2_1(W))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W) | c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W) | c2_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c0_1(W) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))))),
% 1.03/0.94 inference(bind,[status(th)],[])).
% 1.03/0.94 tff(1160,plain,
% 1.03/0.94 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.03/0.94 inference(quant_intro,[status(thm)],[1159])).
% 1.03/0.94 tff(1161,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.03/0.94 tff(1162,plain,
% 1.03/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 1.03/0.94 tff(1163,plain,
% 1.03/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1162, 1158])).
% 1.03/0.94 tff(1164,plain,(
% 1.03/0.94 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.03/0.94 inference(skolemize,[status(sab)],[1163])).
% 1.03/0.94 tff(1165,plain,
% 1.03/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1164, 1157])).
% 1.03/0.94 tff(1166,assumption,(c0_1(a675)), introduced(assumption)).
% 1.03/0.94 tff(1167,plain,
% 1.03/0.94 (~c2_1(a675)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1114, 102, 1083, 1082, 994, 1166])).
% 1.03/0.94 tff(1168,assumption,(hskp28), introduced(assumption)).
% 1.03/0.94 tff(1169,plain,
% 1.03/0.94 (c1_1(a671)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[824, 1168])).
% 1.03/0.94 tff(1170,plain,
% 1.03/0.94 (c0_1(a671)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[835, 1168])).
% 1.03/0.94 tff(1171,plain,
% 1.03/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a675) | c1_1(a675) | c3_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a675) | c1_1(a675) | c3_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1172,plain,
% 1.03/0.94 (((~ndr1_0) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | c1_1(a675) | c3_1(a647) | c0_1(a647) | c2_1(a647)) <=> (c2_1(a675) | c1_1(a675) | c3_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1173,plain,
% 1.03/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | c1_1(a675) | c3_1(a647) | c0_1(a647) | c2_1(a647))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | (c2_1(a675) | c1_1(a675) | c3_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671))))),
% 1.03/0.94 inference(monotonicity,[status(thm)],[1172])).
% 1.03/0.94 tff(1174,plain,
% 1.03/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | c1_1(a675) | c3_1(a647) | c0_1(a647) | c2_1(a647))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a675) | c1_1(a675) | c3_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)))),
% 1.03/0.94 inference(transitivity,[status(thm)],[1173, 1171])).
% 1.03/0.94 tff(1175,plain,
% 1.03/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | c1_1(a675) | c3_1(a647) | c0_1(a647) | c2_1(a647))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(1176,plain,
% 1.03/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | c2_1(a675) | c1_1(a675) | c3_1(a675) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a671)) | (~c3_1(a671)) | (~c0_1(a671))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1175, 1174])).
% 1.03/0.94 tff(1177,plain,
% 1.03/0.94 (~c3_1(a671)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1176, 102, 1170, 1169, 1167, 1083, 1082, 261, 236, 1165, 1155])).
% 1.03/0.94 tff(1178,plain,
% 1.03/0.94 (c2_1(a671)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[813, 1168])).
% 1.03/0.94 tff(1179,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1180,plain,
% 1.03/0.94 (((~ndr1_0) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675))) <=> (c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1181,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671))))),
% 1.03/0.94 inference(monotonicity,[status(thm)],[1180])).
% 1.03/0.94 tff(1182,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)))),
% 1.03/0.94 inference(transitivity,[status(thm)],[1181, 1179])).
% 1.03/0.94 tff(1183,plain,
% 1.03/0.94 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675)))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(1184,plain,
% 1.03/0.94 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a675) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | c3_1(a671) | (~c2_1(a671)) | (~c0_1(a671))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1183, 1182])).
% 1.03/0.94 tff(1185,plain,
% 1.03/0.94 ($false),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1184, 102, 1170, 1178, 1167, 1082, 186, 1166, 1177])).
% 1.03/0.94 tff(1186,plain,((~hskp28) | c3_1(a675) | (~c0_1(a675)) | c1_1(a675) | c0_1(a647) | c3_1(a647) | c2_1(a647)), inference(lemma,lemma(discharge,[]))).
% 1.03/0.94 tff(1187,plain,
% 1.03/0.94 (~hskp28),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1186, 1136, 1091, 1083, 1082, 1135, 1154])).
% 1.03/0.94 tff(1188,plain,
% 1.03/0.94 (~hskp1),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[802, 1187, 1126])).
% 1.03/0.94 tff(1189,plain,
% 1.03/0.94 (hskp14),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[508, 1188, 1126])).
% 1.03/0.94 tff(1190,plain,
% 1.03/0.94 (~c0_1(a665)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[56, 1189])).
% 1.03/0.94 tff(1191,plain,
% 1.03/0.94 (~c1_1(a665)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[50, 1189])).
% 1.03/0.94 tff(1192,plain,
% 1.03/0.94 ($false),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[524, 1191, 1190, 23, 24, 254, 243, 1108])).
% 1.03/0.94 tff(1193,plain,(hskp20 | hskp0 | hskp2 | c1_1(a675) | c3_1(a675)), inference(lemma,lemma(discharge,[]))).
% 1.03/0.94 tff(1194,plain,
% 1.03/0.94 (hskp20),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1193, 1082, 24, 1083, 23])).
% 1.03/0.94 tff(1195,plain,
% 1.03/0.94 (~c3_1(a686)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[705, 1194])).
% 1.03/0.94 tff(1196,plain,
% 1.03/0.94 (c2_1(a686)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[717, 1194])).
% 1.03/0.94 tff(1197,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a675) | c3_1(a686) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | (~c0_1(a686)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a675) | c3_1(a686) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | (~c0_1(a686)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1198,plain,
% 1.03/0.94 (((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675))) <=> (c2_1(a675) | c3_1(a686) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | (~c0_1(a686)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1199,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (c2_1(a675) | c3_1(a686) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | (~c0_1(a686))))),
% 1.03/0.94 inference(monotonicity,[status(thm)],[1198])).
% 1.03/0.94 tff(1200,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a675) | c3_1(a686) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | (~c0_1(a686)))),
% 1.03/0.94 inference(transitivity,[status(thm)],[1199, 1197])).
% 1.03/0.94 tff(1201,plain,
% 1.03/0.94 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | ((~ndr1_0) | c3_1(a686) | (~c2_1(a686)) | (~c0_1(a686)) | c3_1(a675) | c2_1(a675) | (~c0_1(a675)))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(1202,plain,
% 1.03/0.94 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | c2_1(a675) | c3_1(a686) | c3_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | (~c0_1(a686))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 1.03/0.94 tff(1203,plain,
% 1.03/0.94 (~c0_1(a686)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1202, 102, 1196, 1115, 1195, 1082, 186, 1091])).
% 1.03/0.94 tff(1204,plain,
% 1.03/0.94 (c1_1(a686)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[735, 1194])).
% 1.03/0.94 tff(1205,plain,
% 1.03/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a675) | c3_1(a686) | c1_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a675) | c3_1(a686) | c1_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1206,plain,
% 1.03/0.94 (((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686))) <=> (c2_1(a675) | c3_1(a686) | c1_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1207,plain,
% 1.03/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a675) | c3_1(a686) | c1_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686))))),
% 1.03/0.94 inference(monotonicity,[status(thm)],[1206])).
% 1.03/0.94 tff(1208,plain,
% 1.03/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a675) | c3_1(a686) | c1_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686)))),
% 1.03/0.94 inference(transitivity,[status(thm)],[1207, 1205])).
% 1.03/0.94 tff(1209,plain,
% 1.03/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a675) | c1_1(a675) | (~c0_1(a675)) | c0_1(a686) | (~c2_1(a686)) | (~c1_1(a686)) | c3_1(a686) | c0_1(a686) | (~c1_1(a686)))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(1210,plain,
% 1.03/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a675) | c3_1(a686) | c1_1(a675) | (~ndr1_0) | (~c0_1(a675)) | (~c2_1(a686)) | c0_1(a686) | (~c1_1(a686))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 1.03/0.94 tff(1211,plain,
% 1.03/0.94 ($false),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1210, 102, 1204, 1196, 1115, 1195, 1083, 235, 1091, 1203])).
% 1.03/0.94 tff(1212,plain,(c3_1(a675) | c1_1(a675) | hskp2 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.03/0.94 tff(1213,plain,
% 1.03/0.94 ($false),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1212, 1081, 1075, 24, 23])).
% 1.03/0.94 tff(1214,plain,(hskp2 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.03/0.94 tff(1215,plain,
% 1.03/0.94 (hskp2),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1214, 23])).
% 1.03/0.94 tff(1216,plain,
% 1.03/0.94 (((~hskp2) | (~c0_1(a643))) <=> ((~hskp2) | (~c0_1(a643)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1217,plain,
% 1.03/0.94 (((~c0_1(a643)) | (~hskp2)) <=> ((~hskp2) | (~c0_1(a643)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1218,axiom,((~c0_1(a643)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.03/0.94 tff(1219,plain,
% 1.03/0.94 ((~hskp2) | (~c0_1(a643))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 1.03/0.94 tff(1220,plain,
% 1.03/0.94 ((~hskp2) | (~c0_1(a643))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1219, 1216])).
% 1.03/0.94 tff(1221,plain,
% 1.03/0.94 (~c0_1(a643)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1220, 1215])).
% 1.03/0.94 tff(1222,plain,
% 1.03/0.94 (((~hskp2) | c2_1(a643)) <=> ((~hskp2) | c2_1(a643))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1223,axiom,((~hskp2) | c2_1(a643)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.03/0.94 tff(1224,plain,
% 1.03/0.94 ((~hskp2) | c2_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 1.03/0.94 tff(1225,plain,
% 1.03/0.94 ((~hskp2) | c2_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1224, 1222])).
% 1.03/0.94 tff(1226,plain,
% 1.03/0.94 ((~hskp2) | c2_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1225, 1222])).
% 1.03/0.94 tff(1227,plain,
% 1.03/0.94 ((~hskp2) | c2_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1226, 1222])).
% 1.03/0.94 tff(1228,plain,
% 1.03/0.94 ((~hskp2) | c2_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1227, 1222])).
% 1.03/0.94 tff(1229,plain,
% 1.03/0.94 ((~hskp2) | c2_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1228, 1222])).
% 1.03/0.94 tff(1230,plain,
% 1.03/0.94 ((~hskp2) | c2_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1229, 1222])).
% 1.03/0.94 tff(1231,plain,
% 1.03/0.94 ((~hskp2) | c2_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1230, 1222])).
% 1.03/0.94 tff(1232,plain,
% 1.03/0.94 (c2_1(a643)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1231, 1215])).
% 1.03/0.94 tff(1233,plain,
% 1.03/0.94 (((~hskp2) | c1_1(a643)) <=> ((~hskp2) | c1_1(a643))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1234,axiom,((~hskp2) | c1_1(a643)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 1.03/0.94 tff(1235,plain,
% 1.03/0.94 ((~hskp2) | c1_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 1.03/0.94 tff(1236,plain,
% 1.03/0.94 ((~hskp2) | c1_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1235, 1233])).
% 1.03/0.94 tff(1237,plain,
% 1.03/0.94 ((~hskp2) | c1_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1236, 1233])).
% 1.03/0.94 tff(1238,plain,
% 1.03/0.94 ((~hskp2) | c1_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1237, 1233])).
% 1.03/0.94 tff(1239,plain,
% 1.03/0.94 ((~hskp2) | c1_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1238, 1233])).
% 1.03/0.94 tff(1240,plain,
% 1.03/0.94 ((~hskp2) | c1_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1239, 1233])).
% 1.03/0.94 tff(1241,plain,
% 1.03/0.94 ((~hskp2) | c1_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1240, 1233])).
% 1.03/0.94 tff(1242,plain,
% 1.03/0.94 ((~hskp2) | c1_1(a643)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1241, 1233])).
% 1.03/0.94 tff(1243,plain,
% 1.03/0.94 (c1_1(a643)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1242, 1215])).
% 1.03/0.94 tff(1244,assumption,(c1_1(a643)), introduced(assumption)).
% 1.03/0.94 tff(1245,assumption,(~c0_1(a643)), introduced(assumption)).
% 1.03/0.94 tff(1246,assumption,(c2_1(a643)), introduced(assumption)).
% 1.03/0.94 tff(1247,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1248,plain,
% 1.03/0.94 ((hskp5 | (~ndr1_0) | c1_1(a665) | c3_1(a665) | (~c2_1(a665)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665))) <=> (hskp5 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1249,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a665) | c3_1(a665) | (~c2_1(a665)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665)))),
% 1.03/0.94 inference(monotonicity,[status(thm)],[1248])).
% 1.03/0.94 tff(1250,plain,
% 1.03/0.94 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a665) | c3_1(a665) | (~c2_1(a665)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665))),
% 1.03/0.94 inference(transitivity,[status(thm)],[1249, 1247])).
% 1.03/0.94 tff(1251,plain,
% 1.03/0.94 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a665) | c3_1(a665) | (~c2_1(a665)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)))),
% 1.03/0.94 inference(quant_inst,[status(thm)],[])).
% 1.03/0.94 tff(1252,plain,
% 1.03/0.94 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665)),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1251, 1250])).
% 1.03/0.94 tff(1253,plain,
% 1.03/0.94 (c3_1(a665)),
% 1.03/0.94 inference(unit_resolution,[status(thm)],[1252, 102, 2, 68, 57, 51, 12])).
% 1.03/0.94 tff(1254,plain,
% 1.03/0.94 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_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)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 1.03/0.94 inference(bind,[status(th)],[])).
% 1.03/0.94 tff(1255,plain,
% 1.03/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.03/0.94 inference(quant_intro,[status(thm)],[1254])).
% 1.03/0.94 tff(1256,plain,
% 1.03/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.03/0.94 inference(rewrite,[status(thm)],[])).
% 1.03/0.94 tff(1257,plain,
% 1.03/0.94 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_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)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_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)) | (~c1_1(U)) | (~c3_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)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_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)) | (~c1_1(U)) | (~c3_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)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_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)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_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))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_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))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_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))) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_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))) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 1.03/0.94 inference(bind,[status(th)],[])).
% 1.03/0.94 tff(1258,plain,
% 1.03/0.94 (![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))) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.03/0.94 inference(quant_intro,[status(thm)],[1257])).
% 1.03/0.94 tff(1259,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))) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.03/0.94 tff(1260,plain,
% 1.03/0.94 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.03/0.94 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 1.03/0.95 tff(1261,plain,
% 1.03/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1260, 1256])).
% 1.03/0.95 tff(1262,plain,(
% 1.03/0.95 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.03/0.95 inference(skolemize,[status(sab)],[1261])).
% 1.03/0.95 tff(1263,plain,
% 1.03/0.95 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1262, 1255])).
% 1.03/0.95 tff(1264,plain,
% 1.03/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1265,plain,
% 1.03/0.95 (((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1266,plain,
% 1.03/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665))))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[1265])).
% 1.03/0.95 tff(1267,plain,
% 1.03/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 1.03/0.95 inference(transitivity,[status(thm)],[1266, 1264])).
% 1.03/0.95 tff(1268,plain,
% 1.03/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 1.03/0.95 inference(quant_inst,[status(thm)],[])).
% 1.03/0.95 tff(1269,plain,
% 1.03/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 1.03/0.95 tff(1270,plain,
% 1.03/0.95 (~c3_1(a643)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1269, 102, 68, 1244, 1246, 51, 1245, 1263, 1253])).
% 1.03/0.95 tff(1271,plain,
% 1.03/0.95 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.03/0.95 inference(bind,[status(th)],[])).
% 1.03/0.95 tff(1272,plain,
% 1.03/0.95 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.03/0.95 inference(quant_intro,[status(thm)],[1271])).
% 1.03/0.95 tff(1273,plain,
% 1.03/0.95 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1274,plain,
% 1.03/0.95 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp27))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.03/0.95 inference(bind,[status(th)],[])).
% 1.03/0.95 tff(1275,plain,
% 1.03/0.95 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.03/0.95 inference(quant_intro,[status(thm)],[1274])).
% 1.03/0.95 tff(1276,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 1.03/0.95 tff(1277,plain,
% 1.03/0.95 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 1.03/0.95 tff(1278,plain,
% 1.03/0.95 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1277, 1273])).
% 1.03/0.95 tff(1279,plain,(
% 1.03/0.95 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.03/0.95 inference(skolemize,[status(sab)],[1278])).
% 1.03/0.95 tff(1280,plain,
% 1.03/0.95 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1279, 1272])).
% 1.03/0.95 tff(1281,plain,
% 1.03/0.95 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | c1_1(a665) | c0_1(a643) | (~ndr1_0) | c3_1(a643) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c1_1(a665) | c0_1(a643) | (~ndr1_0) | c3_1(a643) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1282,plain,
% 1.03/0.95 ((hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643))) <=> (hskp27 | c1_1(a665) | c0_1(a643) | (~ndr1_0) | c3_1(a643) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1283,plain,
% 1.03/0.95 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | c1_1(a665) | c0_1(a643) | (~ndr1_0) | c3_1(a643) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665))))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[1282])).
% 1.03/0.95 tff(1284,plain,
% 1.03/0.95 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c1_1(a665) | c0_1(a643) | (~ndr1_0) | c3_1(a643) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 1.03/0.95 inference(transitivity,[status(thm)],[1283, 1281])).
% 1.03/0.95 tff(1285,plain,
% 1.03/0.95 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643)))),
% 1.03/0.95 inference(quant_inst,[status(thm)],[])).
% 1.03/0.95 tff(1286,plain,
% 1.03/0.95 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c1_1(a665) | c0_1(a643) | (~ndr1_0) | c3_1(a643) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665))),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 1.03/0.95 tff(1287,plain,
% 1.03/0.95 (hskp27),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1286, 102, 68, 1244, 51, 1245, 1280, 1270, 1253])).
% 1.03/0.95 tff(1288,plain,
% 1.03/0.95 (((~hskp27) | c3_1(a655)) <=> ((~hskp27) | c3_1(a655))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1289,axiom,((~hskp27) | c3_1(a655)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 1.03/0.95 tff(1290,plain,
% 1.03/0.95 ((~hskp27) | c3_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1289, 1288])).
% 1.03/0.95 tff(1291,plain,
% 1.03/0.95 ((~hskp27) | c3_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1290, 1288])).
% 1.03/0.95 tff(1292,plain,
% 1.03/0.95 ((~hskp27) | c3_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1291, 1288])).
% 1.03/0.95 tff(1293,plain,
% 1.03/0.95 ((~hskp27) | c3_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1292, 1288])).
% 1.03/0.95 tff(1294,plain,
% 1.03/0.95 ((~hskp27) | c3_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1293, 1288])).
% 1.03/0.95 tff(1295,plain,
% 1.03/0.95 ((~hskp27) | c3_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1294, 1288])).
% 1.03/0.95 tff(1296,plain,
% 1.03/0.95 ((~hskp27) | c3_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1295, 1288])).
% 1.03/0.95 tff(1297,plain,
% 1.03/0.95 ((~hskp27) | c3_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1296, 1288])).
% 1.03/0.95 tff(1298,plain,
% 1.03/0.95 (c3_1(a655)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1297, 1287])).
% 1.03/0.95 tff(1299,plain,
% 1.03/0.95 (((~hskp27) | c2_1(a655)) <=> ((~hskp27) | c2_1(a655))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1300,axiom,((~hskp27) | c2_1(a655)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 1.03/0.95 tff(1301,plain,
% 1.03/0.95 ((~hskp27) | c2_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 1.03/0.95 tff(1302,plain,
% 1.03/0.95 ((~hskp27) | c2_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1301, 1299])).
% 1.03/0.95 tff(1303,plain,
% 1.03/0.95 ((~hskp27) | c2_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1302, 1299])).
% 1.03/0.95 tff(1304,plain,
% 1.03/0.95 ((~hskp27) | c2_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1303, 1299])).
% 1.03/0.95 tff(1305,plain,
% 1.03/0.95 ((~hskp27) | c2_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1304, 1299])).
% 1.03/0.95 tff(1306,plain,
% 1.03/0.95 ((~hskp27) | c2_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1305, 1299])).
% 1.03/0.95 tff(1307,plain,
% 1.03/0.95 ((~hskp27) | c2_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1306, 1299])).
% 1.03/0.95 tff(1308,plain,
% 1.03/0.95 ((~hskp27) | c2_1(a655)),
% 1.03/0.95 inference(modus_ponens,[status(thm)],[1307, 1299])).
% 1.03/0.95 tff(1309,plain,
% 1.03/0.95 (c2_1(a655)),
% 1.03/0.95 inference(unit_resolution,[status(thm)],[1308, 1287])).
% 1.03/0.95 tff(1310,plain,
% 1.03/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1311,plain,
% 1.03/0.95 (((~ndr1_0) | (~c2_1(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))),
% 1.03/0.95 inference(rewrite,[status(thm)],[])).
% 1.03/0.95 tff(1312,plain,
% 1.03/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655))))),
% 1.03/0.95 inference(monotonicity,[status(thm)],[1311])).
% 1.03/0.95 tff(1313,plain,
% 1.03/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))),
% 1.03/0.95 inference(transitivity,[status(thm)],[1312, 1310])).
% 1.03/0.95 tff(1314,plain,
% 1.03/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 1.03/0.95 inference(quant_inst,[status(thm)],[])).
% 1.03/0.95 tff(1315,plain,
% 1.03/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a665)) | (~c3_1(a665)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 1.03/0.96 tff(1316,plain,
% 1.03/0.96 (~c1_1(a655)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1315, 102, 1309, 1298, 68, 1244, 1246, 51, 1245, 1263, 1253])).
% 1.03/0.96 tff(1317,plain,
% 1.03/0.96 (((~hskp27) | c0_1(a655)) <=> ((~hskp27) | c0_1(a655))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1318,axiom,((~hskp27) | c0_1(a655)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 1.03/0.96 tff(1319,plain,
% 1.03/0.96 ((~hskp27) | c0_1(a655)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 1.03/0.96 tff(1320,plain,
% 1.03/0.96 ((~hskp27) | c0_1(a655)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1319, 1317])).
% 1.03/0.96 tff(1321,plain,
% 1.03/0.96 ((~hskp27) | c0_1(a655)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1320, 1317])).
% 1.03/0.96 tff(1322,plain,
% 1.03/0.96 ((~hskp27) | c0_1(a655)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1321, 1317])).
% 1.03/0.96 tff(1323,plain,
% 1.03/0.96 ((~hskp27) | c0_1(a655)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1322, 1317])).
% 1.03/0.96 tff(1324,plain,
% 1.03/0.96 ((~hskp27) | c0_1(a655)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1323, 1317])).
% 1.03/0.96 tff(1325,plain,
% 1.03/0.96 ((~hskp27) | c0_1(a655)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1324, 1317])).
% 1.03/0.96 tff(1326,plain,
% 1.03/0.96 ((~hskp27) | c0_1(a655)),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1325, 1317])).
% 1.03/0.96 tff(1327,plain,
% 1.03/0.96 (c0_1(a655)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1326, 1287])).
% 1.03/0.96 tff(1328,plain,
% 1.03/0.96 (((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c1_1(a655) | (~c3_1(a655)) | (~c0_1(a655)))) <=> ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp17 | (~ndr1_0) | c1_1(a655) | (~c3_1(a655)) | (~c0_1(a655)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1329,plain,
% 1.03/0.96 ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp28 | hskp17 | (~ndr1_0) | c1_1(a655) | (~c3_1(a655)) | (~c0_1(a655)))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(1330,plain,
% 1.03/0.96 ((~![U: $i] : (hskp28 | hskp17 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp28 | hskp17 | (~ndr1_0) | c1_1(a655) | (~c3_1(a655)) | (~c0_1(a655))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1329, 1328])).
% 1.03/0.96 tff(1331,plain,
% 1.03/0.96 (hskp28 | c1_1(a655)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1330, 102, 1, 1327, 1298, 793])).
% 1.03/0.96 tff(1332,plain,
% 1.03/0.96 (hskp28),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1331, 1316])).
% 1.03/0.96 tff(1333,plain,
% 1.03/0.96 (c2_1(a671)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[813, 1332])).
% 1.03/0.96 tff(1334,plain,
% 1.03/0.96 (c1_1(a671)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[824, 1332])).
% 1.03/0.96 tff(1335,plain,
% 1.03/0.96 (c0_1(a671)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[835, 1332])).
% 1.03/0.96 tff(1336,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | (~c2_1(a655)) | c1_1(a655) | (~c3_1(a655)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | (~c2_1(a655)) | c1_1(a655) | (~c3_1(a655)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1337,plain,
% 1.03/0.96 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a655) | (~c2_1(a655)) | (~c3_1(a655)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | (~c2_1(a655)) | c1_1(a655) | (~c3_1(a655)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1338,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a655) | (~c2_1(a655)) | (~c3_1(a655)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | (~c2_1(a655)) | c1_1(a655) | (~c3_1(a655))))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[1337])).
% 1.03/0.96 tff(1339,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a655) | (~c2_1(a655)) | (~c3_1(a655)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | (~c2_1(a655)) | c1_1(a655) | (~c3_1(a655)))),
% 1.03/0.96 inference(transitivity,[status(thm)],[1338, 1336])).
% 1.03/0.96 tff(1340,plain,
% 1.03/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a655) | (~c2_1(a655)) | (~c3_1(a655)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(1341,plain,
% 1.03/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | (~c2_1(a655)) | c1_1(a655) | (~c3_1(a655))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1340, 1339])).
% 1.03/0.96 tff(1342,plain,
% 1.03/0.96 ($false),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1341, 102, 1335, 1334, 1333, 1309, 1298, 1244, 1246, 1245, 923, 1316])).
% 1.03/0.96 tff(1343,plain,((~hskp14) | (~c1_1(a643)) | (~c2_1(a643)) | c0_1(a643) | hskp17 | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.03/0.96 tff(1344,plain,
% 1.03/0.96 (~hskp14),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1343, 2, 1246, 1245, 1, 1244])).
% 1.03/0.96 tff(1345,plain,
% 1.03/0.96 (hskp1),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[508, 1344, 1])).
% 1.03/0.96 tff(1346,plain,
% 1.03/0.96 (~c1_1(a642)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[391, 1345])).
% 1.03/0.96 tff(1347,plain,
% 1.03/0.96 (c3_1(a642)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[414, 1345])).
% 1.03/0.96 tff(1348,plain,
% 1.03/0.96 (hskp28),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[802, 1345, 1])).
% 1.03/0.96 tff(1349,plain,
% 1.03/0.96 (c2_1(a671)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[813, 1348])).
% 1.03/0.96 tff(1350,plain,
% 1.03/0.96 (c1_1(a671)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[824, 1348])).
% 1.03/0.96 tff(1351,plain,
% 1.03/0.96 (c0_1(a671)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[835, 1348])).
% 1.03/0.96 tff(1352,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1353,plain,
% 1.03/0.96 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1354,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[1353])).
% 1.03/0.96 tff(1355,plain,
% 1.03/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.03/0.96 inference(transitivity,[status(thm)],[1354, 1352])).
% 1.03/0.96 tff(1356,plain,
% 1.03/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(1357,plain,
% 1.03/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 1.03/0.96 tff(1358,plain,
% 1.03/0.96 (~c2_1(a642)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1357, 102, 1351, 1350, 1349, 1244, 1246, 1347, 1245, 1346, 923])).
% 1.03/0.96 tff(1359,plain,
% 1.03/0.96 (c0_1(a642)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[403, 1345])).
% 1.03/0.96 tff(1360,plain,
% 1.03/0.96 (hskp23),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[771, 102, 2, 1359, 1347, 600, 1358])).
% 1.03/0.96 tff(1361,plain,
% 1.03/0.96 (~c3_1(a695)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[613, 1360])).
% 1.03/0.96 tff(1362,plain,
% 1.03/0.96 (~c0_1(a695)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[619, 1360])).
% 1.03/0.96 tff(1363,plain,
% 1.03/0.96 (c2_1(a695)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[641, 1360])).
% 1.03/0.96 tff(1364,plain,
% 1.03/0.96 (~c1_1(a695)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[782, 102, 1363, 1359, 1362, 1361, 1346, 235, 1358])).
% 1.03/0.96 tff(1365,plain,
% 1.03/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695) | (~c2_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695) | (~c2_1(a695)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1366,plain,
% 1.03/0.96 ((hskp5 | (~ndr1_0) | c1_1(a695) | c3_1(a695) | (~c2_1(a695)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695))) <=> (hskp5 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695) | (~c2_1(a695)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1367,plain,
% 1.03/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a695) | c3_1(a695) | (~c2_1(a695)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695) | (~c2_1(a695))))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[1366])).
% 1.03/0.96 tff(1368,plain,
% 1.03/0.96 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a695) | c3_1(a695) | (~c2_1(a695)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695) | (~c2_1(a695)))),
% 1.03/0.96 inference(transitivity,[status(thm)],[1367, 1365])).
% 1.03/0.96 tff(1369,plain,
% 1.03/0.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a695) | c3_1(a695) | (~c2_1(a695)) | c0_1(a695) | c1_1(a695) | (~c2_1(a695)))),
% 1.03/0.96 inference(quant_inst,[status(thm)],[])).
% 1.03/0.96 tff(1370,plain,
% 1.03/0.96 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a695) | c3_1(a695) | (~ndr1_0) | c1_1(a695) | (~c2_1(a695))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 1.03/0.96 tff(1371,plain,
% 1.03/0.96 ($false),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1370, 102, 2, 1363, 1362, 1361, 12, 1364])).
% 1.03/0.96 tff(1372,plain,(hskp5 | (~c1_1(a643)) | (~c2_1(a643)) | c0_1(a643) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.03/0.96 tff(1373,plain,
% 1.03/0.96 (hskp5),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[1372, 1, 1232, 1221, 1243])).
% 1.03/0.96 tff(1374,plain,
% 1.03/0.96 (~c0_1(a647)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[532, 1373])).
% 1.03/0.96 tff(1375,plain,
% 1.03/0.96 (~c3_1(a647)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[674, 1373])).
% 1.03/0.96 tff(1376,assumption,(~hskp1), introduced(assumption)).
% 1.03/0.96 tff(1377,assumption,(c3_1(a665)), introduced(assumption)).
% 1.03/0.96 tff(1378,plain,
% 1.03/0.96 (hskp14),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[508, 1376, 1])).
% 1.03/0.96 tff(1379,plain,
% 1.03/0.96 (~c1_1(a665)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[50, 1378])).
% 1.03/0.96 tff(1380,plain,
% 1.03/0.96 (c2_1(a665)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[67, 1378])).
% 1.03/0.96 tff(1381,plain,
% 1.03/0.96 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)))),
% 1.03/0.96 inference(bind,[status(th)],[])).
% 1.03/0.96 tff(1382,plain,
% 1.03/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.03/0.96 inference(quant_intro,[status(thm)],[1381])).
% 1.03/0.96 tff(1383,plain,
% 1.03/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1384,plain,
% 1.03/0.96 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))))),
% 1.03/0.96 inference(bind,[status(th)],[])).
% 1.03/0.96 tff(1385,plain,
% 1.03/0.96 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.03/0.96 inference(quant_intro,[status(thm)],[1384])).
% 1.03/0.96 tff(1386,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 1.03/0.96 tff(1387,plain,
% 1.03/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1386, 1385])).
% 1.03/0.96 tff(1388,plain,
% 1.03/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1387, 1383])).
% 1.03/0.96 tff(1389,plain,(
% 1.03/0.96 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.03/0.96 inference(skolemize,[status(sab)],[1388])).
% 1.03/0.96 tff(1390,plain,
% 1.03/0.96 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))),
% 1.03/0.96 inference(modus_ponens,[status(thm)],[1389, 1382])).
% 1.03/0.96 tff(1391,plain,
% 1.03/0.96 (~c0_1(a665)),
% 1.03/0.96 inference(unit_resolution,[status(thm)],[56, 1378])).
% 1.03/0.96 tff(1392,plain,
% 1.03/0.96 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | c1_1(a647) | c0_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c1_1(a647) | c0_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1393,plain,
% 1.03/0.96 ((hskp1 | (~ndr1_0) | c0_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | c1_1(a647)) <=> (hskp1 | c1_1(a647) | c0_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))),
% 1.03/0.96 inference(rewrite,[status(thm)],[])).
% 1.03/0.96 tff(1394,plain,
% 1.03/0.96 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | c1_1(a647))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | c1_1(a647) | c0_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665))))),
% 1.03/0.96 inference(monotonicity,[status(thm)],[1393])).
% 1.03/0.96 tff(1395,plain,
% 1.03/0.96 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | c1_1(a647))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c1_1(a647) | c0_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665)))),
% 1.03/0.97 inference(transitivity,[status(thm)],[1394, 1392])).
% 1.03/0.97 tff(1396,plain,
% 1.03/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | c1_1(a647))),
% 1.03/0.97 inference(quant_inst,[status(thm)],[])).
% 1.03/0.97 tff(1397,plain,
% 1.03/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c1_1(a647) | c0_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a665)) | (~c3_1(a665))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1396, 1395])).
% 1.03/0.97 tff(1398,plain,
% 1.03/0.97 (c1_1(a647) | (~c3_1(a665))),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1397, 102, 1376, 1380, 1391, 261, 236, 1390])).
% 1.03/0.97 tff(1399,plain,
% 1.03/0.97 (c1_1(a647)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1398, 1377])).
% 1.03/0.97 tff(1400,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | c1_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c2_1(a665)) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c1_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1401,plain,
% 1.03/0.97 ((hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (hskp27 | c1_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1402,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | c1_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c2_1(a665)) | (~c3_1(a665))))),
% 1.03/0.97 inference(monotonicity,[status(thm)],[1401])).
% 1.03/0.97 tff(1403,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c1_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c2_1(a665)) | (~c3_1(a665)))),
% 1.03/0.97 inference(transitivity,[status(thm)],[1402, 1400])).
% 1.03/0.97 tff(1404,plain,
% 1.03/0.97 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a665) | (~c2_1(a665)) | (~c3_1(a665)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 1.03/0.97 inference(quant_inst,[status(thm)],[])).
% 1.03/0.97 tff(1405,plain,
% 1.03/0.97 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c1_1(a665) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c1_1(a647)) | (~c2_1(a665)) | (~c3_1(a665))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1404, 1403])).
% 1.03/0.97 tff(1406,plain,
% 1.03/0.97 (hskp27 | (~c1_1(a647)) | (~c3_1(a665))),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1405, 102, 1380, 1379, 261, 236, 1280])).
% 1.03/0.97 tff(1407,plain,
% 1.03/0.97 (hskp27),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1406, 1399, 1377])).
% 1.03/0.97 tff(1408,plain,
% 1.03/0.97 (c3_1(a655)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1297, 1407])).
% 1.03/0.97 tff(1409,plain,
% 1.03/0.97 (c2_1(a655)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1308, 1407])).
% 1.03/0.97 tff(1410,plain,
% 1.03/0.97 (~c1_1(a655)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1315, 102, 1409, 1408, 1380, 1244, 1246, 1379, 1245, 1263, 1377])).
% 1.03/0.97 tff(1411,plain,
% 1.03/0.97 (c0_1(a655)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1326, 1407])).
% 1.03/0.97 tff(1412,plain,
% 1.03/0.97 (hskp28 | c1_1(a655)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1330, 102, 1, 1411, 1408, 793])).
% 1.03/0.97 tff(1413,plain,
% 1.03/0.97 (hskp28),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1412, 1410])).
% 1.03/0.97 tff(1414,plain,
% 1.03/0.97 (c2_1(a671)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[813, 1413])).
% 1.03/0.97 tff(1415,plain,
% 1.03/0.97 (c1_1(a671)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[824, 1413])).
% 1.03/0.97 tff(1416,plain,
% 1.03/0.97 (c0_1(a671)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[835, 1413])).
% 1.03/0.97 tff(1417,plain,
% 1.03/0.97 ($false),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1341, 102, 1416, 1415, 1414, 1409, 1408, 1244, 1246, 1245, 923, 1410])).
% 1.03/0.97 tff(1418,plain,((~c3_1(a665)) | (~c1_1(a643)) | (~c2_1(a643)) | c0_1(a643) | hskp17 | c0_1(a647) | c3_1(a647) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.03/0.97 tff(1419,plain,
% 1.03/0.97 (~c3_1(a665)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1418, 1376, 1246, 1245, 1, 261, 236, 1244])).
% 1.03/0.97 tff(1420,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | c0_1(a665) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c0_1(a665) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1421,plain,
% 1.03/0.97 ((hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665) | c0_1(a665) | c1_1(a665)) <=> (hskp1 | c0_1(a665) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1422,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665) | c0_1(a665) | c1_1(a665))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | c0_1(a665) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665)))),
% 1.03/0.97 inference(monotonicity,[status(thm)],[1421])).
% 1.03/0.97 tff(1423,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665) | c0_1(a665) | c1_1(a665))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c0_1(a665) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665))),
% 1.03/0.97 inference(transitivity,[status(thm)],[1422, 1420])).
% 1.03/0.97 tff(1424,plain,
% 1.03/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665) | c0_1(a665) | c1_1(a665))),
% 1.03/0.97 inference(quant_inst,[status(thm)],[])).
% 1.03/0.97 tff(1425,plain,
% 1.03/0.97 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c0_1(a665) | c1_1(a665) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a665)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1424, 1423])).
% 1.03/0.97 tff(1426,plain,
% 1.03/0.97 (~c3_1(a643)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1425, 102, 1376, 1246, 1391, 1379, 1245, 1390, 1419])).
% 1.03/0.97 tff(1427,plain,
% 1.03/0.97 (hskp5 | c3_1(a665)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1252, 102, 1380, 1391, 1379, 12])).
% 1.03/0.97 tff(1428,plain,
% 1.03/0.97 (hskp5),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1427, 1419])).
% 1.03/0.97 tff(1429,plain,
% 1.03/0.97 (c1_1(a647)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1146, 1428])).
% 1.03/0.97 tff(1430,assumption,(~c3_1(a643)), introduced(assumption)).
% 1.03/0.97 tff(1431,assumption,(~hskp6), introduced(assumption)).
% 1.03/0.97 tff(1432,plain,
% 1.03/0.97 (^[U: $i] : refl((hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))),
% 1.03/0.97 inference(bind,[status(th)],[])).
% 1.03/0.97 tff(1433,plain,
% 1.03/0.97 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.03/0.97 inference(quant_intro,[status(thm)],[1432])).
% 1.03/0.97 tff(1434,plain,
% 1.03/0.97 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1435,plain,
% 1.03/0.97 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp6) | hskp3) <=> ((hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp3))), rewrite(((hskp6 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U))) | hskp3) <=> (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp6) | hskp3) <=> (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))))),
% 1.03/0.97 inference(bind,[status(th)],[])).
% 1.03/0.97 tff(1436,plain,
% 1.03/0.97 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp6) | hskp3) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.03/0.97 inference(quant_intro,[status(thm)],[1435])).
% 1.03/0.97 tff(1437,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp6) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.03/0.97 tff(1438,plain,
% 1.03/0.97 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 1.03/0.97 tff(1439,plain,
% 1.03/0.97 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1438, 1434])).
% 1.03/0.97 tff(1440,plain,(
% 1.03/0.97 ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.03/0.97 inference(skolemize,[status(sab)],[1439])).
% 1.03/0.97 tff(1441,plain,
% 1.03/0.97 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1440, 1433])).
% 1.03/0.97 tff(1442,plain,
% 1.03/0.97 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp6 | hskp3 | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp6 | hskp3 | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1443,plain,
% 1.03/0.97 ((hskp6 | hskp3 | (~ndr1_0) | c0_1(a643) | c3_1(a643) | (~c2_1(a643))) <=> (hskp6 | hskp3 | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1444,plain,
% 1.03/0.97 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a643) | c3_1(a643) | (~c2_1(a643)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp6 | hskp3 | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643)))),
% 1.03/0.97 inference(monotonicity,[status(thm)],[1443])).
% 1.03/0.97 tff(1445,plain,
% 1.03/0.97 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a643) | c3_1(a643) | (~c2_1(a643)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp6 | hskp3 | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643))),
% 1.03/0.97 inference(transitivity,[status(thm)],[1444, 1442])).
% 1.03/0.97 tff(1446,plain,
% 1.03/0.97 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a643) | c3_1(a643) | (~c2_1(a643)))),
% 1.03/0.97 inference(quant_inst,[status(thm)],[])).
% 1.03/0.97 tff(1447,plain,
% 1.03/0.97 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | c3_1(U) | (~c2_1(U)))) | hskp6 | hskp3 | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 1.03/0.97 tff(1448,plain,
% 1.03/0.97 (hskp6 | hskp3 | c3_1(a643)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1447, 102, 1246, 1245, 1441])).
% 1.03/0.97 tff(1449,plain,
% 1.03/0.97 (hskp3),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1448, 1431, 1430])).
% 1.03/0.97 tff(1450,plain,
% 1.03/0.97 (((~hskp3) | (~c2_1(a645))) <=> ((~hskp3) | (~c2_1(a645)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1451,plain,
% 1.03/0.97 (((~c2_1(a645)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a645)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1452,axiom,((~c2_1(a645)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.03/0.97 tff(1453,plain,
% 1.03/0.97 ((~hskp3) | (~c2_1(a645))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1452, 1451])).
% 1.03/0.97 tff(1454,plain,
% 1.03/0.97 ((~hskp3) | (~c2_1(a645))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1453, 1450])).
% 1.03/0.97 tff(1455,plain,
% 1.03/0.97 (~c2_1(a645)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1454, 1449])).
% 1.03/0.97 tff(1456,plain,
% 1.03/0.97 (((~hskp3) | c3_1(a645)) <=> ((~hskp3) | c3_1(a645))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1457,axiom,((~hskp3) | c3_1(a645)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.03/0.97 tff(1458,plain,
% 1.03/0.97 ((~hskp3) | c3_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1457, 1456])).
% 1.03/0.97 tff(1459,plain,
% 1.03/0.97 ((~hskp3) | c3_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1458, 1456])).
% 1.03/0.97 tff(1460,plain,
% 1.03/0.97 ((~hskp3) | c3_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1459, 1456])).
% 1.03/0.97 tff(1461,plain,
% 1.03/0.97 ((~hskp3) | c3_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1460, 1456])).
% 1.03/0.97 tff(1462,plain,
% 1.03/0.97 ((~hskp3) | c3_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1461, 1456])).
% 1.03/0.97 tff(1463,plain,
% 1.03/0.97 ((~hskp3) | c3_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1462, 1456])).
% 1.03/0.97 tff(1464,plain,
% 1.03/0.97 ((~hskp3) | c3_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1463, 1456])).
% 1.03/0.97 tff(1465,plain,
% 1.03/0.97 ((~hskp3) | c3_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1464, 1456])).
% 1.03/0.97 tff(1466,plain,
% 1.03/0.97 (c3_1(a645)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1465, 1449])).
% 1.03/0.97 tff(1467,plain,
% 1.03/0.97 (((~hskp3) | c1_1(a645)) <=> ((~hskp3) | c1_1(a645))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1468,axiom,((~hskp3) | c1_1(a645)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.03/0.97 tff(1469,plain,
% 1.03/0.97 ((~hskp3) | c1_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1468, 1467])).
% 1.03/0.97 tff(1470,plain,
% 1.03/0.97 ((~hskp3) | c1_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1469, 1467])).
% 1.03/0.97 tff(1471,plain,
% 1.03/0.97 ((~hskp3) | c1_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1470, 1467])).
% 1.03/0.97 tff(1472,plain,
% 1.03/0.97 ((~hskp3) | c1_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1471, 1467])).
% 1.03/0.97 tff(1473,plain,
% 1.03/0.97 ((~hskp3) | c1_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1472, 1467])).
% 1.03/0.97 tff(1474,plain,
% 1.03/0.97 ((~hskp3) | c1_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1473, 1467])).
% 1.03/0.97 tff(1475,plain,
% 1.03/0.97 ((~hskp3) | c1_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1474, 1467])).
% 1.03/0.97 tff(1476,plain,
% 1.03/0.97 ((~hskp3) | c1_1(a645)),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1475, 1467])).
% 1.03/0.97 tff(1477,plain,
% 1.03/0.97 (c1_1(a645)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1476, 1449])).
% 1.03/0.97 tff(1478,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a647) | c3_1(a647) | c2_1(a645) | (~ndr1_0) | (~c1_1(a645)) | (~c3_1(a645)) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a647) | c3_1(a647) | c2_1(a645) | (~ndr1_0) | (~c1_1(a645)) | (~c3_1(a645)) | (~c1_1(a647)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1479,plain,
% 1.03/0.97 ((hskp6 | (~ndr1_0) | c2_1(a645) | (~c1_1(a645)) | (~c3_1(a645)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (hskp6 | c0_1(a647) | c3_1(a647) | c2_1(a645) | (~ndr1_0) | (~c1_1(a645)) | (~c3_1(a645)) | (~c1_1(a647)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1480,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a645) | (~c1_1(a645)) | (~c3_1(a645)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a647) | c3_1(a647) | c2_1(a645) | (~ndr1_0) | (~c1_1(a645)) | (~c3_1(a645)) | (~c1_1(a647))))),
% 1.03/0.97 inference(monotonicity,[status(thm)],[1479])).
% 1.03/0.97 tff(1481,plain,
% 1.03/0.97 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a645) | (~c1_1(a645)) | (~c3_1(a645)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a647) | c3_1(a647) | c2_1(a645) | (~ndr1_0) | (~c1_1(a645)) | (~c3_1(a645)) | (~c1_1(a647)))),
% 1.03/0.97 inference(transitivity,[status(thm)],[1480, 1478])).
% 1.03/0.97 tff(1482,plain,
% 1.03/0.97 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c2_1(a645) | (~c1_1(a645)) | (~c3_1(a645)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 1.03/0.97 inference(quant_inst,[status(thm)],[])).
% 1.03/0.97 tff(1483,plain,
% 1.03/0.97 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a647) | c3_1(a647) | c2_1(a645) | (~ndr1_0) | (~c1_1(a645)) | (~c3_1(a645)) | (~c1_1(a647))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 1.03/0.97 tff(1484,plain,
% 1.03/0.97 ($false),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1483, 102, 1431, 270, 1477, 1466, 261, 236, 1455, 281])).
% 1.03/0.97 tff(1485,plain,(hskp6 | (~c1_1(a647)) | c0_1(a647) | c3_1(a647) | c3_1(a643) | (~c2_1(a643)) | c0_1(a643)), inference(lemma,lemma(discharge,[]))).
% 1.03/0.97 tff(1486,plain,
% 1.03/0.97 (hskp6),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1485, 1429, 261, 236, 1426, 1246, 1245])).
% 1.03/0.97 tff(1487,plain,
% 1.03/0.97 (~c2_1(a648)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[120, 1486])).
% 1.03/0.97 tff(1488,plain,
% 1.03/0.97 (c0_1(a648)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[328, 1486])).
% 1.03/0.97 tff(1489,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a648) | c0_1(a647) | c3_1(a647) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)) | c1_1(a648) | (~c0_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a648) | c0_1(a647) | c3_1(a647) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)) | c1_1(a648) | (~c0_1(a648)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1490,plain,
% 1.03/0.97 (((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (c2_1(a648) | c0_1(a647) | c3_1(a647) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)) | c1_1(a648) | (~c0_1(a648)))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1491,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a648) | c0_1(a647) | c3_1(a647) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)) | c1_1(a648) | (~c0_1(a648))))),
% 1.03/0.97 inference(monotonicity,[status(thm)],[1490])).
% 1.03/0.97 tff(1492,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a648) | c0_1(a647) | c3_1(a647) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)) | c1_1(a648) | (~c0_1(a648)))),
% 1.03/0.97 inference(transitivity,[status(thm)],[1491, 1489])).
% 1.03/0.97 tff(1493,plain,
% 1.03/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 1.03/0.97 inference(quant_inst,[status(thm)],[])).
% 1.03/0.97 tff(1494,plain,
% 1.03/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a648) | c0_1(a647) | c3_1(a647) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)) | c1_1(a648) | (~c0_1(a648))),
% 1.03/0.97 inference(modus_ponens,[status(thm)],[1493, 1492])).
% 1.03/0.97 tff(1495,plain,
% 1.03/0.97 (c1_1(a648)),
% 1.03/0.97 inference(unit_resolution,[status(thm)],[1494, 102, 1488, 1429, 1244, 1246, 1487, 261, 236, 1245, 235])).
% 1.03/0.97 tff(1496,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a665) | c1_1(a665) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a665)) | c3_1(a665))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a665) | c1_1(a665) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a665)) | c3_1(a665))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1497,plain,
% 1.03/0.97 (((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665)) <=> (c0_1(a665) | c1_1(a665) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a665)) | c3_1(a665))),
% 1.03/0.97 inference(rewrite,[status(thm)],[])).
% 1.03/0.97 tff(1498,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a665) | c1_1(a665) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a665)) | c3_1(a665)))),
% 1.03/0.97 inference(monotonicity,[status(thm)],[1497])).
% 1.03/0.97 tff(1499,plain,
% 1.03/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a665) | c1_1(a665) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a665)) | c3_1(a665))),
% 1.03/0.97 inference(transitivity,[status(thm)],[1498, 1496])).
% 1.03/0.97 tff(1500,plain,
% 1.03/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665))),
% 1.07/0.97 inference(quant_inst,[status(thm)],[])).
% 1.07/0.97 tff(1501,plain,
% 1.07/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c0_1(a665) | c1_1(a665) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a665)) | c3_1(a665)),
% 1.07/0.97 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 1.07/0.97 tff(1502,plain,
% 1.07/0.97 ($false),
% 1.07/0.97 inference(unit_resolution,[status(thm)],[1501, 102, 1380, 1488, 1391, 1379, 1487, 206, 1419, 1495])).
% 1.07/0.97 tff(1503,plain,(hskp1 | (~c1_1(a643)) | (~c2_1(a643)) | c0_1(a647) | c3_1(a647) | c0_1(a643) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.07/0.97 tff(1504,plain,
% 1.07/0.97 (hskp1),
% 1.07/0.97 inference(unit_resolution,[status(thm)],[1503, 261, 1232, 1243, 236, 1221, 1])).
% 1.07/0.97 tff(1505,plain,
% 1.07/0.97 (~c1_1(a642)),
% 1.07/0.97 inference(unit_resolution,[status(thm)],[391, 1504])).
% 1.07/0.97 tff(1506,plain,
% 1.07/0.97 (c3_1(a642)),
% 1.07/0.97 inference(unit_resolution,[status(thm)],[414, 1504])).
% 1.07/0.97 tff(1507,plain,
% 1.07/0.97 (hskp28),
% 1.07/0.97 inference(unit_resolution,[status(thm)],[802, 1504, 1])).
% 1.07/0.97 tff(1508,plain,
% 1.07/0.97 (c2_1(a671)),
% 1.07/0.97 inference(unit_resolution,[status(thm)],[813, 1507])).
% 1.07/0.97 tff(1509,plain,
% 1.07/0.97 (c1_1(a671)),
% 1.07/0.97 inference(unit_resolution,[status(thm)],[824, 1507])).
% 1.07/0.97 tff(1510,plain,
% 1.07/0.97 (c0_1(a671)),
% 1.07/0.97 inference(unit_resolution,[status(thm)],[835, 1507])).
% 1.07/0.97 tff(1511,plain,
% 1.07/0.97 (~c2_1(a642)),
% 1.07/0.97 inference(unit_resolution,[status(thm)],[1357, 102, 1510, 1509, 1508, 1243, 1232, 1506, 1221, 1505, 923])).
% 1.07/0.97 tff(1512,plain,
% 1.07/0.97 (c0_1(a642)),
% 1.07/0.97 inference(unit_resolution,[status(thm)],[403, 1504])).
% 1.07/0.97 tff(1513,plain,
% 1.07/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a647) | c3_1(a647) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a647) | c3_1(a647) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)))),
% 1.07/0.97 inference(rewrite,[status(thm)],[])).
% 1.07/0.97 tff(1514,plain,
% 1.07/0.97 (((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (c0_1(a647) | c3_1(a647) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)))),
% 1.07/0.97 inference(rewrite,[status(thm)],[])).
% 1.07/0.97 tff(1515,plain,
% 1.07/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a647) | c3_1(a647) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647))))),
% 1.07/0.97 inference(monotonicity,[status(thm)],[1514])).
% 1.07/0.97 tff(1516,plain,
% 1.07/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a647) | c3_1(a647) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647)))),
% 1.07/0.97 inference(transitivity,[status(thm)],[1515, 1513])).
% 1.07/0.97 tff(1517,plain,
% 1.07/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a642) | c1_1(a642) | (~c0_1(a642)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 1.07/0.98 inference(quant_inst,[status(thm)],[])).
% 1.07/0.98 tff(1518,plain,
% 1.07/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a647) | c3_1(a647) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | c2_1(a642) | (~c0_1(a642)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c1_1(a647))),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 1.07/0.98 tff(1519,plain,
% 1.07/0.98 (~c1_1(a647)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1518, 102, 1243, 1232, 1512, 261, 236, 1221, 1505, 235, 1511])).
% 1.07/0.98 tff(1520,plain,
% 1.07/0.98 (~c3_1(a665)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[144, 102, 1, 393, 1380, 1379, 22])).
% 1.07/0.98 tff(1521,plain,
% 1.07/0.98 ((hskp18 | hskp7 | hskp1) <=> (hskp18 | hskp7 | hskp1)),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1522,plain,
% 1.07/0.98 (((hskp18 | hskp1) | hskp7) <=> (hskp18 | hskp7 | hskp1)),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1523,plain,
% 1.07/0.98 ((hskp18 | hskp1) <=> (hskp18 | hskp1)),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1524,plain,
% 1.07/0.98 (((hskp18 | hskp1) | hskp7) <=> ((hskp18 | hskp1) | hskp7)),
% 1.07/0.98 inference(monotonicity,[status(thm)],[1523])).
% 1.07/0.98 tff(1525,plain,
% 1.07/0.98 (((hskp18 | hskp1) | hskp7) <=> (hskp18 | hskp7 | hskp1)),
% 1.07/0.98 inference(transitivity,[status(thm)],[1524, 1522])).
% 1.07/0.98 tff(1526,axiom,((hskp18 | hskp1) | hskp7), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause31')).
% 1.07/0.98 tff(1527,plain,
% 1.07/0.98 (hskp18 | hskp7 | hskp1),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1526, 1525])).
% 1.07/0.98 tff(1528,plain,
% 1.07/0.98 (hskp18 | hskp7 | hskp1),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1527, 1521])).
% 1.07/0.98 tff(1529,plain,
% 1.07/0.98 (hskp18 | hskp7 | hskp1),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1528, 1521])).
% 1.07/0.98 tff(1530,plain,
% 1.07/0.98 (hskp18 | hskp7 | hskp1),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1529, 1521])).
% 1.07/0.98 tff(1531,plain,
% 1.07/0.98 (hskp18 | hskp7 | hskp1),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1530, 1521])).
% 1.07/0.98 tff(1532,plain,
% 1.07/0.98 (hskp18 | hskp7 | hskp1),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1531, 1521])).
% 1.07/0.98 tff(1533,plain,
% 1.07/0.98 (hskp18 | hskp7 | hskp1),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1532, 1521])).
% 1.07/0.98 tff(1534,plain,
% 1.07/0.98 (hskp18 | hskp7 | hskp1),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1533, 1521])).
% 1.07/0.98 tff(1535,plain,
% 1.07/0.98 (hskp18),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1534, 1376, 393])).
% 1.07/0.98 tff(1536,plain,
% 1.07/0.98 (~c2_1(a676)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[224, 1535])).
% 1.07/0.98 tff(1537,plain,
% 1.07/0.98 (c1_1(a676)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[659, 1535])).
% 1.07/0.98 tff(1538,plain,
% 1.07/0.98 (c0_1(a676)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[581, 1535])).
% 1.07/0.98 tff(1539,plain,
% 1.07/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a676) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665) | (~c1_1(a676)) | (~c0_1(a676)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a676) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665) | (~c1_1(a676)) | (~c0_1(a676)))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1540,plain,
% 1.07/0.98 (((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665)) <=> (c2_1(a676) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665) | (~c1_1(a676)) | (~c0_1(a676)))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1541,plain,
% 1.07/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a676) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665) | (~c1_1(a676)) | (~c0_1(a676))))),
% 1.07/0.98 inference(monotonicity,[status(thm)],[1540])).
% 1.07/0.98 tff(1542,plain,
% 1.07/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a676) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665) | (~c1_1(a676)) | (~c0_1(a676)))),
% 1.07/0.98 inference(transitivity,[status(thm)],[1541, 1539])).
% 1.07/0.98 tff(1543,plain,
% 1.07/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c0_1(a665) | c1_1(a665) | (~c2_1(a665)) | c3_1(a665) | c1_1(a665) | c0_1(a665))),
% 1.07/0.98 inference(quant_inst,[status(thm)],[])).
% 1.07/0.98 tff(1544,plain,
% 1.07/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c2_1(a676) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c2_1(a665)) | c3_1(a665) | (~c1_1(a676)) | (~c0_1(a676))),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1543, 1542])).
% 1.07/0.98 tff(1545,plain,
% 1.07/0.98 ($false),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1544, 102, 1538, 1537, 1380, 1536, 1391, 1379, 206, 1520])).
% 1.07/0.98 tff(1546,plain,(hskp1 | hskp17 | hskp7), inference(lemma,lemma(discharge,[]))).
% 1.07/0.98 tff(1547,plain,
% 1.07/0.98 (hskp1),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1546, 393, 1])).
% 1.07/0.98 tff(1548,plain,
% 1.07/0.98 (~c1_1(a642)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[391, 1547])).
% 1.07/0.98 tff(1549,plain,
% 1.07/0.98 (c3_1(a642)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[414, 1547])).
% 1.07/0.98 tff(1550,plain,
% 1.07/0.98 (~c2_1(a642)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[423, 102, 1, 393, 1549, 1548, 22])).
% 1.07/0.98 tff(1551,plain,
% 1.07/0.98 (c0_1(a642)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[403, 1547])).
% 1.07/0.98 tff(1552,plain,
% 1.07/0.98 (~c1_1(a647)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1518, 102, 1244, 1246, 1551, 261, 236, 1245, 1548, 235, 1550])).
% 1.07/0.98 tff(1553,plain,
% 1.07/0.98 (~hskp5),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1146, 1552])).
% 1.07/0.98 tff(1554,plain,
% 1.07/0.98 (hskp23 | hskp5 | c2_1(a642)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[771, 102, 1551, 1549, 600])).
% 1.07/0.98 tff(1555,plain,
% 1.07/0.98 (hskp23),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1554, 1553, 1550])).
% 1.07/0.98 tff(1556,plain,
% 1.07/0.98 (~c3_1(a695)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[613, 1555])).
% 1.07/0.98 tff(1557,plain,
% 1.07/0.98 (~c0_1(a695)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[619, 1555])).
% 1.07/0.98 tff(1558,plain,
% 1.07/0.98 (c2_1(a695)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[641, 1555])).
% 1.07/0.98 tff(1559,plain,
% 1.07/0.98 (~c1_1(a695)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[782, 102, 1558, 1551, 1557, 1556, 1548, 235, 1550])).
% 1.07/0.98 tff(1560,plain,
% 1.07/0.98 ($false),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1370, 102, 1553, 1558, 1557, 1556, 12, 1559])).
% 1.07/0.98 tff(1561,plain,(hskp7 | (~c1_1(a643)) | (~c2_1(a643)) | c0_1(a647) | c3_1(a647) | c0_1(a643) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.07/0.98 tff(1562,plain,
% 1.07/0.98 (hskp7),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1561, 261, 1232, 1243, 236, 1221, 1])).
% 1.07/0.98 tff(1563,plain,
% 1.07/0.98 (~c1_1(a651)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[151, 1562])).
% 1.07/0.98 tff(1564,plain,
% 1.07/0.98 (c3_1(a651)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[168, 1562])).
% 1.07/0.98 tff(1565,plain,
% 1.07/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a651) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1566,plain,
% 1.07/0.98 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a651) | (~c2_1(a651)) | (~c3_1(a651)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c1_1(a651) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1567,plain,
% 1.07/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a651) | (~c2_1(a651)) | (~c3_1(a651)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c1_1(a651) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 1.07/0.98 inference(monotonicity,[status(thm)],[1566])).
% 1.07/0.98 tff(1568,plain,
% 1.07/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a651) | (~c2_1(a651)) | (~c3_1(a651)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a651) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/0.98 inference(transitivity,[status(thm)],[1567, 1565])).
% 1.07/0.98 tff(1569,plain,
% 1.07/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a651) | (~c2_1(a651)) | (~c3_1(a651)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 1.07/0.98 inference(quant_inst,[status(thm)],[])).
% 1.07/0.98 tff(1570,plain,
% 1.07/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c1_1(a651) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1569, 1568])).
% 1.07/0.98 tff(1571,plain,
% 1.07/0.98 (~c2_1(a651)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1570, 102, 1510, 1509, 1508, 1564, 1243, 1232, 1563, 1221, 923])).
% 1.07/0.98 tff(1572,plain,
% 1.07/0.98 (^[U: $i] : refl((hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))),
% 1.07/0.98 inference(bind,[status(th)],[])).
% 1.07/0.98 tff(1573,plain,
% 1.07/0.98 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.07/0.98 inference(quant_intro,[status(thm)],[1572])).
% 1.07/0.98 tff(1574,plain,
% 1.07/0.98 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1575,plain,
% 1.07/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp26))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) <=> (hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0) <=> ((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0))), rewrite(((hskp26 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U)) | hskp0) <=> (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0) <=> (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))))),
% 1.07/0.98 inference(bind,[status(th)],[])).
% 1.07/0.98 tff(1576,plain,
% 1.07/0.98 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0) <=> ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.07/0.98 inference(quant_intro,[status(thm)],[1575])).
% 1.07/0.98 tff(1577,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c2_1(U)) | hskp26) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.07/0.98 tff(1578,plain,
% 1.07/0.98 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1577, 1576])).
% 1.07/0.98 tff(1579,plain,
% 1.07/0.98 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1578, 1574])).
% 1.07/0.98 tff(1580,plain,(
% 1.07/0.98 ![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.07/0.98 inference(skolemize,[status(sab)],[1579])).
% 1.07/0.98 tff(1581,plain,
% 1.07/0.98 (![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1580, 1573])).
% 1.07/0.98 tff(1582,plain,
% 1.07/0.98 (~c0_1(a651)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[157, 1562])).
% 1.07/0.98 tff(1583,plain,
% 1.07/0.98 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | c2_1(a651))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | c2_1(a651))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1584,plain,
% 1.07/0.98 ((hskp26 | hskp0 | (~ndr1_0) | c2_1(a651) | c1_1(a651) | c0_1(a651)) <=> (hskp26 | hskp0 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | c2_1(a651))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1585,plain,
% 1.07/0.98 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | c2_1(a651)))),
% 1.07/0.98 inference(monotonicity,[status(thm)],[1584])).
% 1.07/0.98 tff(1586,plain,
% 1.07/0.98 (((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a651) | c1_1(a651) | c0_1(a651))) <=> ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | c2_1(a651))),
% 1.07/0.98 inference(transitivity,[status(thm)],[1585, 1583])).
% 1.07/0.98 tff(1587,plain,
% 1.07/0.98 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | (hskp26 | hskp0 | (~ndr1_0) | c2_1(a651) | c1_1(a651) | c0_1(a651))),
% 1.07/0.98 inference(quant_inst,[status(thm)],[])).
% 1.07/0.98 tff(1588,plain,
% 1.07/0.98 ((~![U: $i] : (hskp26 | hskp0 | (~ndr1_0) | c2_1(U) | c1_1(U) | c0_1(U))) | hskp26 | hskp0 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | c2_1(a651)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1587, 1586])).
% 1.07/0.98 tff(1589,plain,
% 1.07/0.98 (hskp26 | c2_1(a651)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1588, 102, 23, 1582, 1563, 1581])).
% 1.07/0.98 tff(1590,plain,
% 1.07/0.98 (hskp26),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1589, 1571])).
% 1.07/0.98 tff(1591,plain,
% 1.07/0.98 (((~hskp26) | c3_1(a640)) <=> ((~hskp26) | c3_1(a640))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1592,axiom,((~hskp26) | c3_1(a640)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.07/0.98 tff(1593,plain,
% 1.07/0.98 ((~hskp26) | c3_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 1.07/0.98 tff(1594,plain,
% 1.07/0.98 ((~hskp26) | c3_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1593, 1591])).
% 1.07/0.98 tff(1595,plain,
% 1.07/0.98 ((~hskp26) | c3_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1594, 1591])).
% 1.07/0.98 tff(1596,plain,
% 1.07/0.98 ((~hskp26) | c3_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1595, 1591])).
% 1.07/0.98 tff(1597,plain,
% 1.07/0.98 ((~hskp26) | c3_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1596, 1591])).
% 1.07/0.98 tff(1598,plain,
% 1.07/0.98 ((~hskp26) | c3_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1597, 1591])).
% 1.07/0.98 tff(1599,plain,
% 1.07/0.98 ((~hskp26) | c3_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1598, 1591])).
% 1.07/0.98 tff(1600,plain,
% 1.07/0.98 ((~hskp26) | c3_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1599, 1591])).
% 1.07/0.98 tff(1601,plain,
% 1.07/0.98 (c3_1(a640)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1600, 1590])).
% 1.07/0.98 tff(1602,plain,
% 1.07/0.98 (((~hskp26) | c1_1(a640)) <=> ((~hskp26) | c1_1(a640))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1603,axiom,((~hskp26) | c1_1(a640)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.07/0.98 tff(1604,plain,
% 1.07/0.98 ((~hskp26) | c1_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 1.07/0.98 tff(1605,plain,
% 1.07/0.98 ((~hskp26) | c1_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1604, 1602])).
% 1.07/0.98 tff(1606,plain,
% 1.07/0.98 ((~hskp26) | c1_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1605, 1602])).
% 1.07/0.98 tff(1607,plain,
% 1.07/0.98 ((~hskp26) | c1_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1606, 1602])).
% 1.07/0.98 tff(1608,plain,
% 1.07/0.98 ((~hskp26) | c1_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1607, 1602])).
% 1.07/0.98 tff(1609,plain,
% 1.07/0.98 ((~hskp26) | c1_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1608, 1602])).
% 1.07/0.98 tff(1610,plain,
% 1.07/0.98 ((~hskp26) | c1_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1609, 1602])).
% 1.07/0.98 tff(1611,plain,
% 1.07/0.98 ((~hskp26) | c1_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1610, 1602])).
% 1.07/0.98 tff(1612,plain,
% 1.07/0.98 (c1_1(a640)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1611, 1590])).
% 1.07/0.98 tff(1613,plain,
% 1.07/0.98 (((~hskp26) | c0_1(a640)) <=> ((~hskp26) | c0_1(a640))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1614,axiom,((~hskp26) | c0_1(a640)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.07/0.98 tff(1615,plain,
% 1.07/0.98 ((~hskp26) | c0_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 1.07/0.98 tff(1616,plain,
% 1.07/0.98 ((~hskp26) | c0_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1615, 1613])).
% 1.07/0.98 tff(1617,plain,
% 1.07/0.98 ((~hskp26) | c0_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1616, 1613])).
% 1.07/0.98 tff(1618,plain,
% 1.07/0.98 ((~hskp26) | c0_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1617, 1613])).
% 1.07/0.98 tff(1619,plain,
% 1.07/0.98 ((~hskp26) | c0_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1618, 1613])).
% 1.07/0.98 tff(1620,plain,
% 1.07/0.98 ((~hskp26) | c0_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1619, 1613])).
% 1.07/0.98 tff(1621,plain,
% 1.07/0.98 ((~hskp26) | c0_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1620, 1613])).
% 1.07/0.98 tff(1622,plain,
% 1.07/0.98 ((~hskp26) | c0_1(a640)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1621, 1613])).
% 1.07/0.98 tff(1623,plain,
% 1.07/0.98 (c0_1(a640)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1622, 1590])).
% 1.07/0.98 tff(1624,plain,
% 1.07/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c3_1(a640)) | (~c0_1(a640)) | (~c1_1(a640)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c3_1(a640)) | (~c0_1(a640)) | (~c1_1(a640)))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1625,plain,
% 1.07/0.98 (((~ndr1_0) | (~c1_1(a640)) | (~c3_1(a640)) | (~c0_1(a640)) | c3_1(a647) | c2_1(a647) | c1_1(a647) | c3_1(a647) | c0_1(a647) | c2_1(a647)) <=> (c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c3_1(a640)) | (~c0_1(a640)) | (~c1_1(a640)))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1626,plain,
% 1.07/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a640)) | (~c3_1(a640)) | (~c0_1(a640)) | c3_1(a647) | c2_1(a647) | c1_1(a647) | c3_1(a647) | c0_1(a647) | c2_1(a647))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | (c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c3_1(a640)) | (~c0_1(a640)) | (~c1_1(a640))))),
% 1.07/0.98 inference(monotonicity,[status(thm)],[1625])).
% 1.07/0.98 tff(1627,plain,
% 1.07/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a640)) | (~c3_1(a640)) | (~c0_1(a640)) | c3_1(a647) | c2_1(a647) | c1_1(a647) | c3_1(a647) | c0_1(a647) | c2_1(a647))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c3_1(a640)) | (~c0_1(a640)) | (~c1_1(a640)))),
% 1.07/0.98 inference(transitivity,[status(thm)],[1626, 1624])).
% 1.07/0.98 tff(1628,plain,
% 1.07/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | ((~ndr1_0) | (~c1_1(a640)) | (~c3_1(a640)) | (~c0_1(a640)) | c3_1(a647) | c2_1(a647) | c1_1(a647) | c3_1(a647) | c0_1(a647) | c2_1(a647))),
% 1.07/0.98 inference(quant_inst,[status(thm)],[])).
% 1.07/0.98 tff(1629,plain,
% 1.07/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | c1_1(V) | c3_1(W) | c0_1(W) | c2_1(W))) | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c3_1(a640)) | (~c0_1(a640)) | (~c1_1(a640))),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 1.07/0.98 tff(1630,plain,
% 1.07/0.98 (c2_1(a647)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1629, 102, 1623, 1612, 1601, 1519, 261, 236, 1165])).
% 1.07/0.98 tff(1631,plain,
% 1.07/0.98 (~hskp5),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1146, 1519])).
% 1.07/0.98 tff(1632,plain,
% 1.07/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1633,plain,
% 1.07/0.98 ((hskp5 | (~ndr1_0) | c1_1(a647) | c3_1(a647) | (~c2_1(a647)) | c0_1(a647) | c1_1(a647) | (~c2_1(a647))) <=> (hskp5 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1634,plain,
% 1.07/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a647) | c3_1(a647) | (~c2_1(a647)) | c0_1(a647) | c1_1(a647) | (~c2_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647))))),
% 1.07/0.98 inference(monotonicity,[status(thm)],[1633])).
% 1.07/0.98 tff(1635,plain,
% 1.07/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a647) | c3_1(a647) | (~c2_1(a647)) | c0_1(a647) | c1_1(a647) | (~c2_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647)))),
% 1.07/0.98 inference(transitivity,[status(thm)],[1634, 1632])).
% 1.07/0.98 tff(1636,plain,
% 1.07/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a647) | c3_1(a647) | (~c2_1(a647)) | c0_1(a647) | c1_1(a647) | (~c2_1(a647)))),
% 1.07/0.98 inference(quant_inst,[status(thm)],[])).
% 1.07/0.98 tff(1637,plain,
% 1.07/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a647) | c0_1(a647) | c3_1(a647) | (~ndr1_0) | (~c2_1(a647))),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1636, 1635])).
% 1.07/0.98 tff(1638,plain,
% 1.07/0.98 ($false),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1637, 102, 1631, 1519, 261, 236, 12, 1630])).
% 1.07/0.98 tff(1639,plain,(c0_1(a647) | c3_1(a647) | hskp0 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.07/0.98 tff(1640,plain,
% 1.07/0.98 ($false),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1639, 1375, 1374, 23, 1])).
% 1.07/0.98 tff(1641,plain,(hskp17 | hskp0), inference(lemma,lemma(discharge,[]))).
% 1.07/0.98 tff(1642,plain,
% 1.07/0.98 (hskp17),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1641, 23])).
% 1.07/0.98 tff(1643,plain,
% 1.07/0.98 (~c3_1(a675)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1080, 1642])).
% 1.07/0.98 tff(1644,plain,
% 1.07/0.98 (~c1_1(a675)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1074, 1642])).
% 1.07/0.98 tff(1645,plain,
% 1.07/0.98 (c2_1(a675)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1125, 1642])).
% 1.07/0.98 tff(1646,assumption,(c2_1(a675)), introduced(assumption)).
% 1.07/0.98 tff(1647,plain,
% 1.07/0.98 (~c0_1(a675)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1114, 102, 1646, 1083, 1082, 994])).
% 1.07/0.98 tff(1648,plain,
% 1.07/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1649,plain,
% 1.07/0.98 ((hskp5 | (~ndr1_0) | c1_1(a675) | c3_1(a675) | (~c2_1(a675)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675))) <=> (hskp5 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))),
% 1.07/0.98 inference(rewrite,[status(thm)],[])).
% 1.07/0.98 tff(1650,plain,
% 1.07/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a675) | c3_1(a675) | (~c2_1(a675)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675)))),
% 1.07/0.98 inference(monotonicity,[status(thm)],[1649])).
% 1.07/0.98 tff(1651,plain,
% 1.07/0.98 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a675) | c3_1(a675) | (~c2_1(a675)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))),
% 1.07/0.98 inference(transitivity,[status(thm)],[1650, 1648])).
% 1.07/0.98 tff(1652,plain,
% 1.07/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a675) | c3_1(a675) | (~c2_1(a675)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)))),
% 1.07/0.98 inference(quant_inst,[status(thm)],[])).
% 1.07/0.98 tff(1653,plain,
% 1.07/0.98 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c3_1(U) | (~c2_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a675) | c3_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675)),
% 1.07/0.98 inference(modus_ponens,[status(thm)],[1652, 1651])).
% 1.07/0.98 tff(1654,plain,
% 1.07/0.98 (hskp5),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1653, 102, 1646, 1083, 1082, 12, 1647])).
% 1.07/0.98 tff(1655,plain,
% 1.07/0.98 (~c0_1(a647)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[532, 1654])).
% 1.07/0.98 tff(1656,plain,
% 1.07/0.98 (~c3_1(a647)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[674, 1654])).
% 1.07/0.98 tff(1657,plain,
% 1.07/0.98 (c1_1(a647)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1146, 1654])).
% 1.07/0.98 tff(1658,plain,
% 1.07/0.98 (hskp6),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[1485, 1430, 1657, 1656, 1655, 1246, 1245])).
% 1.07/0.98 tff(1659,plain,
% 1.07/0.98 (~c2_1(a648)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[120, 1658])).
% 1.07/0.98 tff(1660,plain,
% 1.07/0.98 (c0_1(a648)),
% 1.07/0.98 inference(unit_resolution,[status(thm)],[328, 1658])).
% 1.07/0.98 tff(1661,plain,
% 1.07/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a648) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643) | (~c1_1(a643)) | c1_1(a648) | (~c0_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a648) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643) | (~c1_1(a643)) | c1_1(a648) | (~c0_1(a648)))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1662,plain,
% 1.07/0.99 (((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643))) <=> (c2_1(a648) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643) | (~c1_1(a643)) | c1_1(a648) | (~c0_1(a648)))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1663,plain,
% 1.07/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a648) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643) | (~c1_1(a643)) | c1_1(a648) | (~c0_1(a648))))),
% 1.07/0.99 inference(monotonicity,[status(thm)],[1662])).
% 1.07/0.99 tff(1664,plain,
% 1.07/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a648) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643) | (~c1_1(a643)) | c1_1(a648) | (~c0_1(a648)))),
% 1.07/0.99 inference(transitivity,[status(thm)],[1663, 1661])).
% 1.07/0.99 tff(1665,plain,
% 1.07/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a648) | c1_1(a648) | (~c0_1(a648)) | c0_1(a643) | (~c2_1(a643)) | (~c1_1(a643)) | c3_1(a643) | c0_1(a643) | (~c1_1(a643)))),
% 1.07/0.99 inference(quant_inst,[status(thm)],[])).
% 1.07/0.99 tff(1666,plain,
% 1.07/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c3_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a648) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | c3_1(a643) | (~c1_1(a643)) | c1_1(a648) | (~c0_1(a648))),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 1.07/0.99 tff(1667,plain,
% 1.07/0.99 (c1_1(a648)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1666, 102, 1660, 1244, 1246, 1659, 1245, 235, 1430])).
% 1.07/0.99 tff(1668,plain,
% 1.07/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a675) | c3_1(a675) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)) | c0_1(a675))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a675) | c3_1(a675) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)) | c0_1(a675))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1669,plain,
% 1.07/0.99 (((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)) | c3_1(a675) | c1_1(a675) | c0_1(a675)) <=> (c1_1(a675) | c3_1(a675) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)) | c0_1(a675))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1670,plain,
% 1.07/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)) | c3_1(a675) | c1_1(a675) | c0_1(a675))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a675) | c3_1(a675) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)) | c0_1(a675)))),
% 1.07/0.99 inference(monotonicity,[status(thm)],[1669])).
% 1.07/0.99 tff(1671,plain,
% 1.07/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)) | c3_1(a675) | c1_1(a675) | c0_1(a675))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a675) | c3_1(a675) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)) | c0_1(a675))),
% 1.07/0.99 inference(transitivity,[status(thm)],[1670, 1668])).
% 1.07/0.99 tff(1672,plain,
% 1.07/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c0_1(a675) | c1_1(a675) | (~c2_1(a675)) | c3_1(a675) | c1_1(a675) | c0_1(a675))),
% 1.07/0.99 inference(quant_inst,[status(thm)],[])).
% 1.07/0.99 tff(1673,plain,
% 1.07/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c2_1(V)) | c3_1(W) | c1_1(W) | c0_1(W))) | c1_1(a675) | c3_1(a675) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)) | c0_1(a675)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1672, 1671])).
% 1.07/0.99 tff(1674,plain,
% 1.07/0.99 ($false),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1673, 102, 1646, 1660, 1083, 1082, 1659, 206, 1647, 1667])).
% 1.07/0.99 tff(1675,plain,(c3_1(a643) | (~c2_1(a675)) | c1_1(a675) | c3_1(a675) | (~c1_1(a643)) | (~c2_1(a643)) | c0_1(a643)), inference(lemma,lemma(discharge,[]))).
% 1.07/0.99 tff(1676,plain,
% 1.07/0.99 (c3_1(a643)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1675, 1645, 1644, 1643, 1243, 1232, 1221])).
% 1.07/0.99 tff(1677,plain,
% 1.07/0.99 (~c0_1(a675)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1114, 102, 1645, 1644, 1643, 994])).
% 1.07/0.99 tff(1678,plain,
% 1.07/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | c1_1(a675) | c3_1(a675) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c0_1(a675))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c1_1(a675) | c3_1(a675) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c0_1(a675))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1679,plain,
% 1.07/0.99 ((hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a675) | c0_1(a675) | c1_1(a675)) <=> (hskp1 | c1_1(a675) | c3_1(a675) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c0_1(a675))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1680,plain,
% 1.07/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a675) | c0_1(a675) | c1_1(a675))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | c1_1(a675) | c3_1(a675) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c0_1(a675)))),
% 1.07/0.99 inference(monotonicity,[status(thm)],[1679])).
% 1.07/0.99 tff(1681,plain,
% 1.07/0.99 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a675) | c0_1(a675) | c1_1(a675))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c1_1(a675) | c3_1(a675) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c0_1(a675))),
% 1.07/0.99 inference(transitivity,[status(thm)],[1680, 1678])).
% 1.07/0.99 tff(1682,plain,
% 1.07/0.99 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | (hskp1 | (~ndr1_0) | c0_1(a643) | (~c2_1(a643)) | (~c3_1(a643)) | c3_1(a675) | c0_1(a675) | c1_1(a675))),
% 1.07/0.99 inference(quant_inst,[status(thm)],[])).
% 1.07/0.99 tff(1683,plain,
% 1.07/0.99 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c1_1(V))) | hskp1 | c1_1(a675) | c3_1(a675) | c0_1(a643) | (~ndr1_0) | (~c2_1(a643)) | (~c3_1(a643)) | c0_1(a675)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 1.07/0.99 tff(1684,plain,
% 1.07/0.99 (hskp1 | (~c3_1(a643))),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1683, 102, 1232, 1644, 1643, 1221, 1390, 1677])).
% 1.07/0.99 tff(1685,plain,
% 1.07/0.99 (hskp1),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1684, 1676])).
% 1.07/0.99 tff(1686,plain,
% 1.07/0.99 (~c1_1(a642)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[391, 1685])).
% 1.07/0.99 tff(1687,plain,
% 1.07/0.99 (c3_1(a642)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[414, 1685])).
% 1.07/0.99 tff(1688,plain,
% 1.07/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1689,plain,
% 1.07/0.99 (((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1690,plain,
% 1.07/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643))))),
% 1.07/0.99 inference(monotonicity,[status(thm)],[1689])).
% 1.07/0.99 tff(1691,plain,
% 1.07/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))),
% 1.07/0.99 inference(transitivity,[status(thm)],[1690, 1688])).
% 1.07/0.99 tff(1692,plain,
% 1.07/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a642) | (~c2_1(a642)) | (~c3_1(a642)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 1.07/0.99 inference(quant_inst,[status(thm)],[])).
% 1.07/0.99 tff(1693,plain,
% 1.07/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a642) | (~ndr1_0) | (~c2_1(a642)) | (~c3_1(a642)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643))),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1692, 1691])).
% 1.07/0.99 tff(1694,plain,
% 1.07/0.99 (~c2_1(a642)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1693, 102, 1243, 1232, 1687, 1221, 1686, 1263, 1676])).
% 1.07/0.99 tff(1695,plain,
% 1.07/0.99 (hskp5),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1653, 102, 1645, 1644, 1643, 12, 1677])).
% 1.07/0.99 tff(1696,plain,
% 1.07/0.99 (~c3_1(a647)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[674, 1695])).
% 1.07/0.99 tff(1697,plain,
% 1.07/0.99 (~c0_1(a647)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[532, 1695])).
% 1.07/0.99 tff(1698,plain,
% 1.07/0.99 (c0_1(a642)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[403, 1685])).
% 1.07/0.99 tff(1699,plain,
% 1.07/0.99 (c1_1(a647)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1146, 1695])).
% 1.07/0.99 tff(1700,plain,
% 1.07/0.99 ($false),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1518, 102, 1699, 1243, 1232, 1698, 1697, 1696, 1221, 1686, 235, 1694])).
% 1.07/0.99 tff(1701,plain,(hskp0), inference(lemma,lemma(discharge,[]))).
% 1.07/0.99 tff(1702,plain,
% 1.07/0.99 (((~hskp0) | (~c1_1(a641))) <=> ((~hskp0) | (~c1_1(a641)))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1703,plain,
% 1.07/0.99 (((~c1_1(a641)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a641)))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1704,axiom,((~c1_1(a641)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.07/0.99 tff(1705,plain,
% 1.07/0.99 ((~hskp0) | (~c1_1(a641))),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1704, 1703])).
% 1.07/0.99 tff(1706,plain,
% 1.07/0.99 ((~hskp0) | (~c1_1(a641))),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1705, 1702])).
% 1.07/0.99 tff(1707,plain,
% 1.07/0.99 (~c1_1(a641)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1706, 1701])).
% 1.07/0.99 tff(1708,plain,
% 1.07/0.99 (((~hskp0) | c3_1(a641)) <=> ((~hskp0) | c3_1(a641))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1709,axiom,((~hskp0) | c3_1(a641)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.07/0.99 tff(1710,plain,
% 1.07/0.99 ((~hskp0) | c3_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1709, 1708])).
% 1.07/0.99 tff(1711,plain,
% 1.07/0.99 ((~hskp0) | c3_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1710, 1708])).
% 1.07/0.99 tff(1712,plain,
% 1.07/0.99 ((~hskp0) | c3_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1711, 1708])).
% 1.07/0.99 tff(1713,plain,
% 1.07/0.99 ((~hskp0) | c3_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1712, 1708])).
% 1.07/0.99 tff(1714,plain,
% 1.07/0.99 ((~hskp0) | c3_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1713, 1708])).
% 1.07/0.99 tff(1715,plain,
% 1.07/0.99 ((~hskp0) | c3_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1714, 1708])).
% 1.07/0.99 tff(1716,plain,
% 1.07/0.99 ((~hskp0) | c3_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1715, 1708])).
% 1.07/0.99 tff(1717,plain,
% 1.07/0.99 ((~hskp0) | c3_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1716, 1708])).
% 1.07/0.99 tff(1718,plain,
% 1.07/0.99 (c3_1(a641)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1717, 1701])).
% 1.07/0.99 tff(1719,plain,
% 1.07/0.99 (((~hskp0) | c2_1(a641)) <=> ((~hskp0) | c2_1(a641))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1720,axiom,((~hskp0) | c2_1(a641)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.07/0.99 tff(1721,plain,
% 1.07/0.99 ((~hskp0) | c2_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1720, 1719])).
% 1.07/0.99 tff(1722,plain,
% 1.07/0.99 ((~hskp0) | c2_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1721, 1719])).
% 1.07/0.99 tff(1723,plain,
% 1.07/0.99 ((~hskp0) | c2_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1722, 1719])).
% 1.07/0.99 tff(1724,plain,
% 1.07/0.99 ((~hskp0) | c2_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1723, 1719])).
% 1.07/0.99 tff(1725,plain,
% 1.07/0.99 ((~hskp0) | c2_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1724, 1719])).
% 1.07/0.99 tff(1726,plain,
% 1.07/0.99 ((~hskp0) | c2_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1725, 1719])).
% 1.07/0.99 tff(1727,plain,
% 1.07/0.99 ((~hskp0) | c2_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1726, 1719])).
% 1.07/0.99 tff(1728,plain,
% 1.07/0.99 ((~hskp0) | c2_1(a641)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1727, 1719])).
% 1.07/0.99 tff(1729,plain,
% 1.07/0.99 (c2_1(a641)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1728, 1701])).
% 1.07/0.99 tff(1730,plain,
% 1.07/0.99 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1731,plain,
% 1.07/0.99 ((hskp17 | hskp7 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641))) <=> (hskp17 | hskp7 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1732,plain,
% 1.07/0.99 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641))))),
% 1.07/0.99 inference(monotonicity,[status(thm)],[1731])).
% 1.07/0.99 tff(1733,plain,
% 1.07/0.99 (((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)))) <=> ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))),
% 1.07/0.99 inference(transitivity,[status(thm)],[1732, 1730])).
% 1.07/0.99 tff(1734,plain,
% 1.07/0.99 ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp17 | hskp7 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)))),
% 1.07/0.99 inference(quant_inst,[status(thm)],[])).
% 1.07/0.99 tff(1735,plain,
% 1.07/0.99 ((~![U: $i] : (hskp17 | hskp7 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp17 | hskp7 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641))),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 1.07/0.99 tff(1736,plain,
% 1.07/0.99 (hskp17 | hskp7),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1735, 102, 1729, 1718, 1707, 22])).
% 1.07/0.99 tff(1737,plain,
% 1.07/0.99 (hskp7),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1736, 1])).
% 1.07/0.99 tff(1738,plain,
% 1.07/0.99 (~c1_1(a651)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[151, 1737])).
% 1.07/0.99 tff(1739,plain,
% 1.07/0.99 (~c0_1(a651)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[157, 1737])).
% 1.07/0.99 tff(1740,plain,
% 1.07/0.99 (c3_1(a651)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[168, 1737])).
% 1.07/0.99 tff(1741,plain,
% 1.07/0.99 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.07/0.99 inference(bind,[status(th)],[])).
% 1.07/0.99 tff(1742,plain,
% 1.07/0.99 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.07/0.99 inference(quant_intro,[status(thm)],[1741])).
% 1.07/0.99 tff(1743,plain,
% 1.07/0.99 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1744,plain,
% 1.07/0.99 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.07/0.99 inference(bind,[status(th)],[])).
% 1.07/0.99 tff(1745,plain,
% 1.07/0.99 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.07/0.99 inference(quant_intro,[status(thm)],[1744])).
% 1.07/0.99 tff(1746,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 1.07/0.99 tff(1747,plain,
% 1.07/0.99 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 1.07/0.99 tff(1748,plain,
% 1.07/0.99 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1747, 1743])).
% 1.07/0.99 tff(1749,plain,(
% 1.07/0.99 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.07/0.99 inference(skolemize,[status(sab)],[1748])).
% 1.07/0.99 tff(1750,plain,
% 1.07/0.99 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1749, 1742])).
% 1.07/0.99 tff(1751,assumption,(c3_1(a651)), introduced(assumption)).
% 1.07/0.99 tff(1752,plain,
% 1.07/0.99 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1753,plain,
% 1.07/0.99 ((hskp8 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651))) <=> (hskp8 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1754,plain,
% 1.07/0.99 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 1.07/0.99 inference(monotonicity,[status(thm)],[1753])).
% 1.07/0.99 tff(1755,plain,
% 1.07/0.99 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/0.99 inference(transitivity,[status(thm)],[1754, 1752])).
% 1.07/0.99 tff(1756,plain,
% 1.07/0.99 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))),
% 1.07/0.99 inference(quant_inst,[status(thm)],[])).
% 1.07/0.99 tff(1757,plain,
% 1.07/0.99 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a651) | c1_1(a651) | (~ndr1_0) | (~c3_1(a651)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1756, 1755])).
% 1.07/0.99 tff(1758,plain,
% 1.07/0.99 (hskp8),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1757, 102, 1170, 1169, 1178, 1751, 366, 365, 1750])).
% 1.07/0.99 tff(1759,plain,
% 1.07/0.99 (((~hskp8) | (~c2_1(a652))) <=> ((~hskp8) | (~c2_1(a652)))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1760,plain,
% 1.07/0.99 (((~c2_1(a652)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a652)))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1761,axiom,((~c2_1(a652)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.07/0.99 tff(1762,plain,
% 1.07/0.99 ((~hskp8) | (~c2_1(a652))),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1761, 1760])).
% 1.07/0.99 tff(1763,plain,
% 1.07/0.99 ((~hskp8) | (~c2_1(a652))),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1762, 1759])).
% 1.07/0.99 tff(1764,plain,
% 1.07/0.99 (~c2_1(a652)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1763, 1758])).
% 1.07/0.99 tff(1765,plain,
% 1.07/0.99 (((~hskp8) | c3_1(a652)) <=> ((~hskp8) | c3_1(a652))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1766,axiom,((~hskp8) | c3_1(a652)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.07/0.99 tff(1767,plain,
% 1.07/0.99 ((~hskp8) | c3_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1766, 1765])).
% 1.07/0.99 tff(1768,plain,
% 1.07/0.99 ((~hskp8) | c3_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1767, 1765])).
% 1.07/0.99 tff(1769,plain,
% 1.07/0.99 ((~hskp8) | c3_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1768, 1765])).
% 1.07/0.99 tff(1770,plain,
% 1.07/0.99 ((~hskp8) | c3_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1769, 1765])).
% 1.07/0.99 tff(1771,plain,
% 1.07/0.99 ((~hskp8) | c3_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1770, 1765])).
% 1.07/0.99 tff(1772,plain,
% 1.07/0.99 ((~hskp8) | c3_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1771, 1765])).
% 1.07/0.99 tff(1773,plain,
% 1.07/0.99 ((~hskp8) | c3_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1772, 1765])).
% 1.07/0.99 tff(1774,plain,
% 1.07/0.99 ((~hskp8) | c3_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1773, 1765])).
% 1.07/0.99 tff(1775,plain,
% 1.07/0.99 (c3_1(a652)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1774, 1758])).
% 1.07/0.99 tff(1776,plain,
% 1.07/0.99 (((~hskp8) | c0_1(a652)) <=> ((~hskp8) | c0_1(a652))),
% 1.07/0.99 inference(rewrite,[status(thm)],[])).
% 1.07/0.99 tff(1777,axiom,((~hskp8) | c0_1(a652)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.07/0.99 tff(1778,plain,
% 1.07/0.99 ((~hskp8) | c0_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 1.07/0.99 tff(1779,plain,
% 1.07/0.99 ((~hskp8) | c0_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1778, 1776])).
% 1.07/0.99 tff(1780,plain,
% 1.07/0.99 ((~hskp8) | c0_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1779, 1776])).
% 1.07/0.99 tff(1781,plain,
% 1.07/0.99 ((~hskp8) | c0_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1780, 1776])).
% 1.07/0.99 tff(1782,plain,
% 1.07/0.99 ((~hskp8) | c0_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1781, 1776])).
% 1.07/0.99 tff(1783,plain,
% 1.07/0.99 ((~hskp8) | c0_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1782, 1776])).
% 1.07/0.99 tff(1784,plain,
% 1.07/0.99 ((~hskp8) | c0_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1783, 1776])).
% 1.07/0.99 tff(1785,plain,
% 1.07/0.99 ((~hskp8) | c0_1(a652)),
% 1.07/0.99 inference(modus_ponens,[status(thm)],[1784, 1776])).
% 1.07/0.99 tff(1786,plain,
% 1.07/0.99 (c0_1(a652)),
% 1.07/0.99 inference(unit_resolution,[status(thm)],[1785, 1758])).
% 1.07/0.99 tff(1787,plain,
% 1.07/0.99 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | c2_1(a652) | (~ndr1_0) | (~c0_1(a652)) | (~c3_1(a652)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | c2_1(a652) | (~ndr1_0) | (~c0_1(a652)) | (~c3_1(a652)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1788,plain,
% 1.07/1.00 ((hskp23 | hskp5 | (~ndr1_0) | c2_1(a652) | (~c3_1(a652)) | (~c0_1(a652))) <=> (hskp23 | hskp5 | c2_1(a652) | (~ndr1_0) | (~c0_1(a652)) | (~c3_1(a652)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1789,plain,
% 1.07/1.00 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a652) | (~c3_1(a652)) | (~c0_1(a652)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | c2_1(a652) | (~ndr1_0) | (~c0_1(a652)) | (~c3_1(a652))))),
% 1.07/1.00 inference(monotonicity,[status(thm)],[1788])).
% 1.07/1.00 tff(1790,plain,
% 1.07/1.00 (((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a652) | (~c3_1(a652)) | (~c0_1(a652)))) <=> ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | c2_1(a652) | (~ndr1_0) | (~c0_1(a652)) | (~c3_1(a652)))),
% 1.07/1.00 inference(transitivity,[status(thm)],[1789, 1787])).
% 1.07/1.00 tff(1791,plain,
% 1.07/1.00 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp23 | hskp5 | (~ndr1_0) | c2_1(a652) | (~c3_1(a652)) | (~c0_1(a652)))),
% 1.07/1.00 inference(quant_inst,[status(thm)],[])).
% 1.07/1.00 tff(1792,plain,
% 1.07/1.00 ((~![U: $i] : (hskp23 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp23 | hskp5 | c2_1(a652) | (~ndr1_0) | (~c0_1(a652)) | (~c3_1(a652))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 1.07/1.00 tff(1793,plain,
% 1.07/1.00 (hskp23),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1792, 102, 2, 1786, 1775, 1764, 600])).
% 1.07/1.00 tff(1794,plain,
% 1.07/1.00 (~c0_1(a695)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[619, 1793])).
% 1.07/1.00 tff(1795,plain,
% 1.07/1.00 (c2_1(a695)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[641, 1793])).
% 1.07/1.00 tff(1796,plain,
% 1.07/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a695) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a695) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1797,plain,
% 1.07/1.00 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695))) <=> (c0_1(a695) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1798,plain,
% 1.07/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a695) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 1.07/1.00 inference(monotonicity,[status(thm)],[1797])).
% 1.07/1.00 tff(1799,plain,
% 1.07/1.00 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a695) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/1.00 inference(transitivity,[status(thm)],[1798, 1796])).
% 1.07/1.00 tff(1800,plain,
% 1.07/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a695) | (~c1_1(a695)) | (~c2_1(a695)))),
% 1.07/1.00 inference(quant_inst,[status(thm)],[])).
% 1.07/1.00 tff(1801,plain,
% 1.07/1.00 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a695) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a695)) | (~c1_1(a695)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 1.07/1.00 tff(1802,plain,
% 1.07/1.00 (~c1_1(a695)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1801, 102, 1170, 1169, 1178, 1795, 1729, 1718, 1794, 1707, 923])).
% 1.07/1.00 tff(1803,plain,
% 1.07/1.00 (~c3_1(a695)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[613, 1793])).
% 1.07/1.00 tff(1804,plain,
% 1.07/1.00 ($false),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1370, 102, 2, 1795, 1794, 1803, 12, 1802])).
% 1.07/1.00 tff(1805,plain,((~hskp28) | hskp5 | (~c3_1(a651)) | c0_1(a651) | c1_1(a651)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.00 tff(1806,plain,
% 1.07/1.00 (~hskp28),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1805, 2, 1740, 1739, 1738])).
% 1.07/1.00 tff(1807,plain,
% 1.07/1.00 (~hskp1),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[802, 1806, 1])).
% 1.07/1.00 tff(1808,plain,
% 1.07/1.00 (hskp14),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[508, 1807, 1])).
% 1.07/1.00 tff(1809,plain,
% 1.07/1.00 (~c1_1(a665)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[50, 1808])).
% 1.07/1.00 tff(1810,plain,
% 1.07/1.00 (~c0_1(a665)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[56, 1808])).
% 1.07/1.00 tff(1811,plain,
% 1.07/1.00 (c2_1(a665)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[67, 1808])).
% 1.07/1.00 tff(1812,plain,
% 1.07/1.00 (c3_1(a665)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1252, 102, 2, 1811, 1810, 1809, 12])).
% 1.07/1.00 tff(1813,plain,
% 1.07/1.00 (^[U: $i] : refl((hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))),
% 1.07/1.00 inference(bind,[status(th)],[])).
% 1.07/1.00 tff(1814,plain,
% 1.07/1.00 (![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.07/1.00 inference(quant_intro,[status(thm)],[1813])).
% 1.07/1.00 tff(1815,plain,
% 1.07/1.00 (![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1816,plain,
% 1.07/1.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp28))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp16) <=> ((hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp16))), rewrite(((hskp28 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U))) | hskp16) <=> (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp16) <=> (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))))),
% 1.07/1.00 inference(bind,[status(th)],[])).
% 1.07/1.00 tff(1817,plain,
% 1.07/1.00 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp16) <=> ![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.07/1.00 inference(quant_intro,[status(thm)],[1816])).
% 1.07/1.00 tff(1818,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp28) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.07/1.00 tff(1819,plain,
% 1.07/1.00 (![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 1.07/1.00 tff(1820,plain,
% 1.07/1.00 (![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1819, 1815])).
% 1.07/1.00 tff(1821,plain,(
% 1.07/1.00 ![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.07/1.00 inference(skolemize,[status(sab)],[1820])).
% 1.07/1.00 tff(1822,plain,
% 1.07/1.00 (![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1821, 1814])).
% 1.07/1.00 tff(1823,plain,
% 1.07/1.00 (^[U: $i] : refl((hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.07/1.00 inference(bind,[status(th)],[])).
% 1.07/1.00 tff(1824,plain,
% 1.07/1.00 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.07/1.00 inference(quant_intro,[status(thm)],[1823])).
% 1.07/1.00 tff(1825,plain,
% 1.07/1.00 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1826,plain,
% 1.07/1.00 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp17))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp19) <=> ((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp19))), rewrite(((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp19) <=> (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp19) <=> (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.07/1.00 inference(bind,[status(th)],[])).
% 1.07/1.00 tff(1827,plain,
% 1.07/1.00 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp19) <=> ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.07/1.00 inference(quant_intro,[status(thm)],[1826])).
% 1.07/1.00 tff(1828,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp17) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.07/1.00 tff(1829,plain,
% 1.07/1.00 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1828, 1827])).
% 1.07/1.00 tff(1830,plain,
% 1.07/1.00 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1829, 1825])).
% 1.07/1.00 tff(1831,plain,(
% 1.07/1.00 ![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.07/1.00 inference(skolemize,[status(sab)],[1830])).
% 1.07/1.00 tff(1832,plain,
% 1.07/1.00 (![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1831, 1824])).
% 1.07/1.00 tff(1833,plain,
% 1.07/1.00 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | hskp17 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | hskp17 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1834,plain,
% 1.07/1.00 ((hskp19 | hskp17 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641))) <=> (hskp19 | hskp17 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1835,plain,
% 1.07/1.00 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | hskp17 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641))))),
% 1.07/1.00 inference(monotonicity,[status(thm)],[1834])).
% 1.07/1.00 tff(1836,plain,
% 1.07/1.00 (((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)))) <=> ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | hskp17 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)))),
% 1.07/1.00 inference(transitivity,[status(thm)],[1835, 1833])).
% 1.07/1.00 tff(1837,plain,
% 1.07/1.00 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp19 | hskp17 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)))),
% 1.07/1.00 inference(quant_inst,[status(thm)],[])).
% 1.07/1.00 tff(1838,plain,
% 1.07/1.00 ((~![U: $i] : (hskp19 | hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp19 | hskp17 | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1837, 1836])).
% 1.07/1.00 tff(1839,plain,
% 1.07/1.00 (hskp19 | hskp17),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1838, 102, 1729, 1718, 1707, 1832])).
% 1.07/1.00 tff(1840,plain,
% 1.07/1.00 (hskp19),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1839, 1])).
% 1.07/1.00 tff(1841,plain,
% 1.07/1.00 (((~hskp19) | (~c2_1(a682))) <=> ((~hskp19) | (~c2_1(a682)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1842,plain,
% 1.07/1.00 (((~c2_1(a682)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a682)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1843,axiom,((~c2_1(a682)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.07/1.00 tff(1844,plain,
% 1.07/1.00 ((~hskp19) | (~c2_1(a682))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 1.07/1.00 tff(1845,plain,
% 1.07/1.00 ((~hskp19) | (~c2_1(a682))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1844, 1841])).
% 1.07/1.00 tff(1846,plain,
% 1.07/1.00 (~c2_1(a682)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1845, 1840])).
% 1.07/1.00 tff(1847,plain,
% 1.07/1.00 (((~hskp19) | (~c1_1(a682))) <=> ((~hskp19) | (~c1_1(a682)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1848,plain,
% 1.07/1.00 (((~c1_1(a682)) | (~hskp19)) <=> ((~hskp19) | (~c1_1(a682)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1849,axiom,((~c1_1(a682)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 1.07/1.00 tff(1850,plain,
% 1.07/1.00 ((~hskp19) | (~c1_1(a682))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 1.07/1.00 tff(1851,plain,
% 1.07/1.00 ((~hskp19) | (~c1_1(a682))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1850, 1847])).
% 1.07/1.00 tff(1852,plain,
% 1.07/1.00 (~c1_1(a682)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1851, 1840])).
% 1.07/1.00 tff(1853,plain,
% 1.07/1.00 (((~hskp19) | c3_1(a682)) <=> ((~hskp19) | c3_1(a682))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1854,axiom,((~hskp19) | c3_1(a682)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.07/1.00 tff(1855,plain,
% 1.07/1.00 ((~hskp19) | c3_1(a682)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 1.07/1.00 tff(1856,plain,
% 1.07/1.00 ((~hskp19) | c3_1(a682)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1855, 1853])).
% 1.07/1.00 tff(1857,plain,
% 1.07/1.00 ((~hskp19) | c3_1(a682)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1856, 1853])).
% 1.07/1.00 tff(1858,plain,
% 1.07/1.00 ((~hskp19) | c3_1(a682)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1857, 1853])).
% 1.07/1.00 tff(1859,plain,
% 1.07/1.00 ((~hskp19) | c3_1(a682)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1858, 1853])).
% 1.07/1.00 tff(1860,plain,
% 1.07/1.00 ((~hskp19) | c3_1(a682)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1859, 1853])).
% 1.07/1.00 tff(1861,plain,
% 1.07/1.00 ((~hskp19) | c3_1(a682)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1860, 1853])).
% 1.07/1.00 tff(1862,plain,
% 1.07/1.00 ((~hskp19) | c3_1(a682)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1861, 1853])).
% 1.07/1.00 tff(1863,plain,
% 1.07/1.00 (c3_1(a682)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1862, 1840])).
% 1.07/1.00 tff(1864,plain,
% 1.07/1.00 (((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp16 | c1_1(a682) | c2_1(a682) | (~ndr1_0) | (~c3_1(a682)))) <=> ((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp28 | hskp16 | c1_1(a682) | c2_1(a682) | (~ndr1_0) | (~c3_1(a682)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1865,plain,
% 1.07/1.00 ((hskp28 | hskp16 | (~ndr1_0) | c2_1(a682) | c1_1(a682) | (~c3_1(a682))) <=> (hskp28 | hskp16 | c1_1(a682) | c2_1(a682) | (~ndr1_0) | (~c3_1(a682)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1866,plain,
% 1.07/1.00 (((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp16 | (~ndr1_0) | c2_1(a682) | c1_1(a682) | (~c3_1(a682)))) <=> ((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp16 | c1_1(a682) | c2_1(a682) | (~ndr1_0) | (~c3_1(a682))))),
% 1.07/1.00 inference(monotonicity,[status(thm)],[1865])).
% 1.07/1.00 tff(1867,plain,
% 1.07/1.00 (((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp16 | (~ndr1_0) | c2_1(a682) | c1_1(a682) | (~c3_1(a682)))) <=> ((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp28 | hskp16 | c1_1(a682) | c2_1(a682) | (~ndr1_0) | (~c3_1(a682)))),
% 1.07/1.00 inference(transitivity,[status(thm)],[1866, 1864])).
% 1.07/1.00 tff(1868,plain,
% 1.07/1.00 ((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | (hskp28 | hskp16 | (~ndr1_0) | c2_1(a682) | c1_1(a682) | (~c3_1(a682)))),
% 1.07/1.00 inference(quant_inst,[status(thm)],[])).
% 1.07/1.00 tff(1869,plain,
% 1.07/1.00 ((~![U: $i] : (hskp28 | hskp16 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c3_1(U)))) | hskp28 | hskp16 | c1_1(a682) | c2_1(a682) | (~ndr1_0) | (~c3_1(a682))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1868, 1867])).
% 1.07/1.00 tff(1870,plain,
% 1.07/1.00 (hskp28 | hskp16),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1869, 102, 1863, 1852, 1846, 1822])).
% 1.07/1.00 tff(1871,plain,
% 1.07/1.00 (hskp16),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1870, 1806])).
% 1.07/1.00 tff(1872,plain,
% 1.07/1.00 (((~hskp16) | (~c3_1(a672))) <=> ((~hskp16) | (~c3_1(a672)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1873,plain,
% 1.07/1.00 (((~c3_1(a672)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a672)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1874,axiom,((~c3_1(a672)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.07/1.00 tff(1875,plain,
% 1.07/1.00 ((~hskp16) | (~c3_1(a672))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1874, 1873])).
% 1.07/1.00 tff(1876,plain,
% 1.07/1.00 ((~hskp16) | (~c3_1(a672))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1875, 1872])).
% 1.07/1.00 tff(1877,plain,
% 1.07/1.00 (~c3_1(a672)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1876, 1871])).
% 1.07/1.00 tff(1878,plain,
% 1.07/1.00 (((~hskp16) | (~c2_1(a672))) <=> ((~hskp16) | (~c2_1(a672)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1879,plain,
% 1.07/1.00 (((~c2_1(a672)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a672)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1880,axiom,((~c2_1(a672)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.07/1.00 tff(1881,plain,
% 1.07/1.00 ((~hskp16) | (~c2_1(a672))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1880, 1879])).
% 1.07/1.00 tff(1882,plain,
% 1.07/1.00 ((~hskp16) | (~c2_1(a672))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1881, 1878])).
% 1.07/1.00 tff(1883,plain,
% 1.07/1.00 (~c2_1(a672)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1882, 1871])).
% 1.07/1.00 tff(1884,plain,
% 1.07/1.00 (((~hskp16) | c1_1(a672)) <=> ((~hskp16) | c1_1(a672))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1885,axiom,((~hskp16) | c1_1(a672)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 1.07/1.00 tff(1886,plain,
% 1.07/1.00 ((~hskp16) | c1_1(a672)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1885, 1884])).
% 1.07/1.00 tff(1887,plain,
% 1.07/1.00 ((~hskp16) | c1_1(a672)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1886, 1884])).
% 1.07/1.00 tff(1888,plain,
% 1.07/1.00 ((~hskp16) | c1_1(a672)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1887, 1884])).
% 1.07/1.00 tff(1889,plain,
% 1.07/1.00 ((~hskp16) | c1_1(a672)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1888, 1884])).
% 1.07/1.00 tff(1890,plain,
% 1.07/1.00 ((~hskp16) | c1_1(a672)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1889, 1884])).
% 1.07/1.00 tff(1891,plain,
% 1.07/1.00 ((~hskp16) | c1_1(a672)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1890, 1884])).
% 1.07/1.00 tff(1892,plain,
% 1.07/1.00 ((~hskp16) | c1_1(a672)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1891, 1884])).
% 1.07/1.00 tff(1893,plain,
% 1.07/1.00 ((~hskp16) | c1_1(a672)),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1892, 1884])).
% 1.07/1.00 tff(1894,plain,
% 1.07/1.00 (c1_1(a672)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1893, 1871])).
% 1.07/1.00 tff(1895,plain,
% 1.07/1.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a672) | c3_1(a672) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a672)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a672) | c3_1(a672) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a672)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1896,plain,
% 1.07/1.00 ((hskp2 | (~ndr1_0) | c2_1(a672) | c3_1(a672) | (~c1_1(a672)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665))) <=> (hskp2 | c2_1(a672) | c3_1(a672) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a672)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1897,plain,
% 1.07/1.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a672) | c3_1(a672) | (~c1_1(a672)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c2_1(a672) | c3_1(a672) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a672))))),
% 1.07/1.00 inference(monotonicity,[status(thm)],[1896])).
% 1.07/1.00 tff(1898,plain,
% 1.07/1.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a672) | c3_1(a672) | (~c1_1(a672)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a672) | c3_1(a672) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a672)))),
% 1.07/1.00 inference(transitivity,[status(thm)],[1897, 1895])).
% 1.07/1.00 tff(1899,plain,
% 1.07/1.00 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a672) | c3_1(a672) | (~c1_1(a672)) | c0_1(a665) | c1_1(a665) | (~c3_1(a665)))),
% 1.07/1.00 inference(quant_inst,[status(thm)],[])).
% 1.07/1.00 tff(1900,plain,
% 1.07/1.00 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c2_1(a672) | c3_1(a672) | c0_1(a665) | c1_1(a665) | (~ndr1_0) | (~c3_1(a665)) | (~c1_1(a672))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 1.07/1.00 tff(1901,plain,
% 1.07/1.00 ($false),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1900, 102, 24, 1894, 1883, 1877, 1810, 1809, 34, 1812])).
% 1.07/1.00 tff(1902,plain,(hskp5 | hskp2 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.07/1.00 tff(1903,plain,
% 1.07/1.00 (hskp2),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1902, 2, 1])).
% 1.07/1.00 tff(1904,plain,
% 1.07/1.00 (c1_1(a643)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1242, 1903])).
% 1.07/1.00 tff(1905,plain,
% 1.07/1.00 (c2_1(a643)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1231, 1903])).
% 1.07/1.00 tff(1906,plain,
% 1.07/1.00 (~c0_1(a643)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1220, 1903])).
% 1.07/1.00 tff(1907,plain,
% 1.07/1.00 ($false),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1372, 1906, 1905, 1, 2, 1904])).
% 1.07/1.00 tff(1908,plain,(hskp5 | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.07/1.00 tff(1909,plain,
% 1.07/1.00 (hskp5),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1908, 1])).
% 1.07/1.00 tff(1910,plain,
% 1.07/1.00 (~c0_1(a647)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[532, 1909])).
% 1.07/1.00 tff(1911,plain,
% 1.07/1.00 (~c3_1(a647)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[674, 1909])).
% 1.07/1.00 tff(1912,plain,
% 1.07/1.00 (hskp5),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1902, 24, 1])).
% 1.07/1.00 tff(1913,plain,
% 1.07/1.00 (c1_1(a647)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1146, 1912])).
% 1.07/1.00 tff(1914,plain,
% 1.07/1.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a651) | c1_1(a651) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a647)) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a651) | c1_1(a651) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a647)) | (~c3_1(a651)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1915,plain,
% 1.07/1.00 ((hskp2 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c1_1(a647)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651))) <=> (hskp2 | c0_1(a651) | c1_1(a651) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a647)) | (~c3_1(a651)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.00 tff(1916,plain,
% 1.07/1.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c1_1(a647)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a651) | c1_1(a651) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a647)) | (~c3_1(a651))))),
% 1.07/1.00 inference(monotonicity,[status(thm)],[1915])).
% 1.07/1.00 tff(1917,plain,
% 1.07/1.00 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c1_1(a647)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a651) | c1_1(a651) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a647)) | (~c3_1(a651)))),
% 1.07/1.00 inference(transitivity,[status(thm)],[1916, 1914])).
% 1.07/1.00 tff(1918,plain,
% 1.07/1.00 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a647) | c3_1(a647) | (~c1_1(a647)) | c0_1(a651) | c1_1(a651) | (~c3_1(a651)))),
% 1.07/1.00 inference(quant_inst,[status(thm)],[])).
% 1.07/1.00 tff(1919,plain,
% 1.07/1.00 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | c3_1(U) | (~c1_1(U)) | c0_1(V) | c1_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a651) | c1_1(a651) | c3_1(a647) | (~ndr1_0) | c2_1(a647) | (~c1_1(a647)) | (~c3_1(a651))),
% 1.07/1.00 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.07/1.00 tff(1920,plain,
% 1.07/1.00 ($false),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1919, 102, 24, 1751, 270, 366, 365, 236, 34, 1155])).
% 1.07/1.00 tff(1921,plain,(c2_1(a647) | hskp2 | (~c3_1(a651)) | (~c1_1(a647)) | c0_1(a651) | c1_1(a651) | c3_1(a647)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.00 tff(1922,plain,
% 1.07/1.00 (c2_1(a647)),
% 1.07/1.00 inference(unit_resolution,[status(thm)],[1921, 24, 1740, 1913, 1739, 1738, 236])).
% 1.07/1.00 tff(1923,plain,
% 1.07/1.00 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | c0_1(a647) | c3_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a647) | c3_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c1_1(a647)))),
% 1.07/1.00 inference(rewrite,[status(thm)],[])).
% 1.07/1.01 tff(1924,plain,
% 1.07/1.01 ((hskp27 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647))) <=> (hskp27 | c0_1(a647) | c3_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c1_1(a647)))),
% 1.07/1.01 inference(rewrite,[status(thm)],[])).
% 1.07/1.01 tff(1925,plain,
% 1.07/1.01 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | c0_1(a647) | c3_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c1_1(a647))))),
% 1.07/1.01 inference(monotonicity,[status(thm)],[1924])).
% 1.07/1.01 tff(1926,plain,
% 1.07/1.01 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a647) | c3_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c1_1(a647)))),
% 1.07/1.01 inference(transitivity,[status(thm)],[1925, 1923])).
% 1.07/1.01 tff(1927,plain,
% 1.07/1.01 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp27 | (~ndr1_0) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a647) | c0_1(a647) | (~c1_1(a647)))),
% 1.07/1.01 inference(quant_inst,[status(thm)],[])).
% 1.07/1.01 tff(1928,plain,
% 1.07/1.01 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp27 | c0_1(a647) | c3_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c1_1(a647))),
% 1.07/1.01 inference(modus_ponens,[status(thm)],[1927, 1926])).
% 1.07/1.01 tff(1929,plain,
% 1.07/1.01 (hskp27 | c0_1(a647) | (~c1_1(a647))),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1928, 102, 1729, 1718, 236, 1707, 1280])).
% 1.07/1.01 tff(1930,plain,
% 1.07/1.01 (hskp27),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1929, 1913, 261])).
% 1.07/1.01 tff(1931,plain,
% 1.07/1.01 (c3_1(a655)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1297, 1930])).
% 1.07/1.01 tff(1932,plain,
% 1.07/1.01 (c2_1(a655)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1308, 1930])).
% 1.07/1.01 tff(1933,plain,
% 1.07/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))),
% 1.07/1.01 inference(rewrite,[status(thm)],[])).
% 1.07/1.01 tff(1934,plain,
% 1.07/1.01 (((~ndr1_0) | (~c2_1(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647))) <=> (c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))),
% 1.07/1.01 inference(rewrite,[status(thm)],[])).
% 1.07/1.01 tff(1935,plain,
% 1.07/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655))))),
% 1.07/1.01 inference(monotonicity,[status(thm)],[1934])).
% 1.07/1.01 tff(1936,plain,
% 1.07/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655)))),
% 1.07/1.01 inference(transitivity,[status(thm)],[1935, 1933])).
% 1.07/1.01 tff(1937,plain,
% 1.07/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a655)) | (~c1_1(a655)) | (~c3_1(a655)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647)))),
% 1.07/1.01 inference(quant_inst,[status(thm)],[])).
% 1.07/1.01 tff(1938,plain,
% 1.07/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c1_1(a655)) | (~c2_1(a655)) | (~c3_1(a655))),
% 1.07/1.01 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 1.07/1.01 tff(1939,plain,
% 1.07/1.01 ((~c2_1(a647)) | (~c1_1(a655))),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1938, 102, 1932, 1931, 1913, 1729, 1718, 261, 1707, 1263])).
% 1.07/1.01 tff(1940,plain,
% 1.07/1.01 (~c1_1(a655)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1939, 1922])).
% 1.07/1.01 tff(1941,plain,
% 1.07/1.01 (c0_1(a655)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1326, 1930])).
% 1.07/1.01 tff(1942,plain,
% 1.07/1.01 (hskp28 | c1_1(a655)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1330, 102, 1, 1941, 1931, 793])).
% 1.07/1.01 tff(1943,plain,
% 1.07/1.01 (hskp28),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1942, 1940])).
% 1.07/1.01 tff(1944,plain,
% 1.07/1.01 (c2_1(a671)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[813, 1943])).
% 1.07/1.01 tff(1945,plain,
% 1.07/1.01 (c1_1(a671)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[824, 1943])).
% 1.07/1.01 tff(1946,plain,
% 1.07/1.01 (c0_1(a671)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[835, 1943])).
% 1.07/1.01 tff(1947,plain,
% 1.07/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/1.01 inference(rewrite,[status(thm)],[])).
% 1.07/1.01 tff(1948,plain,
% 1.07/1.01 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647))) <=> (c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/1.01 inference(rewrite,[status(thm)],[])).
% 1.07/1.01 tff(1949,plain,
% 1.07/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 1.07/1.01 inference(monotonicity,[status(thm)],[1948])).
% 1.07/1.01 tff(1950,plain,
% 1.07/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/1.01 inference(transitivity,[status(thm)],[1949, 1947])).
% 1.07/1.01 tff(1951,plain,
% 1.07/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a647) | (~c1_1(a647)) | (~c2_1(a647)))),
% 1.07/1.01 inference(quant_inst,[status(thm)],[])).
% 1.07/1.01 tff(1952,plain,
% 1.07/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a647) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a647)) | (~c1_1(a647)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 1.07/1.01 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 1.07/1.01 tff(1953,plain,
% 1.07/1.01 ($false),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1952, 102, 1946, 1945, 1944, 1913, 1729, 1718, 261, 1707, 923, 1922])).
% 1.07/1.01 tff(1954,plain,(hskp2 | c0_1(a647) | hskp17 | c3_1(a647)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.01 tff(1955,plain,
% 1.07/1.01 (hskp2),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1954, 261, 1, 236])).
% 1.07/1.01 tff(1956,plain,
% 1.07/1.01 (~c0_1(a643)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1220, 1955])).
% 1.07/1.01 tff(1957,plain,
% 1.07/1.01 (c2_1(a643)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1231, 1955])).
% 1.07/1.01 tff(1958,plain,
% 1.07/1.01 (c1_1(a643)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1242, 1955])).
% 1.07/1.01 tff(1959,plain,
% 1.07/1.01 (hskp1),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1503, 1957, 1, 1958, 236, 1956, 261])).
% 1.07/1.01 tff(1960,plain,
% 1.07/1.01 (hskp28),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[802, 1959, 1])).
% 1.07/1.01 tff(1961,plain,
% 1.07/1.01 (c2_1(a671)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[813, 1960])).
% 1.07/1.01 tff(1962,plain,
% 1.07/1.01 (c1_1(a671)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[824, 1960])).
% 1.07/1.01 tff(1963,plain,
% 1.07/1.01 (c0_1(a671)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[835, 1960])).
% 1.07/1.01 tff(1964,plain,
% 1.07/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/1.01 inference(rewrite,[status(thm)],[])).
% 1.07/1.01 tff(1965,plain,
% 1.07/1.01 (((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/1.01 inference(rewrite,[status(thm)],[])).
% 1.07/1.01 tff(1966,plain,
% 1.07/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))))),
% 1.07/1.01 inference(monotonicity,[status(thm)],[1965])).
% 1.07/1.01 tff(1967,plain,
% 1.07/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)))),
% 1.07/1.01 inference(transitivity,[status(thm)],[1966, 1964])).
% 1.07/1.01 tff(1968,plain,
% 1.07/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 1.07/1.01 inference(quant_inst,[status(thm)],[])).
% 1.07/1.01 tff(1969,plain,
% 1.07/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c1_1(a643)) | (~c2_1(a671)) | (~c1_1(a671)) | (~c0_1(a671))),
% 1.07/1.01 inference(modus_ponens,[status(thm)],[1968, 1967])).
% 1.07/1.01 tff(1970,plain,
% 1.07/1.01 ($false),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1969, 102, 1963, 1962, 1961, 1958, 1957, 1729, 1718, 1956, 1707, 923])).
% 1.07/1.01 tff(1971,plain,(c0_1(a647) | hskp17 | c3_1(a647)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.01 tff(1972,plain,
% 1.07/1.01 ($false),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1971, 1911, 1910, 1])).
% 1.07/1.01 tff(1973,plain,(hskp17), inference(lemma,lemma(discharge,[]))).
% 1.07/1.01 tff(1974,plain,
% 1.07/1.01 (c2_1(a675)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1125, 1973])).
% 1.07/1.01 tff(1975,plain,
% 1.07/1.01 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))))),
% 1.07/1.01 inference(bind,[status(th)],[])).
% 1.07/1.01 tff(1976,plain,
% 1.07/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.07/1.01 inference(quant_intro,[status(thm)],[1975])).
% 1.07/1.01 tff(1977,plain,
% 1.07/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.07/1.01 inference(rewrite,[status(thm)],[])).
% 1.07/1.01 tff(1978,plain,
% 1.07/1.01 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))))),
% 1.07/1.01 inference(bind,[status(th)],[])).
% 1.07/1.01 tff(1979,plain,
% 1.07/1.01 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.07/1.01 inference(quant_intro,[status(thm)],[1978])).
% 1.07/1.01 tff(1980,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c2_1(U)) | c1_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 1.07/1.01 tff(1981,plain,
% 1.07/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.07/1.01 inference(modus_ponens,[status(thm)],[1980, 1979])).
% 1.07/1.01 tff(1982,plain,
% 1.07/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.07/1.01 inference(modus_ponens,[status(thm)],[1981, 1977])).
% 1.07/1.01 tff(1983,plain,(
% 1.07/1.01 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.07/1.01 inference(skolemize,[status(sab)],[1982])).
% 1.07/1.01 tff(1984,plain,
% 1.07/1.01 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))),
% 1.07/1.01 inference(modus_ponens,[status(thm)],[1983, 1976])).
% 1.07/1.01 tff(1985,plain,
% 1.07/1.01 (~c3_1(a675)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1080, 1973])).
% 1.07/1.01 tff(1986,plain,
% 1.07/1.01 (~c1_1(a675)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1074, 1973])).
% 1.07/1.01 tff(1987,assumption,(hskp18), introduced(assumption)).
% 1.07/1.01 tff(1988,plain,
% 1.07/1.01 (~c2_1(a676)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[224, 1987])).
% 1.07/1.01 tff(1989,plain,
% 1.07/1.01 (c1_1(a676)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[659, 1987])).
% 1.07/1.01 tff(1990,plain,
% 1.07/1.01 (c0_1(a676)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[581, 1987])).
% 1.07/1.01 tff(1991,plain,
% 1.07/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a676) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a676) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)))),
% 1.07/1.01 inference(rewrite,[status(thm)],[])).
% 1.07/1.01 tff(1992,plain,
% 1.07/1.01 (((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675))) <=> (c2_1(a676) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)))),
% 1.07/1.01 inference(rewrite,[status(thm)],[])).
% 1.07/1.01 tff(1993,plain,
% 1.07/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c2_1(a676) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a675)) | (~c1_1(a676)) | (~c0_1(a676))))),
% 1.07/1.01 inference(monotonicity,[status(thm)],[1992])).
% 1.07/1.01 tff(1994,plain,
% 1.07/1.01 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a676) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a675)) | (~c1_1(a676)) | (~c0_1(a676)))),
% 1.07/1.01 inference(transitivity,[status(thm)],[1993, 1991])).
% 1.07/1.01 tff(1995,plain,
% 1.07/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a676) | (~c1_1(a676)) | (~c0_1(a676)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675)))),
% 1.07/1.01 inference(quant_inst,[status(thm)],[])).
% 1.07/1.01 tff(1996,plain,
% 1.07/1.01 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c2_1(a676) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a675)) | (~c1_1(a676)) | (~c0_1(a676))),
% 1.07/1.01 inference(modus_ponens,[status(thm)],[1995, 1994])).
% 1.07/1.01 tff(1997,plain,
% 1.07/1.01 ($false),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1996, 102, 1990, 1989, 1974, 1729, 1718, 1988, 1986, 1985, 1707, 1984])).
% 1.07/1.01 tff(1998,plain,(~hskp18), inference(lemma,lemma(discharge,[]))).
% 1.07/1.01 tff(1999,plain,
% 1.07/1.01 (~c0_1(a675)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1114, 102, 1974, 1986, 1985, 994])).
% 1.07/1.01 tff(2000,plain,
% 1.07/1.01 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | c1_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c1_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))),
% 1.07/1.01 inference(rewrite,[status(thm)],[])).
% 1.07/1.01 tff(2001,plain,
% 1.07/1.01 ((hskp6 | hskp2 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | (~c2_1(a675))) <=> (hskp6 | hskp2 | c1_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))),
% 1.07/1.01 inference(rewrite,[status(thm)],[])).
% 1.07/1.01 tff(2002,plain,
% 1.07/1.01 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | (~c2_1(a675)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | c1_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675)))),
% 1.07/1.01 inference(monotonicity,[status(thm)],[2001])).
% 1.07/1.01 tff(2003,plain,
% 1.07/1.01 (((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | (~c2_1(a675)))) <=> ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c1_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675))),
% 1.07/1.01 inference(transitivity,[status(thm)],[2002, 2000])).
% 1.07/1.01 tff(2004,plain,
% 1.07/1.01 ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp2 | (~ndr1_0) | c1_1(a675) | c0_1(a675) | (~c2_1(a675)))),
% 1.07/1.01 inference(quant_inst,[status(thm)],[])).
% 1.07/1.01 tff(2005,plain,
% 1.07/1.01 ((~![U: $i] : (hskp6 | hskp2 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp2 | c1_1(a675) | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675)),
% 1.07/1.01 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 1.07/1.01 tff(2006,plain,
% 1.07/1.01 (hskp6 | hskp2 | c0_1(a675)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[2005, 102, 1974, 1986, 44])).
% 1.07/1.01 tff(2007,plain,
% 1.07/1.01 (hskp6),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[2006, 24, 1999])).
% 1.07/1.01 tff(2008,plain,
% 1.07/1.01 (~c2_1(a648)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[120, 2007])).
% 1.07/1.01 tff(2009,plain,
% 1.07/1.01 (~c3_1(a648)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[114, 2007])).
% 1.07/1.01 tff(2010,assumption,(hskp20), introduced(assumption)).
% 1.07/1.01 tff(2011,plain,
% 1.07/1.01 (~c3_1(a686)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[705, 2010])).
% 1.07/1.01 tff(2012,assumption,(ndr1_0), introduced(assumption)).
% 1.07/1.01 tff(2013,assumption,(~c1_1(a641)), introduced(assumption)).
% 1.07/1.01 tff(2014,assumption,(c3_1(a641)), introduced(assumption)).
% 1.07/1.01 tff(2015,assumption,(c2_1(a641)), introduced(assumption)).
% 1.07/1.01 tff(2016,assumption,(~c3_1(a648)), introduced(assumption)).
% 1.07/1.01 tff(2017,assumption,(~c2_1(a648)), introduced(assumption)).
% 1.07/1.01 tff(2018,plain,
% 1.07/1.01 (c1_1(a686)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[735, 2010])).
% 1.07/1.01 tff(2019,plain,
% 1.07/1.01 (c2_1(a686)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[717, 2010])).
% 1.07/1.01 tff(2020,plain,
% 1.07/1.01 ((~ndr1_0) | (~c2_1(a675)) | (~c0_1(a675))),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[1114, 1083, 1082, 994])).
% 1.07/1.01 tff(2021,plain,
% 1.07/1.01 (~c0_1(a675)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[2020, 1646, 2012])).
% 1.07/1.01 tff(2022,plain,
% 1.07/1.01 (hskp6 | hskp2 | (~ndr1_0) | (~c2_1(a675)) | c0_1(a675)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[2005, 1083, 44])).
% 1.07/1.01 tff(2023,plain,
% 1.07/1.01 (hskp6),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[2022, 1646, 2012, 24, 2021])).
% 1.07/1.01 tff(2024,plain,
% 1.07/1.01 (c0_1(a648)),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[328, 2023])).
% 1.07/1.01 tff(2025,plain,
% 1.07/1.01 ((~ndr1_0) | (~c0_1(a648)) | (~c2_1(a686)) | (~c0_1(a686))),
% 1.07/1.01 inference(unit_resolution,[status(thm)],[724, 1024, 2017, 2016, 186])).
% 1.07/1.02 tff(2026,plain,
% 1.07/1.02 (~c0_1(a686)),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[2025, 2024, 2012, 1025])).
% 1.07/1.02 tff(2027,plain,
% 1.07/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a675) | c3_1(a675) | c2_1(a648) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a675) | c3_1(a675) | c2_1(a648) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)))),
% 1.07/1.02 inference(rewrite,[status(thm)],[])).
% 1.07/1.02 tff(2028,plain,
% 1.07/1.02 (((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675))) <=> (c1_1(a675) | c3_1(a675) | c2_1(a648) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)))),
% 1.07/1.02 inference(rewrite,[status(thm)],[])).
% 1.07/1.02 tff(2029,plain,
% 1.07/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | (c1_1(a675) | c3_1(a675) | c2_1(a648) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675))))),
% 1.07/1.02 inference(monotonicity,[status(thm)],[2028])).
% 1.07/1.02 tff(2030,plain,
% 1.07/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a675) | c3_1(a675) | c2_1(a648) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675)))),
% 1.07/1.02 inference(transitivity,[status(thm)],[2029, 2027])).
% 1.07/1.02 tff(2031,plain,
% 1.07/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c3_1(a675) | c1_1(a675) | (~c2_1(a675)))),
% 1.07/1.02 inference(quant_inst,[status(thm)],[])).
% 1.07/1.02 tff(2032,plain,
% 1.07/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c3_1(W) | c1_1(W) | (~c2_1(W)))) | c1_1(a675) | c3_1(a675) | c2_1(a648) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675))),
% 1.07/1.02 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 1.07/1.02 tff(2033,plain,
% 1.07/1.02 (c1_1(a675) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c0_1(a648)) | (~c1_1(a648)) | (~c2_1(a675))),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[2032, 1082, 2017, 2013, 1984])).
% 1.07/1.02 tff(2034,plain,
% 1.07/1.02 (~c1_1(a648)),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[2033, 2024, 2012, 2015, 2014, 1083, 1646])).
% 1.07/1.02 tff(2035,plain,
% 1.07/1.02 ($false),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[742, 2012, 1026, 1025, 2024, 1024, 2017, 235, 2034, 2026])).
% 1.07/1.02 tff(2036,plain,((~c2_1(a675)) | (~ndr1_0) | (~c1_1(a686)) | (~c2_1(a686)) | c3_1(a686) | c2_1(a648) | c3_1(a648) | (~c2_1(a641)) | (~c3_1(a641)) | c1_1(a675) | c3_1(a675) | c1_1(a641) | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.07/1.02 tff(2037,plain,
% 1.07/1.02 ($false),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[2036, 2019, 2018, 24, 1646, 1024, 2017, 2016, 2015, 2014, 1083, 1082, 2013, 2012])).
% 1.07/1.02 tff(2038,plain,((~hskp20) | hskp2 | (~c2_1(a675)) | c3_1(a686) | c2_1(a648) | c3_1(a648) | (~c2_1(a641)) | (~c3_1(a641)) | c1_1(a675) | c3_1(a675) | c1_1(a641) | (~ndr1_0)), inference(lemma,lemma(discharge,[]))).
% 1.07/1.02 tff(2039,plain,
% 1.07/1.02 ((~hskp20) | hskp2 | (~c2_1(a675)) | c3_1(a686) | c2_1(a648) | c3_1(a648) | (~c2_1(a641)) | (~c3_1(a641)) | c1_1(a675) | c3_1(a675) | c1_1(a641)),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[2038, 102])).
% 1.07/1.02 tff(2040,plain,
% 1.07/1.02 ((~hskp20) | hskp2 | (~c2_1(a675)) | c3_1(a686) | c2_1(a648) | c3_1(a648) | c1_1(a675) | c3_1(a675)),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[2039, 1729, 1718, 1707])).
% 1.07/1.02 tff(2041,plain,
% 1.07/1.02 ($false),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[2040, 2011, 2010, 1974, 24, 2009, 2008, 1986, 1985])).
% 1.07/1.02 tff(2042,plain,((~hskp20) | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.07/1.02 tff(2043,plain,
% 1.07/1.02 (~hskp20),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[2042, 24])).
% 1.07/1.02 tff(2044,plain,
% 1.07/1.02 ($false),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[218, 2043, 24, 1998])).
% 1.07/1.02 tff(2045,plain,(hskp2), inference(lemma,lemma(discharge,[]))).
% 1.07/1.02 tff(2046,plain,
% 1.07/1.02 (c2_1(a643)),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[1231, 2045])).
% 1.07/1.02 tff(2047,plain,
% 1.07/1.02 (~c0_1(a643)),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[1220, 2045])).
% 1.07/1.02 tff(2048,plain,
% 1.07/1.02 (c1_1(a643)),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[1242, 2045])).
% 1.07/1.02 tff(2049,plain,
% 1.07/1.02 (c3_1(a643)),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[1675, 2048, 1986, 1985, 2047, 2046, 1974])).
% 1.07/1.02 tff(2050,plain,
% 1.07/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))),
% 1.07/1.02 inference(rewrite,[status(thm)],[])).
% 1.07/1.02 tff(2051,plain,
% 1.07/1.02 (((~ndr1_0) | (~c2_1(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643))) <=> (c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))),
% 1.07/1.02 inference(rewrite,[status(thm)],[])).
% 1.07/1.02 tff(2052,plain,
% 1.07/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643))))),
% 1.07/1.02 inference(monotonicity,[status(thm)],[2051])).
% 1.07/1.02 tff(2053,plain,
% 1.07/1.02 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643)))),
% 1.07/1.02 inference(transitivity,[status(thm)],[2052, 2050])).
% 1.07/1.02 tff(2054,plain,
% 1.07/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_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(a643)) | (~c1_1(a643)) | (~c3_1(a643)) | c1_1(a641) | (~c2_1(a641)) | (~c3_1(a641)) | c0_1(a643) | (~c1_1(a643)) | (~c2_1(a643)))),
% 1.07/1.02 inference(quant_inst,[status(thm)],[])).
% 1.07/1.02 tff(2055,plain,
% 1.07/1.02 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a643) | c1_1(a641) | (~ndr1_0) | (~c2_1(a641)) | (~c3_1(a641)) | (~c2_1(a643)) | (~c3_1(a643)) | (~c1_1(a643))),
% 1.07/1.02 inference(modus_ponens,[status(thm)],[2054, 2053])).
% 1.07/1.02 tff(2056,plain,
% 1.07/1.02 ($false),
% 1.07/1.02 inference(unit_resolution,[status(thm)],[2055, 102, 2048, 2046, 1729, 1718, 2047, 1707, 1263, 2049])).
% 1.07/1.02 % SZS output end Proof
%------------------------------------------------------------------------------