%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN488-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 : Sat Jun 21 05:39:19 AM UTC 2025
% Result : Unsatisfiable 1.07s 1.24s
% Output : Proof 1.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN488-1 : TPTP v9.0.0. Released v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:38:42 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.07/1.24 % SZS status Unsatisfiable
% 1.07/1.24 % SZS output start Proof
% 1.07/1.24 tff(c1_1_type, type, (
% 1.07/1.24 c1_1: $i > $o)).
% 1.07/1.24 tff(a2455_type, type, (
% 1.07/1.24 a2455: $i)).
% 1.07/1.24 tff(a2425_type, type, (
% 1.07/1.24 a2425: $i)).
% 1.07/1.24 tff(a2408_type, type, (
% 1.07/1.24 a2408: $i)).
% 1.07/1.24 tff(a2409_type, type, (
% 1.07/1.24 a2409: $i)).
% 1.07/1.24 tff(c0_1_type, type, (
% 1.07/1.24 c0_1: $i > $o)).
% 1.07/1.24 tff(a2403_type, type, (
% 1.07/1.24 a2403: $i)).
% 1.07/1.24 tff(a2435_type, type, (
% 1.07/1.24 a2435: $i)).
% 1.07/1.24 tff(c2_1_type, type, (
% 1.07/1.24 c2_1: $i > $o)).
% 1.07/1.24 tff(c3_1_type, type, (
% 1.07/1.24 c3_1: $i > $o)).
% 1.07/1.24 tff(ndr1_0_type, type, (
% 1.07/1.24 ndr1_0: $o)).
% 1.07/1.24 tff(hskp1_type, type, (
% 1.07/1.24 hskp1: $o)).
% 1.07/1.24 tff(a2413_type, type, (
% 1.07/1.24 a2413: $i)).
% 1.07/1.24 tff(hskp9_type, type, (
% 1.07/1.24 hskp9: $o)).
% 1.07/1.24 tff(a2432_type, type, (
% 1.07/1.24 a2432: $i)).
% 1.07/1.24 tff(hskp19_type, type, (
% 1.07/1.24 hskp19: $o)).
% 1.07/1.24 tff(hskp14_type, type, (
% 1.07/1.24 hskp14: $o)).
% 1.07/1.24 tff(hskp23_type, type, (
% 1.07/1.24 hskp23: $o)).
% 1.07/1.24 tff(hskp29_type, type, (
% 1.07/1.24 hskp29: $o)).
% 1.07/1.24 tff(hskp5_type, type, (
% 1.07/1.24 hskp5: $o)).
% 1.07/1.24 tff(hskp16_type, type, (
% 1.07/1.24 hskp16: $o)).
% 1.07/1.24 tff(a2414_type, type, (
% 1.07/1.24 a2414: $i)).
% 1.07/1.24 tff(a2417_type, type, (
% 1.07/1.24 a2417: $i)).
% 1.07/1.24 tff(a2422_type, type, (
% 1.07/1.24 a2422: $i)).
% 1.07/1.24 tff(hskp15_type, type, (
% 1.07/1.24 hskp15: $o)).
% 1.07/1.24 tff(a2418_type, type, (
% 1.07/1.24 a2418: $i)).
% 1.07/1.24 tff(hskp13_type, type, (
% 1.07/1.24 hskp13: $o)).
% 1.07/1.24 tff(a2404_type, type, (
% 1.07/1.24 a2404: $i)).
% 1.07/1.24 tff(hskp20_type, type, (
% 1.07/1.24 hskp20: $o)).
% 1.07/1.24 tff(hskp12_type, type, (
% 1.07/1.24 hskp12: $o)).
% 1.07/1.24 tff(a2478_type, type, (
% 1.07/1.24 a2478: $i)).
% 1.07/1.24 tff(hskp10_type, type, (
% 1.07/1.24 hskp10: $o)).
% 1.07/1.24 tff(hskp25_type, type, (
% 1.07/1.24 hskp25: $o)).
% 1.07/1.24 tff(hskp11_type, type, (
% 1.07/1.24 hskp11: $o)).
% 1.07/1.24 tff(a2416_type, type, (
% 1.07/1.24 a2416: $i)).
% 1.07/1.24 tff(hskp31_type, type, (
% 1.07/1.24 hskp31: $o)).
% 1.07/1.24 tff(hskp27_type, type, (
% 1.07/1.24 hskp27: $o)).
% 1.07/1.24 tff(a2450_type, type, (
% 1.07/1.24 a2450: $i)).
% 1.07/1.24 tff(hskp30_type, type, (
% 1.07/1.24 hskp30: $o)).
% 1.07/1.24 tff(a2420_type, type, (
% 1.07/1.24 a2420: $i)).
% 1.07/1.24 tff(hskp6_type, type, (
% 1.07/1.24 hskp6: $o)).
% 1.07/1.24 tff(a2410_type, type, (
% 1.07/1.24 a2410: $i)).
% 1.07/1.24 tff(a2498_type, type, (
% 1.07/1.24 a2498: $i)).
% 1.07/1.24 tff(a2500_type, type, (
% 1.07/1.24 a2500: $i)).
% 1.07/1.24 tff(a2407_type, type, (
% 1.07/1.24 a2407: $i)).
% 1.07/1.24 tff(hskp4_type, type, (
% 1.07/1.24 hskp4: $o)).
% 1.07/1.24 tff(a2405_type, type, (
% 1.07/1.24 a2405: $i)).
% 1.07/1.24 tff(a2484_type, type, (
% 1.07/1.24 a2484: $i)).
% 1.07/1.24 tff(hskp26_type, type, (
% 1.07/1.24 hskp26: $o)).
% 1.07/1.24 tff(hskp3_type, type, (
% 1.07/1.24 hskp3: $o)).
% 1.07/1.24 tff(hskp24_type, type, (
% 1.07/1.24 hskp24: $o)).
% 1.07/1.24 tff(a2468_type, type, (
% 1.07/1.24 a2468: $i)).
% 1.07/1.24 tff(hskp2_type, type, (
% 1.07/1.24 hskp2: $o)).
% 1.07/1.24 tff(hskp22_type, type, (
% 1.07/1.24 hskp22: $o)).
% 1.07/1.24 tff(a2453_type, type, (
% 1.07/1.24 a2453: $i)).
% 1.07/1.24 tff(hskp0_type, type, (
% 1.07/1.24 hskp0: $o)).
% 1.07/1.24 tff(a2402_type, type, (
% 1.07/1.24 a2402: $i)).
% 1.07/1.24 tff(a2427_type, type, (
% 1.07/1.24 a2427: $i)).
% 1.07/1.24 tff(hskp17_type, type, (
% 1.07/1.24 hskp17: $o)).
% 1.07/1.24 tff(hskp21_type, type, (
% 1.07/1.24 hskp21: $o)).
% 1.07/1.24 tff(a2406_type, type, (
% 1.07/1.24 a2406: $i)).
% 1.07/1.24 tff(hskp28_type, type, (
% 1.07/1.24 hskp28: $o)).
% 1.07/1.24 tff(a2437_type, type, (
% 1.07/1.24 a2437: $i)).
% 1.07/1.24 tff(a2411_type, type, (
% 1.07/1.24 a2411: $i)).
% 1.07/1.24 tff(hskp7_type, type, (
% 1.07/1.24 hskp7: $o)).
% 1.07/1.24 tff(hskp18_type, type, (
% 1.07/1.24 hskp18: $o)).
% 1.07/1.24 tff(a2428_type, type, (
% 1.07/1.24 a2428: $i)).
% 1.07/1.24 tff(1,assumption,(~c1_1(a2408)), introduced(assumption)).
% 1.07/1.24 tff(2,plain,
% 1.07/1.24 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(3,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[2])).
% 1.07/1.24 tff(4,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(5,plain,
% 1.07/1.24 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(6,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[5])).
% 1.07/1.24 tff(7,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause198')).
% 1.07/1.24 tff(8,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[7, 6])).
% 1.07/1.24 tff(9,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.07/1.24 tff(10,plain,(
% 1.07/1.24 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(skolemize,[status(sab)],[9])).
% 1.07/1.24 tff(11,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[10, 3])).
% 1.07/1.24 tff(12,plain,
% 1.07/1.24 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(13,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[12])).
% 1.07/1.24 tff(14,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(15,plain,
% 1.07/1.24 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(16,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[15])).
% 1.07/1.24 tff(17,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause196')).
% 1.07/1.24 tff(18,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.07/1.24 tff(19,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[18, 14])).
% 1.07/1.24 tff(20,plain,(
% 1.07/1.24 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(skolemize,[status(sab)],[19])).
% 1.07/1.24 tff(21,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[20, 13])).
% 1.07/1.24 tff(22,assumption,(~hskp1), introduced(assumption)).
% 1.07/1.24 tff(23,plain,
% 1.07/1.24 (^[U: $i] : refl((hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(24,plain,
% 1.07/1.24 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[23])).
% 1.07/1.24 tff(25,plain,
% 1.07/1.24 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(26,plain,
% 1.07/1.24 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp1))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) | hskp9) <=> ((hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp9))), rewrite(((hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp9) <=> (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) | hskp9) <=> (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(27,plain,
% 1.07/1.24 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) | hskp9) <=> ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[26])).
% 1.07/1.24 tff(28,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp1) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause156')).
% 1.07/1.24 tff(29,plain,
% 1.07/1.24 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[28, 27])).
% 1.07/1.24 tff(30,plain,
% 1.07/1.24 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[29, 25])).
% 1.07/1.24 tff(31,plain,(
% 1.07/1.24 ![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.07/1.24 inference(skolemize,[status(sab)],[30])).
% 1.07/1.24 tff(32,plain,
% 1.07/1.24 (![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[31, 24])).
% 1.07/1.24 tff(33,plain,
% 1.07/1.24 (^[U: $i] : refl((hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(34,plain,
% 1.07/1.24 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[33])).
% 1.07/1.24 tff(35,plain,
% 1.07/1.24 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(36,plain,
% 1.07/1.24 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp14))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) <=> (hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp23) <=> ((hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23))), rewrite(((hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp23) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp23) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(37,plain,
% 1.07/1.24 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp23) <=> ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[36])).
% 1.07/1.24 tff(38,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp14) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 1.07/1.24 tff(39,plain,
% 1.07/1.24 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.07/1.24 tff(40,plain,
% 1.07/1.24 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[39, 35])).
% 1.07/1.24 tff(41,plain,(
% 1.07/1.24 ![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.24 inference(skolemize,[status(sab)],[40])).
% 1.07/1.24 tff(42,plain,
% 1.07/1.24 (![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[41, 34])).
% 1.07/1.24 tff(43,assumption,(~hskp19), introduced(assumption)).
% 1.07/1.24 tff(44,plain,
% 1.07/1.24 (^[U: $i] : refl((hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(45,plain,
% 1.07/1.24 (![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[44])).
% 1.07/1.24 tff(46,plain,
% 1.07/1.24 (![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(47,plain,
% 1.07/1.24 (^[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) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp19) <=> ((hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp19))), rewrite(((hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp19) <=> (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(48,plain,
% 1.07/1.24 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp19) <=> ![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[47])).
% 1.07/1.24 tff(49,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp5) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause151')).
% 1.07/1.24 tff(50,plain,
% 1.07/1.24 (![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.07/1.24 tff(51,plain,
% 1.07/1.24 (![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[50, 46])).
% 1.07/1.24 tff(52,plain,(
% 1.07/1.24 ![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.07/1.24 inference(skolemize,[status(sab)],[51])).
% 1.07/1.24 tff(53,plain,
% 1.07/1.24 (![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[52, 45])).
% 1.07/1.24 tff(54,plain,
% 1.07/1.24 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(55,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[54])).
% 1.07/1.24 tff(56,plain,
% 1.07/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(57,plain,
% 1.07/1.24 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(58,plain,
% 1.07/1.25 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[57])).
% 1.07/1.25 tff(59,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c2_1(U)) | c0_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause200')).
% 1.07/1.25 tff(60,plain,
% 1.07/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[59, 58])).
% 1.07/1.25 tff(61,plain,
% 1.07/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[60, 56])).
% 1.07/1.25 tff(62,plain,(
% 1.07/1.25 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.25 inference(skolemize,[status(sab)],[61])).
% 1.07/1.25 tff(63,plain,
% 1.07/1.25 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[62, 55])).
% 1.07/1.25 tff(64,assumption,(~hskp16), introduced(assumption)).
% 1.07/1.25 tff(65,assumption,(~hskp13), introduced(assumption)).
% 1.07/1.25 tff(66,plain,
% 1.07/1.25 (^[U: $i] : refl((hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(67,plain,
% 1.07/1.25 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[66])).
% 1.07/1.25 tff(68,plain,
% 1.07/1.25 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(69,plain,
% 1.07/1.25 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp16))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) | hskp13) <=> ((hskp16 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp13))), rewrite(((hskp16 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp13) <=> (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) | hskp13) <=> (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(70,plain,
% 1.07/1.25 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) | hskp13) <=> ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[69])).
% 1.07/1.25 tff(71,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp16) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 1.07/1.25 tff(72,plain,
% 1.07/1.25 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.07/1.25 tff(73,plain,
% 1.07/1.25 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.07/1.25 tff(74,plain,(
% 1.07/1.25 ![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.07/1.25 inference(skolemize,[status(sab)],[73])).
% 1.07/1.25 tff(75,plain,
% 1.07/1.25 (![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[74, 67])).
% 1.07/1.25 tff(76,plain,
% 1.07/1.25 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(77,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[76])).
% 1.07/1.25 tff(78,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(79,plain,
% 1.07/1.25 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(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)) | (~c1_1(V)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c1_1(V)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(80,plain,
% 1.07/1.25 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[79])).
% 1.07/1.25 tff(81,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 1.07/1.25 tff(82,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.07/1.25 tff(83,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[82, 78])).
% 1.07/1.25 tff(84,plain,(
% 1.07/1.25 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(skolemize,[status(sab)],[83])).
% 1.07/1.25 tff(85,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[84, 77])).
% 1.07/1.25 tff(86,plain,
% 1.07/1.25 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(87,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[86])).
% 1.07/1.25 tff(88,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(89,plain,
% 1.07/1.25 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(90,plain,
% 1.07/1.25 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[89])).
% 1.07/1.25 tff(91,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 1.07/1.25 tff(92,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.07/1.25 tff(93,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[92, 88])).
% 1.07/1.25 tff(94,plain,(
% 1.07/1.25 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.07/1.25 inference(skolemize,[status(sab)],[93])).
% 1.07/1.25 tff(95,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[94, 87])).
% 1.07/1.25 tff(96,assumption,(~hskp10), introduced(assumption)).
% 1.07/1.25 tff(97,plain,
% 1.07/1.25 (^[U: $i] : refl((hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(98,plain,
% 1.07/1.25 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[97])).
% 1.07/1.25 tff(99,plain,
% 1.07/1.25 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(100,plain,
% 1.07/1.25 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp19) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp19) | hskp25) <=> ((hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25))), rewrite(((hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp19) | hskp25) <=> (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(101,plain,
% 1.07/1.25 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp19) | hskp25) <=> ![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[100])).
% 1.07/1.25 tff(102,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp19) | hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 1.07/1.25 tff(103,plain,
% 1.07/1.25 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.07/1.25 tff(104,plain,
% 1.07/1.25 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[103, 99])).
% 1.07/1.25 tff(105,plain,(
% 1.07/1.25 ![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.25 inference(skolemize,[status(sab)],[104])).
% 1.07/1.25 tff(106,plain,
% 1.07/1.25 (![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[105, 98])).
% 1.07/1.25 tff(107,assumption,(hskp25), introduced(assumption)).
% 1.07/1.25 tff(108,plain,
% 1.07/1.25 (((~hskp25) | c2_1(a2478)) <=> ((~hskp25) | c2_1(a2478))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(109,axiom,((~hskp25) | c2_1(a2478)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 1.07/1.25 tff(110,plain,
% 1.07/1.25 ((~hskp25) | c2_1(a2478)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.07/1.25 tff(111,plain,
% 1.07/1.25 ((~hskp25) | c2_1(a2478)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[110, 108])).
% 1.07/1.25 tff(112,plain,
% 1.07/1.25 ((~hskp25) | c2_1(a2478)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[111, 108])).
% 1.07/1.25 tff(113,plain,
% 1.07/1.25 ((~hskp25) | c2_1(a2478)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[112, 108])).
% 1.07/1.25 tff(114,plain,
% 1.07/1.25 ((~hskp25) | c2_1(a2478)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[113, 108])).
% 1.07/1.25 tff(115,plain,
% 1.07/1.25 (c2_1(a2478)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[114, 107])).
% 1.07/1.25 tff(116,plain,
% 1.07/1.25 (((~hskp25) | (~c0_1(a2478))) <=> ((~hskp25) | (~c0_1(a2478)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(117,plain,
% 1.07/1.25 (((~c0_1(a2478)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a2478)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(118,axiom,((~c0_1(a2478)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause91')).
% 1.07/1.25 tff(119,plain,
% 1.07/1.25 ((~hskp25) | (~c0_1(a2478))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.07/1.25 tff(120,plain,
% 1.07/1.25 ((~hskp25) | (~c0_1(a2478))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[119, 116])).
% 1.07/1.25 tff(121,plain,
% 1.07/1.25 (~c0_1(a2478)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[120, 107])).
% 1.07/1.25 tff(122,plain,
% 1.07/1.25 (((~hskp25) | (~c3_1(a2478))) <=> ((~hskp25) | (~c3_1(a2478)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(123,plain,
% 1.07/1.25 (((~c3_1(a2478)) | (~hskp25)) <=> ((~hskp25) | (~c3_1(a2478)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(124,axiom,((~c3_1(a2478)) | (~hskp25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 1.07/1.25 tff(125,plain,
% 1.07/1.25 ((~hskp25) | (~c3_1(a2478))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.07/1.25 tff(126,plain,
% 1.07/1.25 ((~hskp25) | (~c3_1(a2478))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[125, 122])).
% 1.07/1.25 tff(127,plain,
% 1.07/1.25 (~c3_1(a2478)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[126, 107])).
% 1.07/1.25 tff(128,plain,
% 1.07/1.25 (^[U: $i] : refl((hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) <=> (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(129,plain,
% 1.07/1.25 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) <=> ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[128])).
% 1.07/1.25 tff(130,plain,
% 1.07/1.25 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) <=> ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(131,plain,
% 1.07/1.25 (^[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) | c1_1(U) | (~c3_1(U)) | c2_1(U))), (((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))), ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp10) | hskp16) <=> ((hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) | hskp16))), rewrite(((hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U)) | hskp16) <=> (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))), (((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp10) | hskp16) <=> (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(132,plain,
% 1.07/1.25 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp10) | hskp16) <=> ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[131])).
% 1.07/1.25 tff(133,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp10) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 1.07/1.25 tff(134,plain,
% 1.07/1.25 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.07/1.25 tff(135,plain,
% 1.07/1.25 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[134, 130])).
% 1.07/1.25 tff(136,plain,(
% 1.07/1.25 ![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.07/1.25 inference(skolemize,[status(sab)],[135])).
% 1.07/1.25 tff(137,plain,
% 1.07/1.25 (![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[136, 129])).
% 1.07/1.25 tff(138,assumption,(hskp11), introduced(assumption)).
% 1.07/1.25 tff(139,plain,
% 1.07/1.25 (((~hskp11) | (~c2_1(a2416))) <=> ((~hskp11) | (~c2_1(a2416)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(140,plain,
% 1.07/1.25 (((~c2_1(a2416)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a2416)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(141,axiom,((~c2_1(a2416)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 1.07/1.25 tff(142,plain,
% 1.07/1.25 ((~hskp11) | (~c2_1(a2416))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[141, 140])).
% 1.07/1.25 tff(143,plain,
% 1.07/1.25 ((~hskp11) | (~c2_1(a2416))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[142, 139])).
% 1.07/1.25 tff(144,plain,
% 1.07/1.25 (~c2_1(a2416)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[143, 138])).
% 1.07/1.25 tff(145,plain,
% 1.07/1.25 (((~hskp11) | (~c1_1(a2416))) <=> ((~hskp11) | (~c1_1(a2416)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(146,plain,
% 1.07/1.25 (((~c1_1(a2416)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a2416)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(147,axiom,((~c1_1(a2416)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 1.07/1.25 tff(148,plain,
% 1.07/1.25 ((~hskp11) | (~c1_1(a2416))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[147, 146])).
% 1.07/1.25 tff(149,plain,
% 1.07/1.25 ((~hskp11) | (~c1_1(a2416))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[148, 145])).
% 1.07/1.25 tff(150,plain,
% 1.07/1.25 (~c1_1(a2416)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[149, 138])).
% 1.07/1.25 tff(151,plain,
% 1.07/1.25 (((~hskp11) | c3_1(a2416)) <=> ((~hskp11) | c3_1(a2416))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(152,axiom,((~hskp11) | c3_1(a2416)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 1.07/1.25 tff(153,plain,
% 1.07/1.25 ((~hskp11) | c3_1(a2416)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.07/1.25 tff(154,plain,
% 1.07/1.25 ((~hskp11) | c3_1(a2416)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[153, 151])).
% 1.07/1.25 tff(155,plain,
% 1.07/1.25 ((~hskp11) | c3_1(a2416)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[154, 151])).
% 1.07/1.25 tff(156,plain,
% 1.07/1.25 ((~hskp11) | c3_1(a2416)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[155, 151])).
% 1.07/1.25 tff(157,plain,
% 1.07/1.25 ((~hskp11) | c3_1(a2416)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[156, 151])).
% 1.07/1.25 tff(158,plain,
% 1.07/1.25 (c3_1(a2416)),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[157, 138])).
% 1.07/1.25 tff(159,assumption,(~ndr1_0), introduced(assumption)).
% 1.07/1.25 tff(160,plain,
% 1.07/1.25 ((ndr1_0 | (~hskp25)) <=> (ndr1_0 | (~hskp25))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(161,plain,
% 1.07/1.25 (((~hskp25) | ndr1_0) <=> (ndr1_0 | (~hskp25))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(162,axiom,((~hskp25) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause7')).
% 1.07/1.25 tff(163,plain,
% 1.07/1.25 (ndr1_0 | (~hskp25)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[162, 161])).
% 1.07/1.25 tff(164,plain,
% 1.07/1.25 (ndr1_0 | (~hskp25)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[163, 160])).
% 1.07/1.25 tff(165,plain,
% 1.07/1.25 (~hskp25),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[164, 159])).
% 1.07/1.25 tff(166,plain,
% 1.07/1.25 (((~hskp31) | ndr1_0) <=> ((~hskp31) | ndr1_0)),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(167,axiom,((~hskp31) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause1')).
% 1.07/1.25 tff(168,plain,
% 1.07/1.25 ((~hskp31) | ndr1_0),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.07/1.25 tff(169,plain,
% 1.07/1.25 ((~hskp31) | ndr1_0),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[168, 166])).
% 1.07/1.25 tff(170,plain,
% 1.07/1.25 ((~hskp31) | ndr1_0),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[169, 166])).
% 1.07/1.25 tff(171,plain,
% 1.07/1.25 ((~hskp31) | ndr1_0),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[170, 166])).
% 1.07/1.25 tff(172,plain,
% 1.07/1.25 ((~hskp31) | ndr1_0),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[171, 166])).
% 1.07/1.25 tff(173,plain,
% 1.07/1.25 (~hskp31),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[172, 159])).
% 1.07/1.25 tff(174,plain,
% 1.07/1.25 ((ndr1_0 | (~hskp27)) <=> (ndr1_0 | (~hskp27))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(175,plain,
% 1.07/1.25 (((~hskp27) | ndr1_0) <=> (ndr1_0 | (~hskp27))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(176,axiom,((~hskp27) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause5')).
% 1.07/1.25 tff(177,plain,
% 1.07/1.25 (ndr1_0 | (~hskp27)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.07/1.25 tff(178,plain,
% 1.07/1.25 (ndr1_0 | (~hskp27)),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[177, 174])).
% 1.07/1.25 tff(179,plain,
% 1.07/1.25 (~hskp27),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[178, 159])).
% 1.07/1.25 tff(180,plain,
% 1.07/1.25 ((hskp31 | hskp27 | hskp25) <=> (hskp31 | hskp27 | hskp25)),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(181,plain,
% 1.07/1.25 (((hskp31 | hskp25) | hskp27) <=> (hskp31 | hskp27 | hskp25)),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(182,plain,
% 1.07/1.25 ((hskp31 | hskp25) <=> (hskp31 | hskp25)),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(183,plain,
% 1.07/1.25 (((hskp31 | hskp25) | hskp27) <=> ((hskp31 | hskp25) | hskp27)),
% 1.07/1.25 inference(monotonicity,[status(thm)],[182])).
% 1.07/1.25 tff(184,plain,
% 1.07/1.25 (((hskp31 | hskp25) | hskp27) <=> (hskp31 | hskp27 | hskp25)),
% 1.07/1.25 inference(transitivity,[status(thm)],[183, 181])).
% 1.07/1.25 tff(185,axiom,((hskp31 | hskp25) | hskp27), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 1.07/1.25 tff(186,plain,
% 1.07/1.25 (hskp31 | hskp27 | hskp25),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.07/1.25 tff(187,plain,
% 1.07/1.25 (hskp31 | hskp27 | hskp25),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[186, 180])).
% 1.07/1.25 tff(188,plain,
% 1.07/1.25 (hskp31 | hskp27 | hskp25),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[187, 180])).
% 1.07/1.25 tff(189,plain,
% 1.07/1.25 (hskp31 | hskp27 | hskp25),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[188, 180])).
% 1.07/1.25 tff(190,plain,
% 1.07/1.25 (hskp31 | hskp27 | hskp25),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[189, 180])).
% 1.07/1.25 tff(191,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[190, 179, 173, 165])).
% 1.07/1.25 tff(192,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(193,plain,
% 1.07/1.25 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(194,plain,
% 1.07/1.25 ((hskp16 | hskp10 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | c2_1(a2416)) <=> (hskp16 | hskp10 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(195,plain,
% 1.07/1.25 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | c2_1(a2416))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[194])).
% 1.07/1.25 tff(196,plain,
% 1.07/1.25 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | c2_1(a2416))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)))),
% 1.07/1.25 inference(transitivity,[status(thm)],[195, 193])).
% 1.07/1.25 tff(197,plain,
% 1.07/1.25 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | c2_1(a2416))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(198,plain,
% 1.07/1.25 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[197, 196])).
% 1.07/1.25 tff(199,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[198, 192, 64, 96, 158, 150, 144, 137])).
% 1.07/1.25 tff(200,plain,((~hskp11) | hskp16 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(201,plain,
% 1.07/1.25 (~hskp11),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[200, 64, 96])).
% 1.07/1.25 tff(202,plain,
% 1.07/1.25 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(203,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[202])).
% 1.07/1.25 tff(204,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(205,plain,
% 1.07/1.25 (^[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) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(206,plain,
% 1.07/1.25 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[205])).
% 1.07/1.25 tff(207,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 1.07/1.25 tff(208,plain,
% 1.07/1.25 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[207, 206])).
% 1.10/1.26 tff(209,plain,
% 1.10/1.26 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[208, 204])).
% 1.10/1.26 tff(210,plain,(
% 1.10/1.26 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.10/1.26 inference(skolemize,[status(sab)],[209])).
% 1.10/1.26 tff(211,plain,
% 1.10/1.26 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[210, 203])).
% 1.10/1.26 tff(212,assumption,(hskp12), introduced(assumption)).
% 1.10/1.26 tff(213,plain,
% 1.10/1.26 (((~hskp12) | (~c1_1(a2417))) <=> ((~hskp12) | (~c1_1(a2417)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(214,plain,
% 1.10/1.26 (((~c1_1(a2417)) | (~hskp12)) <=> ((~hskp12) | (~c1_1(a2417)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(215,axiom,((~c1_1(a2417)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 1.10/1.26 tff(216,plain,
% 1.10/1.26 ((~hskp12) | (~c1_1(a2417))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.10/1.26 tff(217,plain,
% 1.10/1.26 ((~hskp12) | (~c1_1(a2417))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[216, 213])).
% 1.10/1.26 tff(218,plain,
% 1.10/1.26 (~c1_1(a2417)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[217, 212])).
% 1.10/1.26 tff(219,plain,
% 1.10/1.26 (((~hskp12) | (~c0_1(a2417))) <=> ((~hskp12) | (~c0_1(a2417)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(220,plain,
% 1.10/1.26 (((~c0_1(a2417)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a2417)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(221,axiom,((~c0_1(a2417)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 1.10/1.26 tff(222,plain,
% 1.10/1.26 ((~hskp12) | (~c0_1(a2417))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[221, 220])).
% 1.10/1.26 tff(223,plain,
% 1.10/1.26 ((~hskp12) | (~c0_1(a2417))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[222, 219])).
% 1.10/1.26 tff(224,plain,
% 1.10/1.26 (~c0_1(a2417)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[223, 212])).
% 1.10/1.26 tff(225,plain,
% 1.10/1.26 (((~hskp12) | c3_1(a2417)) <=> ((~hskp12) | c3_1(a2417))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(226,axiom,((~hskp12) | c3_1(a2417)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 1.10/1.26 tff(227,plain,
% 1.10/1.26 ((~hskp12) | c3_1(a2417)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[226, 225])).
% 1.10/1.26 tff(228,plain,
% 1.10/1.26 ((~hskp12) | c3_1(a2417)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[227, 225])).
% 1.10/1.26 tff(229,plain,
% 1.10/1.26 ((~hskp12) | c3_1(a2417)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[228, 225])).
% 1.10/1.26 tff(230,plain,
% 1.10/1.26 ((~hskp12) | c3_1(a2417)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[229, 225])).
% 1.10/1.26 tff(231,plain,
% 1.10/1.26 ((~hskp12) | c3_1(a2417)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[230, 225])).
% 1.10/1.26 tff(232,plain,
% 1.10/1.26 (c3_1(a2417)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[231, 212])).
% 1.10/1.26 tff(233,plain,
% 1.10/1.26 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(234,plain,
% 1.10/1.26 ((hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417))) <=> (hskp10 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(235,plain,
% 1.10/1.26 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[234])).
% 1.10/1.26 tff(236,plain,
% 1.10/1.26 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[235, 233])).
% 1.10/1.26 tff(237,plain,
% 1.10/1.26 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(238,plain,
% 1.10/1.26 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[237, 236])).
% 1.10/1.26 tff(239,plain,
% 1.10/1.26 (~c2_1(a2417)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[238, 192, 96, 232, 224, 218, 211])).
% 1.10/1.26 tff(240,plain,
% 1.10/1.26 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(241,plain,
% 1.10/1.26 ((hskp16 | hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | c2_1(a2417)) <=> (hskp16 | hskp10 | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(242,plain,
% 1.10/1.26 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | c2_1(a2417))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[241])).
% 1.10/1.26 tff(243,plain,
% 1.10/1.26 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | c2_1(a2417))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[242, 240])).
% 1.10/1.26 tff(244,plain,
% 1.10/1.26 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | c2_1(a2417))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(245,plain,
% 1.10/1.26 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[244, 243])).
% 1.10/1.26 tff(246,plain,
% 1.10/1.26 ($false),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[245, 192, 64, 96, 232, 218, 137, 239])).
% 1.10/1.26 tff(247,plain,((~hskp12) | hskp16 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.10/1.26 tff(248,plain,
% 1.10/1.26 (~hskp12),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[247, 64, 96])).
% 1.10/1.26 tff(249,plain,
% 1.10/1.26 (^[U: $i] : refl((hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))),
% 1.10/1.26 inference(bind,[status(th)],[])).
% 1.10/1.26 tff(250,plain,
% 1.10/1.26 (![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.10/1.26 inference(quant_intro,[status(thm)],[249])).
% 1.10/1.26 tff(251,plain,
% 1.10/1.26 (![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(252,plain,
% 1.10/1.26 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp16) | hskp12) <=> ((hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp12))), rewrite(((hskp16 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U))) | hskp12) <=> (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp16) | hskp12) <=> (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))))),
% 1.10/1.26 inference(bind,[status(th)],[])).
% 1.10/1.26 tff(253,plain,
% 1.10/1.26 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp16) | hskp12) <=> ![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.10/1.26 inference(quant_intro,[status(thm)],[252])).
% 1.10/1.26 tff(254,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp16) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 1.10/1.26 tff(255,plain,
% 1.10/1.26 (![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[254, 253])).
% 1.10/1.26 tff(256,plain,
% 1.10/1.26 (![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[255, 251])).
% 1.10/1.26 tff(257,plain,(
% 1.10/1.26 ![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.10/1.26 inference(skolemize,[status(sab)],[256])).
% 1.10/1.26 tff(258,plain,
% 1.10/1.26 (![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[257, 250])).
% 1.10/1.26 tff(259,assumption,(~c3_1(a2478)), introduced(assumption)).
% 1.10/1.26 tff(260,assumption,(c2_1(a2478)), introduced(assumption)).
% 1.10/1.26 tff(261,plain,
% 1.10/1.26 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | c3_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c3_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(262,plain,
% 1.10/1.26 ((hskp16 | hskp12 | (~ndr1_0) | c3_1(a2478) | c1_1(a2478) | (~c2_1(a2478))) <=> (hskp16 | hskp12 | c3_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(263,plain,
% 1.10/1.26 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2478) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | c3_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[262])).
% 1.10/1.26 tff(264,plain,
% 1.10/1.26 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2478) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c3_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[263, 261])).
% 1.10/1.26 tff(265,plain,
% 1.10/1.26 ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2478) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(266,plain,
% 1.10/1.26 ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c3_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[265, 264])).
% 1.10/1.26 tff(267,plain,
% 1.10/1.26 (hskp16 | hskp12 | c1_1(a2478)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[266, 192, 260, 259, 258])).
% 1.10/1.26 tff(268,plain,
% 1.10/1.26 (c1_1(a2478)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[267, 248, 64])).
% 1.10/1.26 tff(269,plain,
% 1.10/1.26 (^[U: $i] : refl((hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.10/1.26 inference(bind,[status(th)],[])).
% 1.10/1.26 tff(270,plain,
% 1.10/1.26 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.10/1.26 inference(quant_intro,[status(thm)],[269])).
% 1.10/1.26 tff(271,plain,
% 1.10/1.26 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(272,plain,
% 1.10/1.26 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp12))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp11) <=> ((hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp11))), rewrite(((hskp12 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp11) <=> (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp11) <=> (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.10/1.26 inference(bind,[status(th)],[])).
% 1.10/1.26 tff(273,plain,
% 1.10/1.26 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp11) <=> ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.10/1.26 inference(quant_intro,[status(thm)],[272])).
% 1.10/1.26 tff(274,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp12) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 1.10/1.26 tff(275,plain,
% 1.10/1.26 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[274, 273])).
% 1.10/1.26 tff(276,plain,
% 1.10/1.26 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[275, 271])).
% 1.10/1.26 tff(277,plain,(
% 1.10/1.26 ![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.10/1.26 inference(skolemize,[status(sab)],[276])).
% 1.10/1.26 tff(278,plain,
% 1.10/1.26 (![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[277, 270])).
% 1.10/1.26 tff(279,assumption,(~c0_1(a2478)), introduced(assumption)).
% 1.10/1.26 tff(280,plain,
% 1.10/1.26 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2478) | (~ndr1_0) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2478) | (~ndr1_0) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(281,plain,
% 1.10/1.26 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a2478) | (~c2_1(a2478)) | (~c1_1(a2478))) <=> (hskp12 | hskp11 | c0_1(a2478) | (~ndr1_0) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(282,plain,
% 1.10/1.26 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2478) | (~c2_1(a2478)) | (~c1_1(a2478)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2478) | (~ndr1_0) | (~c1_1(a2478)) | (~c2_1(a2478))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[281])).
% 1.10/1.26 tff(283,plain,
% 1.10/1.26 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2478) | (~c2_1(a2478)) | (~c1_1(a2478)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2478) | (~ndr1_0) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[282, 280])).
% 1.10/1.26 tff(284,plain,
% 1.10/1.26 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2478) | (~c2_1(a2478)) | (~c1_1(a2478)))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(285,plain,
% 1.10/1.26 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2478) | (~ndr1_0) | (~c1_1(a2478)) | (~c2_1(a2478))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[284, 283])).
% 1.10/1.26 tff(286,plain,
% 1.10/1.26 (hskp12 | hskp11 | (~c1_1(a2478))),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[285, 192, 260, 279, 278])).
% 1.10/1.26 tff(287,plain,
% 1.10/1.26 ($false),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[286, 268, 248, 201])).
% 1.10/1.26 tff(288,plain,(hskp16 | (~c2_1(a2478)) | c0_1(a2478) | c3_1(a2478) | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.10/1.26 tff(289,plain,
% 1.10/1.26 ($false),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[288, 127, 121, 96, 64, 115])).
% 1.10/1.26 tff(290,plain,((~hskp25) | hskp10 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.10/1.26 tff(291,plain,
% 1.10/1.26 (~hskp25),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[290, 64, 96])).
% 1.10/1.26 tff(292,assumption,(hskp19), introduced(assumption)).
% 1.10/1.26 tff(293,plain,
% 1.10/1.26 (((~hskp19) | (~c0_1(a2432))) <=> ((~hskp19) | (~c0_1(a2432)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(294,plain,
% 1.10/1.26 (((~c0_1(a2432)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a2432)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(295,axiom,((~c0_1(a2432)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 1.10/1.26 tff(296,plain,
% 1.10/1.26 ((~hskp19) | (~c0_1(a2432))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[295, 294])).
% 1.10/1.26 tff(297,plain,
% 1.10/1.26 ((~hskp19) | (~c0_1(a2432))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[296, 293])).
% 1.10/1.26 tff(298,plain,
% 1.10/1.26 (~c0_1(a2432)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[297, 292])).
% 1.10/1.26 tff(299,plain,
% 1.10/1.26 (((~hskp19) | c1_1(a2432)) <=> ((~hskp19) | c1_1(a2432))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(300,axiom,((~hskp19) | c1_1(a2432)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 1.10/1.26 tff(301,plain,
% 1.10/1.26 ((~hskp19) | c1_1(a2432)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[300, 299])).
% 1.10/1.26 tff(302,plain,
% 1.10/1.26 ((~hskp19) | c1_1(a2432)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[301, 299])).
% 1.10/1.26 tff(303,plain,
% 1.10/1.26 ((~hskp19) | c1_1(a2432)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[302, 299])).
% 1.10/1.26 tff(304,plain,
% 1.10/1.26 ((~hskp19) | c1_1(a2432)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[303, 299])).
% 1.10/1.26 tff(305,plain,
% 1.10/1.26 ((~hskp19) | c1_1(a2432)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[304, 299])).
% 1.10/1.26 tff(306,plain,
% 1.10/1.26 (c1_1(a2432)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[305, 292])).
% 1.10/1.26 tff(307,assumption,(~hskp11), introduced(assumption)).
% 1.10/1.26 tff(308,assumption,(~hskp12), introduced(assumption)).
% 1.10/1.26 tff(309,plain,
% 1.10/1.26 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2432) | (~ndr1_0) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2432) | (~ndr1_0) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(310,plain,
% 1.10/1.26 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a2432) | (~c2_1(a2432)) | (~c1_1(a2432))) <=> (hskp12 | hskp11 | c0_1(a2432) | (~ndr1_0) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(311,plain,
% 1.10/1.26 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2432) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2432) | (~ndr1_0) | (~c2_1(a2432)) | (~c1_1(a2432))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[310])).
% 1.10/1.26 tff(312,plain,
% 1.10/1.26 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2432) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2432) | (~ndr1_0) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[311, 309])).
% 1.10/1.26 tff(313,plain,
% 1.10/1.26 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2432) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(314,plain,
% 1.10/1.26 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2432) | (~ndr1_0) | (~c2_1(a2432)) | (~c1_1(a2432))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[313, 312])).
% 1.10/1.26 tff(315,plain,
% 1.10/1.26 (~c2_1(a2432)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[314, 192, 308, 307, 306, 298, 278])).
% 1.10/1.26 tff(316,assumption,(hskp13), introduced(assumption)).
% 1.10/1.26 tff(317,plain,
% 1.10/1.26 (((~hskp13) | (~c0_1(a2418))) <=> ((~hskp13) | (~c0_1(a2418)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(318,plain,
% 1.10/1.26 (((~c0_1(a2418)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a2418)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(319,axiom,((~c0_1(a2418)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 1.10/1.26 tff(320,plain,
% 1.10/1.26 ((~hskp13) | (~c0_1(a2418))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[319, 318])).
% 1.10/1.26 tff(321,plain,
% 1.10/1.26 ((~hskp13) | (~c0_1(a2418))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[320, 317])).
% 1.10/1.26 tff(322,plain,
% 1.10/1.26 (~c0_1(a2418)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[321, 316])).
% 1.10/1.26 tff(323,plain,
% 1.10/1.26 (((~hskp13) | c2_1(a2418)) <=> ((~hskp13) | c2_1(a2418))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(324,axiom,((~hskp13) | c2_1(a2418)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 1.10/1.26 tff(325,plain,
% 1.10/1.26 ((~hskp13) | c2_1(a2418)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[324, 323])).
% 1.10/1.26 tff(326,plain,
% 1.10/1.26 ((~hskp13) | c2_1(a2418)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[325, 323])).
% 1.10/1.26 tff(327,plain,
% 1.10/1.26 ((~hskp13) | c2_1(a2418)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[326, 323])).
% 1.10/1.26 tff(328,plain,
% 1.10/1.26 ((~hskp13) | c2_1(a2418)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[327, 323])).
% 1.10/1.26 tff(329,plain,
% 1.10/1.26 ((~hskp13) | c2_1(a2418)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[328, 323])).
% 1.10/1.26 tff(330,plain,
% 1.10/1.26 (c2_1(a2418)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[329, 316])).
% 1.10/1.26 tff(331,plain,
% 1.10/1.26 (((~hskp13) | c1_1(a2418)) <=> ((~hskp13) | c1_1(a2418))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(332,axiom,((~hskp13) | c1_1(a2418)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 1.10/1.26 tff(333,plain,
% 1.10/1.26 ((~hskp13) | c1_1(a2418)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[332, 331])).
% 1.10/1.26 tff(334,plain,
% 1.10/1.26 ((~hskp13) | c1_1(a2418)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[333, 331])).
% 1.10/1.26 tff(335,plain,
% 1.10/1.26 ((~hskp13) | c1_1(a2418)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[334, 331])).
% 1.10/1.26 tff(336,plain,
% 1.10/1.26 ((~hskp13) | c1_1(a2418)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[335, 331])).
% 1.10/1.26 tff(337,plain,
% 1.10/1.26 ((~hskp13) | c1_1(a2418)),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[336, 331])).
% 1.10/1.26 tff(338,plain,
% 1.10/1.26 (c1_1(a2418)),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[337, 316])).
% 1.10/1.26 tff(339,plain,
% 1.10/1.26 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(340,plain,
% 1.10/1.26 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418))) <=> (hskp12 | hskp11 | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(341,plain,
% 1.10/1.26 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[340])).
% 1.10/1.26 tff(342,plain,
% 1.10/1.26 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[341, 339])).
% 1.10/1.26 tff(343,plain,
% 1.10/1.26 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(344,plain,
% 1.10/1.26 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[343, 342])).
% 1.10/1.26 tff(345,plain,
% 1.10/1.26 ($false),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[344, 192, 308, 307, 338, 330, 322, 278])).
% 1.10/1.26 tff(346,plain,((~hskp13) | hskp12 | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.10/1.26 tff(347,plain,
% 1.10/1.26 (~hskp13),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[346, 308, 307])).
% 1.10/1.26 tff(348,plain,
% 1.10/1.26 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(349,plain,
% 1.10/1.26 ((hskp16 | hskp13 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432))) <=> (hskp16 | hskp13 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(350,plain,
% 1.10/1.26 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.10/1.26 inference(monotonicity,[status(thm)],[349])).
% 1.10/1.26 tff(351,plain,
% 1.10/1.26 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.10/1.26 inference(transitivity,[status(thm)],[350, 348])).
% 1.10/1.26 tff(352,plain,
% 1.10/1.26 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.10/1.26 inference(quant_inst,[status(thm)],[])).
% 1.10/1.26 tff(353,plain,
% 1.10/1.26 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432))),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[352, 351])).
% 1.10/1.26 tff(354,plain,
% 1.10/1.26 ($false),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[353, 192, 64, 347, 306, 298, 75, 315])).
% 1.10/1.26 tff(355,plain,((~hskp19) | hskp16 | hskp12 | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.10/1.26 tff(356,plain,
% 1.10/1.26 (~hskp19),
% 1.10/1.26 inference(unit_resolution,[status(thm)],[355, 64, 248, 201])).
% 1.10/1.26 tff(357,plain,
% 1.10/1.26 ((hskp25 | hskp19 | hskp5) <=> (hskp25 | hskp19 | hskp5)),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(358,plain,
% 1.10/1.26 (((hskp19 | hskp5) | hskp25) <=> (hskp25 | hskp19 | hskp5)),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(359,plain,
% 1.10/1.26 ((hskp5 | hskp19) <=> (hskp19 | hskp5)),
% 1.10/1.26 inference(rewrite,[status(thm)],[])).
% 1.10/1.26 tff(360,plain,
% 1.10/1.26 (((hskp5 | hskp19) | hskp25) <=> ((hskp19 | hskp5) | hskp25)),
% 1.10/1.26 inference(monotonicity,[status(thm)],[359])).
% 1.10/1.26 tff(361,plain,
% 1.10/1.26 (((hskp5 | hskp19) | hskp25) <=> (hskp25 | hskp19 | hskp5)),
% 1.10/1.26 inference(transitivity,[status(thm)],[360, 358])).
% 1.10/1.26 tff(362,axiom,((hskp5 | hskp19) | hskp25), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 1.10/1.26 tff(363,plain,
% 1.10/1.26 (hskp25 | hskp19 | hskp5),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[362, 361])).
% 1.10/1.26 tff(364,plain,
% 1.10/1.26 (hskp25 | hskp19 | hskp5),
% 1.10/1.26 inference(modus_ponens,[status(thm)],[363, 357])).
% 1.10/1.26 tff(365,plain,
% 1.10/1.26 (hskp25 | hskp19 | hskp5),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[364, 357])).
% 1.10/1.27 tff(366,plain,
% 1.10/1.27 (hskp25 | hskp19 | hskp5),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[365, 357])).
% 1.10/1.27 tff(367,plain,
% 1.10/1.27 (hskp25 | hskp19 | hskp5),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[366, 357])).
% 1.10/1.27 tff(368,plain,
% 1.10/1.27 (hskp5),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[367, 356, 291])).
% 1.10/1.27 tff(369,plain,
% 1.10/1.27 (((~hskp5) | (~c2_1(a2408))) <=> ((~hskp5) | (~c2_1(a2408)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(370,plain,
% 1.10/1.27 (((~c2_1(a2408)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a2408)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(371,axiom,((~c2_1(a2408)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 1.10/1.27 tff(372,plain,
% 1.10/1.27 ((~hskp5) | (~c2_1(a2408))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[371, 370])).
% 1.10/1.27 tff(373,plain,
% 1.10/1.27 ((~hskp5) | (~c2_1(a2408))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[372, 369])).
% 1.10/1.27 tff(374,plain,
% 1.10/1.27 (~c2_1(a2408)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[373, 368])).
% 1.10/1.27 tff(375,plain,
% 1.10/1.27 (((~hskp5) | c0_1(a2408)) <=> ((~hskp5) | c0_1(a2408))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(376,axiom,((~hskp5) | c0_1(a2408)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause79')).
% 1.10/1.27 tff(377,plain,
% 1.10/1.27 ((~hskp5) | c0_1(a2408)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[376, 375])).
% 1.10/1.27 tff(378,plain,
% 1.10/1.27 ((~hskp5) | c0_1(a2408)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[377, 375])).
% 1.10/1.27 tff(379,plain,
% 1.10/1.27 ((~hskp5) | c0_1(a2408)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[378, 375])).
% 1.10/1.27 tff(380,plain,
% 1.10/1.27 ((~hskp5) | c0_1(a2408)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[379, 375])).
% 1.10/1.27 tff(381,plain,
% 1.10/1.27 ((~hskp5) | c0_1(a2408)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[380, 375])).
% 1.10/1.27 tff(382,plain,
% 1.10/1.27 (c0_1(a2408)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[381, 368])).
% 1.10/1.27 tff(383,plain,
% 1.10/1.27 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(384,plain,
% 1.10/1.27 ((hskp25 | hskp19 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408))) <=> (hskp25 | hskp19 | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(385,plain,
% 1.10/1.27 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[384])).
% 1.10/1.27 tff(386,plain,
% 1.10/1.27 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 1.10/1.27 inference(transitivity,[status(thm)],[385, 383])).
% 1.10/1.27 tff(387,plain,
% 1.10/1.27 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(388,plain,
% 1.10/1.27 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[387, 386])).
% 1.10/1.27 tff(389,plain,
% 1.10/1.27 (~c1_1(a2408)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[388, 192, 291, 356, 382, 374, 106])).
% 1.10/1.27 tff(390,plain,
% 1.10/1.27 (((~hskp5) | c3_1(a2408)) <=> ((~hskp5) | c3_1(a2408))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(391,axiom,((~hskp5) | c3_1(a2408)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 1.10/1.27 tff(392,plain,
% 1.10/1.27 ((~hskp5) | c3_1(a2408)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[391, 390])).
% 1.10/1.27 tff(393,plain,
% 1.10/1.27 ((~hskp5) | c3_1(a2408)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[392, 390])).
% 1.10/1.27 tff(394,plain,
% 1.10/1.27 ((~hskp5) | c3_1(a2408)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[393, 390])).
% 1.10/1.27 tff(395,plain,
% 1.10/1.27 ((~hskp5) | c3_1(a2408)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[394, 390])).
% 1.10/1.27 tff(396,plain,
% 1.10/1.27 ((~hskp5) | c3_1(a2408)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[395, 390])).
% 1.10/1.27 tff(397,plain,
% 1.10/1.27 (c3_1(a2408)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[396, 368])).
% 1.10/1.27 tff(398,plain,
% 1.10/1.27 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(399,plain,
% 1.10/1.27 ((hskp16 | hskp10 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | c2_1(a2408)) <=> (hskp16 | hskp10 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(400,plain,
% 1.10/1.27 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | c2_1(a2408))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[399])).
% 1.10/1.27 tff(401,plain,
% 1.10/1.27 (((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | c2_1(a2408))) <=> ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.10/1.27 inference(transitivity,[status(thm)],[400, 398])).
% 1.10/1.27 tff(402,plain,
% 1.10/1.27 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | (hskp16 | hskp10 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | c2_1(a2408))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(403,plain,
% 1.10/1.27 ((~![U: $i] : (hskp16 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U))) | hskp16 | hskp10 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[402, 401])).
% 1.10/1.27 tff(404,plain,
% 1.10/1.27 ($false),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[403, 192, 64, 96, 397, 374, 137, 389])).
% 1.10/1.27 tff(405,plain,(hskp16 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.10/1.27 tff(406,plain,
% 1.10/1.27 (hskp16),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[405, 96])).
% 1.10/1.27 tff(407,plain,
% 1.10/1.27 (((~hskp16) | (~c3_1(a2425))) <=> ((~hskp16) | (~c3_1(a2425)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(408,plain,
% 1.10/1.27 (((~c3_1(a2425)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a2425)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(409,axiom,((~c3_1(a2425)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 1.10/1.27 tff(410,plain,
% 1.10/1.27 ((~hskp16) | (~c3_1(a2425))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[409, 408])).
% 1.10/1.27 tff(411,plain,
% 1.10/1.27 ((~hskp16) | (~c3_1(a2425))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[410, 407])).
% 1.10/1.27 tff(412,plain,
% 1.10/1.27 (~c3_1(a2425)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[411, 406])).
% 1.10/1.27 tff(413,plain,
% 1.10/1.27 (((~hskp16) | (~c2_1(a2425))) <=> ((~hskp16) | (~c2_1(a2425)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(414,plain,
% 1.10/1.27 (((~c2_1(a2425)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a2425)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(415,axiom,((~c2_1(a2425)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 1.10/1.27 tff(416,plain,
% 1.10/1.27 ((~hskp16) | (~c2_1(a2425))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[415, 414])).
% 1.10/1.27 tff(417,plain,
% 1.10/1.27 ((~hskp16) | (~c2_1(a2425))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[416, 413])).
% 1.10/1.27 tff(418,plain,
% 1.10/1.27 (~c2_1(a2425)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[417, 406])).
% 1.10/1.27 tff(419,plain,
% 1.10/1.27 (((~hskp16) | c0_1(a2425)) <=> ((~hskp16) | c0_1(a2425))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(420,axiom,((~hskp16) | c0_1(a2425)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 1.10/1.27 tff(421,plain,
% 1.10/1.27 ((~hskp16) | c0_1(a2425)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[420, 419])).
% 1.10/1.27 tff(422,plain,
% 1.10/1.27 ((~hskp16) | c0_1(a2425)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[421, 419])).
% 1.10/1.27 tff(423,plain,
% 1.10/1.27 ((~hskp16) | c0_1(a2425)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[422, 419])).
% 1.10/1.27 tff(424,plain,
% 1.10/1.27 ((~hskp16) | c0_1(a2425)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[423, 419])).
% 1.10/1.27 tff(425,plain,
% 1.10/1.27 ((~hskp16) | c0_1(a2425)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[424, 419])).
% 1.10/1.27 tff(426,plain,
% 1.10/1.27 (c0_1(a2425)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[425, 406])).
% 1.10/1.27 tff(427,plain,
% 1.10/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp10 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(428,plain,
% 1.10/1.27 ((hskp10 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425))) <=> (hskp10 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(429,plain,
% 1.10/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[428])).
% 1.10/1.27 tff(430,plain,
% 1.10/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp10 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))),
% 1.10/1.27 inference(transitivity,[status(thm)],[429, 427])).
% 1.10/1.27 tff(431,plain,
% 1.10/1.27 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(432,plain,
% 1.10/1.27 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp10 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[431, 430])).
% 1.10/1.27 tff(433,plain,
% 1.10/1.27 (c1_1(a2425)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[432, 192, 96, 426, 418, 412, 95])).
% 1.10/1.27 tff(434,plain,
% 1.10/1.27 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(435,plain,
% 1.10/1.27 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[434])).
% 1.10/1.27 tff(436,plain,
% 1.10/1.27 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(437,plain,
% 1.10/1.27 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp10) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp10))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(438,plain,
% 1.10/1.27 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp10) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[437])).
% 1.10/1.27 tff(439,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause194')).
% 1.10/1.27 tff(440,plain,
% 1.10/1.27 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[439, 438])).
% 1.10/1.27 tff(441,plain,
% 1.10/1.27 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[440, 436])).
% 1.10/1.27 tff(442,plain,(
% 1.10/1.27 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.10/1.27 inference(skolemize,[status(sab)],[441])).
% 1.10/1.27 tff(443,plain,
% 1.10/1.27 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[442, 435])).
% 1.10/1.27 tff(444,plain,
% 1.10/1.27 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(445,plain,
% 1.10/1.27 ((hskp19 | hskp5 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c0_1(a2425))) <=> (hskp19 | hskp5 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(446,plain,
% 1.10/1.27 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[445])).
% 1.10/1.27 tff(447,plain,
% 1.10/1.27 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)))),
% 1.10/1.27 inference(transitivity,[status(thm)],[446, 444])).
% 1.10/1.27 tff(448,plain,
% 1.10/1.27 ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c0_1(a2425)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(449,plain,
% 1.10/1.27 ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[448, 447])).
% 1.10/1.27 tff(450,plain,
% 1.10/1.27 (hskp19 | hskp5),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[449, 192, 426, 418, 412, 53])).
% 1.10/1.27 tff(451,plain,
% 1.10/1.27 (hskp5),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[450, 43])).
% 1.10/1.27 tff(452,plain,
% 1.10/1.27 (c3_1(a2408)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[396, 451])).
% 1.10/1.27 tff(453,plain,
% 1.10/1.27 (~c2_1(a2408)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[373, 451])).
% 1.10/1.27 tff(454,plain,
% 1.10/1.27 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(455,plain,
% 1.10/1.27 ((hskp25 | hskp19 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425))) <=> (hskp25 | hskp19 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(456,plain,
% 1.10/1.27 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[455])).
% 1.10/1.27 tff(457,plain,
% 1.10/1.27 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.27 inference(transitivity,[status(thm)],[456, 454])).
% 1.10/1.27 tff(458,plain,
% 1.10/1.27 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(459,plain,
% 1.10/1.27 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[458, 457])).
% 1.10/1.27 tff(460,plain,
% 1.10/1.27 (hskp25 | hskp19 | (~c1_1(a2425))),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[459, 192, 426, 418, 106])).
% 1.10/1.27 tff(461,plain,
% 1.10/1.27 (hskp25),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[460, 43, 433])).
% 1.10/1.27 tff(462,plain,
% 1.10/1.27 (c2_1(a2478)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[114, 461])).
% 1.10/1.27 tff(463,plain,
% 1.10/1.27 (~c3_1(a2478)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[126, 461])).
% 1.10/1.27 tff(464,plain,
% 1.10/1.27 (~c0_1(a2478)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[120, 461])).
% 1.10/1.27 tff(465,assumption,(hskp23), introduced(assumption)).
% 1.10/1.27 tff(466,plain,
% 1.10/1.27 (^[U: $i] : refl((hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(467,plain,
% 1.10/1.27 (![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[466])).
% 1.10/1.27 tff(468,plain,
% 1.10/1.27 (![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(469,plain,
% 1.10/1.27 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp15))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(470,plain,
% 1.10/1.27 (![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[469])).
% 1.10/1.27 tff(471,axiom,(![U: $i] : (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 1.10/1.27 tff(472,plain,
% 1.10/1.27 (![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[471, 470])).
% 1.10/1.27 tff(473,plain,
% 1.10/1.27 (![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[472, 468])).
% 1.10/1.27 tff(474,plain,(
% 1.10/1.27 ![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.27 inference(skolemize,[status(sab)],[473])).
% 1.10/1.27 tff(475,plain,
% 1.10/1.27 (![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[474, 467])).
% 1.10/1.27 tff(476,plain,
% 1.10/1.27 (((~hskp23) | (~c0_1(a2455))) <=> ((~hskp23) | (~c0_1(a2455)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(477,plain,
% 1.10/1.27 (((~c0_1(a2455)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a2455)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(478,axiom,((~c0_1(a2455)) | (~hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 1.10/1.27 tff(479,plain,
% 1.10/1.27 ((~hskp23) | (~c0_1(a2455))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[478, 477])).
% 1.10/1.27 tff(480,plain,
% 1.10/1.27 ((~hskp23) | (~c0_1(a2455))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[479, 476])).
% 1.10/1.27 tff(481,plain,
% 1.10/1.27 (~c0_1(a2455)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[480, 465])).
% 1.10/1.27 tff(482,plain,
% 1.10/1.27 (((~hskp23) | c3_1(a2455)) <=> ((~hskp23) | c3_1(a2455))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(483,axiom,((~hskp23) | c3_1(a2455)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 1.10/1.27 tff(484,plain,
% 1.10/1.27 ((~hskp23) | c3_1(a2455)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[483, 482])).
% 1.10/1.27 tff(485,plain,
% 1.10/1.27 ((~hskp23) | c3_1(a2455)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[484, 482])).
% 1.10/1.27 tff(486,plain,
% 1.10/1.27 ((~hskp23) | c3_1(a2455)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[485, 482])).
% 1.10/1.27 tff(487,plain,
% 1.10/1.27 ((~hskp23) | c3_1(a2455)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[486, 482])).
% 1.10/1.27 tff(488,plain,
% 1.10/1.27 ((~hskp23) | c3_1(a2455)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[487, 482])).
% 1.10/1.27 tff(489,plain,
% 1.10/1.27 (c3_1(a2455)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[488, 465])).
% 1.10/1.27 tff(490,plain,
% 1.10/1.27 (((~hskp23) | c2_1(a2455)) <=> ((~hskp23) | c2_1(a2455))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(491,axiom,((~hskp23) | c2_1(a2455)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 1.10/1.27 tff(492,plain,
% 1.10/1.27 ((~hskp23) | c2_1(a2455)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[491, 490])).
% 1.10/1.27 tff(493,plain,
% 1.10/1.27 ((~hskp23) | c2_1(a2455)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[492, 490])).
% 1.10/1.27 tff(494,plain,
% 1.10/1.27 ((~hskp23) | c2_1(a2455)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[493, 490])).
% 1.10/1.27 tff(495,plain,
% 1.10/1.27 ((~hskp23) | c2_1(a2455)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[494, 490])).
% 1.10/1.27 tff(496,plain,
% 1.10/1.27 ((~hskp23) | c2_1(a2455)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[495, 490])).
% 1.10/1.27 tff(497,plain,
% 1.10/1.27 (c2_1(a2455)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[496, 465])).
% 1.10/1.27 tff(498,assumption,(~hskp15), introduced(assumption)).
% 1.10/1.27 tff(499,plain,
% 1.10/1.27 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(500,plain,
% 1.10/1.27 ((hskp15 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455))) <=> (hskp15 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(501,plain,
% 1.10/1.27 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[500])).
% 1.10/1.27 tff(502,plain,
% 1.10/1.27 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.10/1.27 inference(transitivity,[status(thm)],[501, 499])).
% 1.10/1.27 tff(503,plain,
% 1.10/1.27 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(504,plain,
% 1.10/1.27 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[503, 502])).
% 1.10/1.27 tff(505,plain,
% 1.10/1.27 ($false),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[504, 192, 498, 497, 489, 481, 475])).
% 1.10/1.27 tff(506,plain,((~hskp23) | hskp15), inference(lemma,lemma(discharge,[]))).
% 1.10/1.27 tff(507,plain,
% 1.10/1.27 (hskp15),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[506, 465])).
% 1.10/1.27 tff(508,plain,
% 1.10/1.27 (((~hskp15) | c3_1(a2422)) <=> ((~hskp15) | c3_1(a2422))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(509,axiom,((~hskp15) | c3_1(a2422)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 1.10/1.27 tff(510,plain,
% 1.10/1.27 ((~hskp15) | c3_1(a2422)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[509, 508])).
% 1.10/1.27 tff(511,plain,
% 1.10/1.27 ((~hskp15) | c3_1(a2422)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[510, 508])).
% 1.10/1.27 tff(512,plain,
% 1.10/1.27 ((~hskp15) | c3_1(a2422)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[511, 508])).
% 1.10/1.27 tff(513,plain,
% 1.10/1.27 ((~hskp15) | c3_1(a2422)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[512, 508])).
% 1.10/1.27 tff(514,plain,
% 1.10/1.27 ((~hskp15) | c3_1(a2422)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[513, 508])).
% 1.10/1.27 tff(515,plain,
% 1.10/1.27 (c3_1(a2422)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[514, 507])).
% 1.10/1.27 tff(516,plain,
% 1.10/1.27 (((~hskp15) | c1_1(a2422)) <=> ((~hskp15) | c1_1(a2422))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(517,axiom,((~hskp15) | c1_1(a2422)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 1.10/1.27 tff(518,plain,
% 1.10/1.27 ((~hskp15) | c1_1(a2422)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[517, 516])).
% 1.10/1.27 tff(519,plain,
% 1.10/1.27 ((~hskp15) | c1_1(a2422)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[518, 516])).
% 1.10/1.27 tff(520,plain,
% 1.10/1.27 ((~hskp15) | c1_1(a2422)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[519, 516])).
% 1.10/1.27 tff(521,plain,
% 1.10/1.27 ((~hskp15) | c1_1(a2422)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[520, 516])).
% 1.10/1.27 tff(522,plain,
% 1.10/1.27 ((~hskp15) | c1_1(a2422)),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[521, 516])).
% 1.10/1.27 tff(523,plain,
% 1.10/1.27 (c1_1(a2422)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[522, 507])).
% 1.10/1.27 tff(524,plain,
% 1.10/1.27 (((~hskp15) | (~c2_1(a2422))) <=> ((~hskp15) | (~c2_1(a2422)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(525,plain,
% 1.10/1.27 (((~c2_1(a2422)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a2422)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(526,axiom,((~c2_1(a2422)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 1.10/1.27 tff(527,plain,
% 1.10/1.27 ((~hskp15) | (~c2_1(a2422))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[526, 525])).
% 1.10/1.27 tff(528,plain,
% 1.10/1.27 ((~hskp15) | (~c2_1(a2422))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[527, 524])).
% 1.10/1.27 tff(529,plain,
% 1.10/1.27 (~c2_1(a2422)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[528, 507])).
% 1.10/1.27 tff(530,plain,
% 1.10/1.27 (hskp16),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[288, 96, 279, 259, 260])).
% 1.10/1.27 tff(531,plain,
% 1.10/1.27 (~c3_1(a2425)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[411, 530])).
% 1.10/1.27 tff(532,plain,
% 1.10/1.27 (~c2_1(a2425)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[417, 530])).
% 1.10/1.27 tff(533,plain,
% 1.10/1.27 (c0_1(a2425)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[425, 530])).
% 1.10/1.27 tff(534,plain,
% 1.10/1.27 (c1_1(a2425)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[432, 192, 96, 533, 532, 531, 95])).
% 1.10/1.27 tff(535,assumption,(c3_1(a2455)), introduced(assumption)).
% 1.10/1.27 tff(536,assumption,(c2_1(a2455)), introduced(assumption)).
% 1.10/1.27 tff(537,plain,
% 1.10/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(538,plain,
% 1.10/1.27 ((hskp10 | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425))) <=> (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(539,plain,
% 1.10/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455))))),
% 1.10/1.27 inference(monotonicity,[status(thm)],[538])).
% 1.10/1.27 tff(540,plain,
% 1.10/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.10/1.27 inference(transitivity,[status(thm)],[539, 537])).
% 1.10/1.27 tff(541,plain,
% 1.10/1.27 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.27 inference(quant_inst,[status(thm)],[])).
% 1.10/1.27 tff(542,plain,
% 1.10/1.27 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455))),
% 1.10/1.27 inference(modus_ponens,[status(thm)],[541, 540])).
% 1.10/1.27 tff(543,plain,
% 1.10/1.27 ((~c1_1(a2425)) | (~c1_1(a2455))),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[542, 192, 96, 536, 535, 533, 531, 443])).
% 1.10/1.27 tff(544,plain,
% 1.10/1.27 (~c1_1(a2455)),
% 1.10/1.27 inference(unit_resolution,[status(thm)],[543, 534])).
% 1.10/1.27 tff(545,plain,
% 1.10/1.27 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W))))),
% 1.10/1.27 inference(bind,[status(th)],[])).
% 1.10/1.27 tff(546,plain,
% 1.10/1.27 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.10/1.27 inference(quant_intro,[status(thm)],[545])).
% 1.10/1.27 tff(547,plain,
% 1.10/1.27 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.10/1.27 inference(rewrite,[status(thm)],[])).
% 1.10/1.27 tff(548,plain,
% 1.10/1.27 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))))),
% 1.10/1.28 inference(bind,[status(th)],[])).
% 1.10/1.28 tff(549,plain,
% 1.10/1.28 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.10/1.28 inference(quant_intro,[status(thm)],[548])).
% 1.10/1.28 tff(550,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause204')).
% 1.10/1.28 tff(551,plain,
% 1.10/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[550, 549])).
% 1.10/1.28 tff(552,plain,
% 1.10/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[551, 547])).
% 1.10/1.28 tff(553,plain,(
% 1.10/1.28 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.10/1.28 inference(skolemize,[status(sab)],[552])).
% 1.10/1.28 tff(554,plain,
% 1.10/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[553, 546])).
% 1.10/1.28 tff(555,plain,
% 1.10/1.28 (^[V: $i, U: $i] : refl((hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.10/1.28 inference(bind,[status(th)],[])).
% 1.10/1.28 tff(556,plain,
% 1.10/1.28 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.28 inference(quant_intro,[status(thm)],[555])).
% 1.10/1.28 tff(557,plain,
% 1.10/1.28 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(558,plain,
% 1.10/1.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp30) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp30))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp30) <=> (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.10/1.28 inference(bind,[status(th)],[])).
% 1.10/1.28 tff(559,plain,
% 1.10/1.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp30) <=> ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.28 inference(quant_intro,[status(thm)],[558])).
% 1.10/1.28 tff(560,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | hskp30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause193')).
% 1.10/1.28 tff(561,plain,
% 1.10/1.28 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[560, 559])).
% 1.10/1.28 tff(562,plain,
% 1.10/1.28 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[561, 557])).
% 1.10/1.28 tff(563,plain,(
% 1.10/1.28 ![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.28 inference(skolemize,[status(sab)],[562])).
% 1.10/1.28 tff(564,plain,
% 1.10/1.28 (![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[563, 556])).
% 1.10/1.28 tff(565,assumption,(~c2_1(a2422)), introduced(assumption)).
% 1.10/1.28 tff(566,assumption,(c3_1(a2422)), introduced(assumption)).
% 1.10/1.28 tff(567,assumption,(c1_1(a2422)), introduced(assumption)).
% 1.10/1.28 tff(568,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(569,plain,
% 1.10/1.28 ((hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2422) | (~c1_1(a2422)) | (~c3_1(a2422))) <=> (hskp30 | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(570,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2422) | (~c1_1(a2422)) | (~c3_1(a2422)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c1_1(a2425)) | (~c0_1(a2425))))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[569])).
% 1.10/1.28 tff(571,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2422) | (~c1_1(a2422)) | (~c3_1(a2422)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.28 inference(transitivity,[status(thm)],[570, 568])).
% 1.10/1.28 tff(572,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2422) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(573,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c1_1(a2425)) | (~c0_1(a2425))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[572, 571])).
% 1.10/1.28 tff(574,plain,
% 1.10/1.28 (hskp30 | (~c1_1(a2425))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[573, 192, 533, 567, 566, 531, 565, 564])).
% 1.10/1.28 tff(575,plain,
% 1.10/1.28 (hskp30),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[574, 534])).
% 1.10/1.28 tff(576,plain,
% 1.10/1.28 (((~hskp30) | c3_1(a2450)) <=> ((~hskp30) | c3_1(a2450))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(577,axiom,((~hskp30) | c3_1(a2450)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 1.10/1.28 tff(578,plain,
% 1.10/1.28 ((~hskp30) | c3_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[577, 576])).
% 1.10/1.28 tff(579,plain,
% 1.10/1.28 ((~hskp30) | c3_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[578, 576])).
% 1.10/1.28 tff(580,plain,
% 1.10/1.28 ((~hskp30) | c3_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[579, 576])).
% 1.10/1.28 tff(581,plain,
% 1.10/1.28 ((~hskp30) | c3_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[580, 576])).
% 1.10/1.28 tff(582,plain,
% 1.10/1.28 ((~hskp30) | c3_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[581, 576])).
% 1.10/1.28 tff(583,plain,
% 1.10/1.28 (c3_1(a2450)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[582, 575])).
% 1.10/1.28 tff(584,plain,
% 1.10/1.28 (((~hskp30) | c1_1(a2450)) <=> ((~hskp30) | c1_1(a2450))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(585,axiom,((~hskp30) | c1_1(a2450)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 1.10/1.28 tff(586,plain,
% 1.10/1.28 ((~hskp30) | c1_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[585, 584])).
% 1.10/1.28 tff(587,plain,
% 1.10/1.28 ((~hskp30) | c1_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[586, 584])).
% 1.10/1.28 tff(588,plain,
% 1.10/1.28 ((~hskp30) | c1_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[587, 584])).
% 1.10/1.28 tff(589,plain,
% 1.10/1.28 ((~hskp30) | c1_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[588, 584])).
% 1.10/1.28 tff(590,plain,
% 1.10/1.28 ((~hskp30) | c1_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[589, 584])).
% 1.10/1.28 tff(591,plain,
% 1.10/1.28 (c1_1(a2450)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[590, 575])).
% 1.10/1.28 tff(592,plain,
% 1.10/1.28 (((~hskp30) | c0_1(a2450)) <=> ((~hskp30) | c0_1(a2450))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(593,axiom,((~hskp30) | c0_1(a2450)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 1.10/1.28 tff(594,plain,
% 1.10/1.28 ((~hskp30) | c0_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[593, 592])).
% 1.10/1.28 tff(595,plain,
% 1.10/1.28 ((~hskp30) | c0_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[594, 592])).
% 1.10/1.28 tff(596,plain,
% 1.10/1.28 ((~hskp30) | c0_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[595, 592])).
% 1.10/1.28 tff(597,plain,
% 1.10/1.28 ((~hskp30) | c0_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[596, 592])).
% 1.10/1.28 tff(598,plain,
% 1.10/1.28 ((~hskp30) | c0_1(a2450)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[597, 592])).
% 1.10/1.28 tff(599,plain,
% 1.10/1.28 (c0_1(a2450)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[598, 575])).
% 1.10/1.28 tff(600,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(601,plain,
% 1.10/1.28 (((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(602,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[601])).
% 1.10/1.28 tff(603,plain,
% 1.10/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.10/1.28 inference(transitivity,[status(thm)],[602, 600])).
% 1.10/1.28 tff(604,plain,
% 1.10/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(605,plain,
% 1.10/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[604, 603])).
% 1.10/1.28 tff(606,plain,
% 1.10/1.28 ($false),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[605, 192, 599, 591, 583, 536, 535, 533, 532, 531, 554, 544])).
% 1.10/1.28 tff(607,plain,(hskp10 | (~c2_1(a2455)) | (~c3_1(a2455)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2422) | c0_1(a2478) | c3_1(a2478) | (~c2_1(a2478))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.28 tff(608,plain,
% 1.10/1.28 ($false),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[607, 529, 523, 96, 279, 259, 497, 489, 515, 260])).
% 1.10/1.28 tff(609,plain,((~hskp23) | hskp10 | c0_1(a2478) | c3_1(a2478) | (~c2_1(a2478))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.28 tff(610,plain,
% 1.10/1.28 (~hskp23),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[609, 464, 96, 463, 462])).
% 1.10/1.28 tff(611,assumption,(~c2_1(a2408)), introduced(assumption)).
% 1.10/1.28 tff(612,assumption,(c3_1(a2408)), introduced(assumption)).
% 1.10/1.28 tff(613,plain,
% 1.10/1.28 (hskp16 | hskp10),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[403, 192, 612, 611, 137, 1])).
% 1.10/1.28 tff(614,plain,
% 1.10/1.28 (hskp16),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[613, 96])).
% 1.10/1.28 tff(615,plain,
% 1.10/1.28 (~c3_1(a2425)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[411, 614])).
% 1.10/1.28 tff(616,plain,
% 1.10/1.28 (~c2_1(a2425)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[417, 614])).
% 1.10/1.28 tff(617,plain,
% 1.10/1.28 (c0_1(a2425)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[425, 614])).
% 1.10/1.28 tff(618,plain,
% 1.10/1.28 (c1_1(a2425)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[432, 192, 96, 617, 616, 615, 95])).
% 1.10/1.28 tff(619,plain,
% 1.10/1.28 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.10/1.28 inference(bind,[status(th)],[])).
% 1.10/1.28 tff(620,plain,
% 1.10/1.28 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.28 inference(quant_intro,[status(thm)],[619])).
% 1.10/1.28 tff(621,plain,
% 1.10/1.28 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(622,plain,
% 1.10/1.28 (^[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) | c3_1(U) | 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) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp23))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.10/1.28 inference(bind,[status(th)],[])).
% 1.10/1.28 tff(623,plain,
% 1.10/1.28 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.28 inference(quant_intro,[status(thm)],[622])).
% 1.10/1.28 tff(624,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c1_1(V)) | c2_1(V)) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 1.10/1.28 tff(625,plain,
% 1.10/1.28 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[624, 623])).
% 1.10/1.28 tff(626,plain,
% 1.10/1.28 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[625, 621])).
% 1.10/1.28 tff(627,plain,(
% 1.10/1.28 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.28 inference(skolemize,[status(sab)],[626])).
% 1.10/1.28 tff(628,plain,
% 1.10/1.28 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[627, 620])).
% 1.10/1.28 tff(629,assumption,(~hskp23), introduced(assumption)).
% 1.10/1.28 tff(630,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c1_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c1_1(a2425)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(631,plain,
% 1.10/1.28 ((hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp23 | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c1_1(a2425)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(632,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c1_1(a2425))))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[631])).
% 1.10/1.28 tff(633,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c1_1(a2425)))),
% 1.10/1.28 inference(transitivity,[status(thm)],[632, 630])).
% 1.10/1.28 tff(634,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(635,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c1_1(a2425))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[634, 633])).
% 1.10/1.28 tff(636,plain,
% 1.10/1.28 ($false),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[635, 192, 629, 612, 616, 615, 611, 628, 1, 618])).
% 1.10/1.28 tff(637,plain,(hskp10 | hskp23 | (~c3_1(a2408)) | c2_1(a2408) | c1_1(a2408)), inference(lemma,lemma(discharge,[]))).
% 1.10/1.28 tff(638,plain,
% 1.10/1.28 (c1_1(a2408)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[637, 610, 96, 453, 452])).
% 1.10/1.28 tff(639,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(640,plain,
% 1.10/1.28 ((hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408))) <=> (hskp30 | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(641,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2425)) | (~c0_1(a2425))))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[640])).
% 1.10/1.28 tff(642,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.28 inference(transitivity,[status(thm)],[641, 639])).
% 1.10/1.28 tff(643,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408)))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(644,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2425)) | (~c0_1(a2425))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[643, 642])).
% 1.10/1.28 tff(645,plain,
% 1.10/1.28 (hskp30 | (~c1_1(a2408))),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[644, 192, 426, 452, 412, 453, 564, 433])).
% 1.10/1.28 tff(646,plain,
% 1.10/1.28 (hskp30),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[645, 638])).
% 1.10/1.28 tff(647,plain,
% 1.10/1.28 (c3_1(a2450)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[582, 646])).
% 1.10/1.28 tff(648,plain,
% 1.10/1.28 (c1_1(a2450)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[590, 646])).
% 1.10/1.28 tff(649,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(650,plain,
% 1.10/1.28 ((hskp10 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425))) <=> (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.28 inference(rewrite,[status(thm)],[])).
% 1.10/1.28 tff(651,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c1_1(a2425)) | (~c0_1(a2425))))),
% 1.10/1.28 inference(monotonicity,[status(thm)],[650])).
% 1.10/1.28 tff(652,plain,
% 1.10/1.28 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.28 inference(transitivity,[status(thm)],[651, 649])).
% 1.10/1.28 tff(653,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.28 inference(quant_inst,[status(thm)],[])).
% 1.10/1.28 tff(654,plain,
% 1.10/1.28 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c1_1(a2425)) | (~c0_1(a2425))),
% 1.10/1.28 inference(modus_ponens,[status(thm)],[653, 652])).
% 1.10/1.28 tff(655,plain,
% 1.10/1.28 (~c2_1(a2450)),
% 1.10/1.28 inference(unit_resolution,[status(thm)],[654, 192, 96, 648, 647, 426, 412, 443, 433])).
% 1.10/1.29 tff(656,plain,
% 1.10/1.29 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))),
% 1.10/1.29 inference(bind,[status(th)],[])).
% 1.10/1.29 tff(657,plain,
% 1.10/1.29 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.10/1.29 inference(quant_intro,[status(thm)],[656])).
% 1.10/1.29 tff(658,plain,
% 1.10/1.29 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(659,plain,
% 1.10/1.29 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))))),
% 1.10/1.29 inference(bind,[status(th)],[])).
% 1.10/1.29 tff(660,plain,
% 1.10/1.29 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.10/1.29 inference(quant_intro,[status(thm)],[659])).
% 1.10/1.29 tff(661,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c3_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause195')).
% 1.10/1.29 tff(662,plain,
% 1.10/1.29 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[661, 660])).
% 1.10/1.29 tff(663,plain,
% 1.10/1.29 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[662, 658])).
% 1.10/1.29 tff(664,plain,(
% 1.10/1.29 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.10/1.29 inference(skolemize,[status(sab)],[663])).
% 1.10/1.29 tff(665,plain,
% 1.10/1.29 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[664, 657])).
% 1.10/1.29 tff(666,plain,
% 1.10/1.29 (c0_1(a2408)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[381, 451])).
% 1.10/1.29 tff(667,plain,
% 1.10/1.29 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(668,plain,
% 1.10/1.29 ((hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408))) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(669,plain,
% 1.10/1.29 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[668])).
% 1.10/1.29 tff(670,plain,
% 1.10/1.29 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[669, 667])).
% 1.10/1.29 tff(671,plain,
% 1.10/1.29 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(672,plain,
% 1.10/1.29 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[671, 670])).
% 1.10/1.29 tff(673,plain,
% 1.10/1.29 (hskp23 | hskp14 | (~c1_1(a2408))),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[672, 192, 666, 452, 42])).
% 1.10/1.29 tff(674,plain,
% 1.10/1.29 (hskp14),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[673, 610, 638])).
% 1.10/1.29 tff(675,plain,
% 1.10/1.29 (((~hskp14) | (~c3_1(a2420))) <=> ((~hskp14) | (~c3_1(a2420)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(676,plain,
% 1.10/1.29 (((~c3_1(a2420)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a2420)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(677,axiom,((~c3_1(a2420)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 1.10/1.29 tff(678,plain,
% 1.10/1.29 ((~hskp14) | (~c3_1(a2420))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[677, 676])).
% 1.10/1.29 tff(679,plain,
% 1.10/1.29 ((~hskp14) | (~c3_1(a2420))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[678, 675])).
% 1.10/1.29 tff(680,plain,
% 1.10/1.29 (~c3_1(a2420)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[679, 674])).
% 1.10/1.29 tff(681,plain,
% 1.10/1.29 (((~hskp14) | c2_1(a2420)) <=> ((~hskp14) | c2_1(a2420))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(682,axiom,((~hskp14) | c2_1(a2420)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 1.10/1.29 tff(683,plain,
% 1.10/1.29 ((~hskp14) | c2_1(a2420)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[682, 681])).
% 1.10/1.29 tff(684,plain,
% 1.10/1.29 ((~hskp14) | c2_1(a2420)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[683, 681])).
% 1.10/1.29 tff(685,plain,
% 1.10/1.29 ((~hskp14) | c2_1(a2420)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[684, 681])).
% 1.10/1.29 tff(686,plain,
% 1.10/1.29 ((~hskp14) | c2_1(a2420)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[685, 681])).
% 1.10/1.29 tff(687,plain,
% 1.10/1.29 ((~hskp14) | c2_1(a2420)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[686, 681])).
% 1.10/1.29 tff(688,plain,
% 1.10/1.29 (c2_1(a2420)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[687, 674])).
% 1.10/1.29 tff(689,plain,
% 1.10/1.29 (((~hskp14) | c1_1(a2420)) <=> ((~hskp14) | c1_1(a2420))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(690,axiom,((~hskp14) | c1_1(a2420)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 1.10/1.29 tff(691,plain,
% 1.10/1.29 ((~hskp14) | c1_1(a2420)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[690, 689])).
% 1.10/1.29 tff(692,plain,
% 1.10/1.29 ((~hskp14) | c1_1(a2420)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[691, 689])).
% 1.10/1.29 tff(693,plain,
% 1.10/1.29 ((~hskp14) | c1_1(a2420)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[692, 689])).
% 1.10/1.29 tff(694,plain,
% 1.10/1.29 ((~hskp14) | c1_1(a2420)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[693, 689])).
% 1.10/1.29 tff(695,plain,
% 1.10/1.29 ((~hskp14) | c1_1(a2420)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[694, 689])).
% 1.10/1.29 tff(696,plain,
% 1.10/1.29 (c1_1(a2420)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[695, 674])).
% 1.10/1.29 tff(697,plain,
% 1.10/1.29 (hskp5),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[449, 192, 43, 533, 532, 531, 53])).
% 1.10/1.29 tff(698,plain,
% 1.10/1.29 (~c2_1(a2408)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[373, 697])).
% 1.10/1.29 tff(699,plain,
% 1.10/1.29 (c3_1(a2408)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[396, 697])).
% 1.10/1.29 tff(700,plain,
% 1.10/1.29 (c1_1(a2408)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[637, 699, 96, 698, 629])).
% 1.10/1.29 tff(701,plain,
% 1.10/1.29 (hskp30),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[644, 192, 533, 699, 531, 698, 564, 700, 534])).
% 1.10/1.29 tff(702,plain,
% 1.10/1.29 (c3_1(a2450)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[582, 701])).
% 1.10/1.29 tff(703,plain,
% 1.10/1.29 (c1_1(a2450)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[590, 701])).
% 1.10/1.29 tff(704,plain,
% 1.10/1.29 (~c2_1(a2450)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[654, 192, 96, 703, 702, 533, 531, 443, 534])).
% 1.10/1.29 tff(705,assumption,(c1_1(a2425)), introduced(assumption)).
% 1.10/1.29 tff(706,assumption,(~c3_1(a2425)), introduced(assumption)).
% 1.10/1.29 tff(707,assumption,(~c2_1(a2425)), introduced(assumption)).
% 1.10/1.29 tff(708,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2425) | c3_1(a2425) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c1_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2425) | c3_1(a2425) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c1_1(a2425)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(709,plain,
% 1.10/1.29 ((hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416))) <=> (hskp23 | c2_1(a2425) | c3_1(a2425) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c1_1(a2425)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(710,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2425) | c3_1(a2425) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c1_1(a2425))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[709])).
% 1.10/1.29 tff(711,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2425) | c3_1(a2425) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c1_1(a2425)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[710, 708])).
% 1.10/1.29 tff(712,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(713,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2425) | c3_1(a2425) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c1_1(a2425))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[712, 711])).
% 1.10/1.29 tff(714,plain,
% 1.10/1.29 ($false),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[713, 192, 629, 158, 707, 706, 150, 144, 628, 705])).
% 1.10/1.29 tff(715,plain,((~hskp11) | hskp23 | c2_1(a2425) | c3_1(a2425) | (~c1_1(a2425))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.29 tff(716,plain,
% 1.10/1.29 (~hskp11),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[715, 534, 532, 531, 629])).
% 1.10/1.29 tff(717,plain,
% 1.10/1.29 (c0_1(a2408)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[381, 697])).
% 1.10/1.29 tff(718,plain,
% 1.10/1.29 (hskp14),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[672, 192, 629, 717, 699, 42, 700])).
% 1.10/1.29 tff(719,plain,
% 1.10/1.29 (~c3_1(a2420)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[679, 718])).
% 1.10/1.29 tff(720,plain,
% 1.10/1.29 (c2_1(a2420)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[687, 718])).
% 1.10/1.29 tff(721,plain,
% 1.10/1.29 (c1_1(a2420)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[695, 718])).
% 1.10/1.29 tff(722,assumption,(~c2_1(a2435)), introduced(assumption)).
% 1.10/1.29 tff(723,assumption,(c2_1(a2420)), introduced(assumption)).
% 1.10/1.29 tff(724,assumption,(c1_1(a2420)), introduced(assumption)).
% 1.10/1.29 tff(725,plain,
% 1.10/1.29 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(726,plain,
% 1.10/1.29 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420))) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(727,plain,
% 1.10/1.29 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[726])).
% 1.10/1.29 tff(728,plain,
% 1.10/1.29 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[727, 725])).
% 1.10/1.29 tff(729,plain,
% 1.10/1.29 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420)))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(730,plain,
% 1.10/1.29 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[729, 728])).
% 1.10/1.29 tff(731,plain,
% 1.10/1.29 (hskp12 | c0_1(a2420)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[730, 192, 307, 724, 723, 278])).
% 1.10/1.29 tff(732,plain,
% 1.10/1.29 (c0_1(a2420)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[731, 308])).
% 1.10/1.29 tff(733,assumption,(~c3_1(a2420)), introduced(assumption)).
% 1.10/1.29 tff(734,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c0_1(a2420)) | (~c2_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c0_1(a2420)) | (~c2_1(a2420)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(735,plain,
% 1.10/1.29 ((hskp20 | (~ndr1_0) | (~c2_1(a2420)) | (~c1_1(a2420)) | (~c0_1(a2420)) | c3_1(a2420) | (~c0_1(a2420)) | (~c2_1(a2420))) <=> (hskp20 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c0_1(a2420)) | (~c2_1(a2420)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(736,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2420)) | (~c1_1(a2420)) | (~c0_1(a2420)) | c3_1(a2420) | (~c0_1(a2420)) | (~c2_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c0_1(a2420)) | (~c2_1(a2420))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[735])).
% 1.10/1.29 tff(737,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2420)) | (~c1_1(a2420)) | (~c0_1(a2420)) | c3_1(a2420) | (~c0_1(a2420)) | (~c2_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c0_1(a2420)) | (~c2_1(a2420)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[736, 734])).
% 1.10/1.29 tff(738,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2420)) | (~c1_1(a2420)) | (~c0_1(a2420)) | c3_1(a2420) | (~c0_1(a2420)) | (~c2_1(a2420)))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(739,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c0_1(a2420)) | (~c2_1(a2420))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[738, 737])).
% 1.10/1.29 tff(740,plain,
% 1.10/1.29 (hskp20 | (~c0_1(a2420))),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[739, 192, 724, 723, 733, 665])).
% 1.10/1.29 tff(741,plain,
% 1.10/1.29 (hskp20),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[740, 732])).
% 1.10/1.29 tff(742,plain,
% 1.10/1.29 (((~hskp20) | c3_1(a2435)) <=> ((~hskp20) | c3_1(a2435))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(743,axiom,((~hskp20) | c3_1(a2435)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 1.10/1.29 tff(744,plain,
% 1.10/1.29 ((~hskp20) | c3_1(a2435)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[743, 742])).
% 1.10/1.29 tff(745,plain,
% 1.10/1.29 ((~hskp20) | c3_1(a2435)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[744, 742])).
% 1.10/1.29 tff(746,plain,
% 1.10/1.29 ((~hskp20) | c3_1(a2435)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[745, 742])).
% 1.10/1.29 tff(747,plain,
% 1.10/1.29 ((~hskp20) | c3_1(a2435)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[746, 742])).
% 1.10/1.29 tff(748,plain,
% 1.10/1.29 ((~hskp20) | c3_1(a2435)),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[747, 742])).
% 1.10/1.29 tff(749,plain,
% 1.10/1.29 (c3_1(a2435)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[748, 741])).
% 1.10/1.29 tff(750,plain,
% 1.10/1.29 (((~hskp20) | (~c0_1(a2435))) <=> ((~hskp20) | (~c0_1(a2435)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(751,plain,
% 1.10/1.29 (((~c0_1(a2435)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a2435)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(752,axiom,((~c0_1(a2435)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 1.10/1.29 tff(753,plain,
% 1.10/1.29 ((~hskp20) | (~c0_1(a2435))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[752, 751])).
% 1.10/1.29 tff(754,plain,
% 1.10/1.29 ((~hskp20) | (~c0_1(a2435))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[753, 750])).
% 1.10/1.29 tff(755,plain,
% 1.10/1.29 (~c0_1(a2435)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[754, 741])).
% 1.10/1.29 tff(756,assumption,(c1_1(a2408)), introduced(assumption)).
% 1.10/1.29 tff(757,plain,
% 1.10/1.29 (^[V: $i, U: $i] : refl((hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.10/1.29 inference(bind,[status(th)],[])).
% 1.10/1.29 tff(758,plain,
% 1.10/1.29 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.10/1.29 inference(quant_intro,[status(thm)],[757])).
% 1.10/1.29 tff(759,plain,
% 1.10/1.29 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(760,plain,
% 1.10/1.29 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp12) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp12) <=> (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.10/1.29 inference(bind,[status(th)],[])).
% 1.10/1.29 tff(761,plain,
% 1.10/1.29 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp12) <=> ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.10/1.29 inference(quant_intro,[status(thm)],[760])).
% 1.10/1.29 tff(762,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause189')).
% 1.10/1.29 tff(763,plain,
% 1.10/1.29 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[762, 761])).
% 1.10/1.29 tff(764,plain,
% 1.10/1.29 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[763, 759])).
% 1.10/1.29 tff(765,plain,(
% 1.10/1.29 ![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.10/1.29 inference(skolemize,[status(sab)],[764])).
% 1.10/1.29 tff(766,plain,
% 1.10/1.29 (![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[765, 758])).
% 1.10/1.29 tff(767,assumption,(c0_1(a2408)), introduced(assumption)).
% 1.10/1.29 tff(768,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2435)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(769,plain,
% 1.10/1.29 ((hskp12 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435))) <=> (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2435)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(770,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2435))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[769])).
% 1.10/1.29 tff(771,plain,
% 1.10/1.29 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2435)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[770, 768])).
% 1.10/1.29 tff(772,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(773,plain,
% 1.10/1.29 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2435))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[772, 771])).
% 1.10/1.29 tff(774,plain,
% 1.10/1.29 (hskp12 | c0_1(a2435) | (~c3_1(a2435))),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[773, 192, 767, 612, 722, 766, 756])).
% 1.10/1.29 tff(775,plain,
% 1.10/1.29 ($false),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[774, 755, 749, 308])).
% 1.10/1.29 tff(776,plain,(hskp12 | (~c0_1(a2408)) | (~c3_1(a2408)) | c2_1(a2435) | (~c1_1(a2408)) | (~c1_1(a2420)) | (~c2_1(a2420)) | c3_1(a2420) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.10/1.29 tff(777,plain,
% 1.10/1.29 (hskp12),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[776, 717, 699, 722, 700, 721, 720, 719, 716])).
% 1.10/1.29 tff(778,plain,
% 1.10/1.29 (~c1_1(a2417)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[217, 777])).
% 1.10/1.29 tff(779,plain,
% 1.10/1.29 (c3_1(a2417)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[231, 777])).
% 1.10/1.29 tff(780,plain,
% 1.10/1.29 (c0_1(a2450)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[598, 701])).
% 1.10/1.29 tff(781,plain,
% 1.10/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c0_1(a2425)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c0_1(a2425)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(782,plain,
% 1.10/1.29 (((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417))) <=> (c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c0_1(a2425)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(783,plain,
% 1.10/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c0_1(a2425))))),
% 1.10/1.29 inference(monotonicity,[status(thm)],[782])).
% 1.10/1.29 tff(784,plain,
% 1.10/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c0_1(a2425)))),
% 1.10/1.29 inference(transitivity,[status(thm)],[783, 781])).
% 1.10/1.29 tff(785,plain,
% 1.10/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.10/1.29 inference(quant_inst,[status(thm)],[])).
% 1.10/1.29 tff(786,plain,
% 1.10/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c0_1(a2425))),
% 1.10/1.29 inference(modus_ponens,[status(thm)],[785, 784])).
% 1.10/1.29 tff(787,plain,
% 1.10/1.29 (~c2_1(a2417)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[786, 192, 780, 703, 702, 533, 779, 532, 531, 778, 554])).
% 1.10/1.29 tff(788,plain,
% 1.10/1.29 (~c0_1(a2417)),
% 1.10/1.29 inference(unit_resolution,[status(thm)],[223, 777])).
% 1.10/1.29 tff(789,plain,
% 1.10/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2425)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2425)))),
% 1.10/1.29 inference(rewrite,[status(thm)],[])).
% 1.10/1.29 tff(790,plain,
% 1.10/1.29 (((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c1_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2425)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(791,plain,
% 1.10/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c1_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2425))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[790])).
% 1.10/1.30 tff(792,plain,
% 1.10/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c1_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2425)))),
% 1.10/1.30 inference(transitivity,[status(thm)],[791, 789])).
% 1.10/1.30 tff(793,plain,
% 1.10/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c1_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(794,plain,
% 1.10/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2425))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[793, 792])).
% 1.10/1.30 tff(795,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[794, 192, 703, 702, 532, 531, 788, 778, 11, 787, 704, 534])).
% 1.10/1.30 tff(796,plain,(hskp10 | c2_1(a2435) | hskp23 | hskp19 | c0_1(a2478) | c3_1(a2478) | (~c2_1(a2478))), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(797,plain,
% 1.10/1.30 (c2_1(a2435)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[796, 610, 96, 43, 464, 463, 462])).
% 1.10/1.30 tff(798,plain,
% 1.10/1.30 (((~hskp20) | (~c2_1(a2435))) <=> ((~hskp20) | (~c2_1(a2435)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(799,plain,
% 1.10/1.30 (((~c2_1(a2435)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a2435)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(800,axiom,((~c2_1(a2435)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 1.10/1.30 tff(801,plain,
% 1.10/1.30 ((~hskp20) | (~c2_1(a2435))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[800, 799])).
% 1.10/1.30 tff(802,plain,
% 1.10/1.30 ((~hskp20) | (~c2_1(a2435))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[801, 798])).
% 1.10/1.30 tff(803,plain,
% 1.10/1.30 (~hskp20),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[802, 797])).
% 1.10/1.30 tff(804,plain,
% 1.10/1.30 (~c0_1(a2420)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[739, 192, 803, 696, 688, 680, 665])).
% 1.10/1.30 tff(805,plain,
% 1.10/1.30 (~hskp11),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[715, 610, 418, 412, 433])).
% 1.10/1.30 tff(806,plain,
% 1.10/1.30 (hskp12 | c0_1(a2420)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[730, 192, 805, 696, 688, 278])).
% 1.10/1.30 tff(807,plain,
% 1.10/1.30 (hskp12),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[806, 804])).
% 1.10/1.30 tff(808,plain,
% 1.10/1.30 (~c1_1(a2417)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[217, 807])).
% 1.10/1.30 tff(809,plain,
% 1.10/1.30 (c3_1(a2417)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[231, 807])).
% 1.10/1.30 tff(810,plain,
% 1.10/1.30 (c0_1(a2450)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[598, 646])).
% 1.10/1.30 tff(811,plain,
% 1.10/1.30 (~c2_1(a2417)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[786, 192, 810, 648, 647, 426, 809, 418, 412, 808, 554])).
% 1.10/1.30 tff(812,plain,
% 1.10/1.30 (~c0_1(a2417)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[223, 807])).
% 1.10/1.30 tff(813,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[794, 192, 648, 647, 418, 412, 812, 808, 11, 811, 655, 433])).
% 1.10/1.30 tff(814,plain,(hskp19 | hskp10), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(815,plain,
% 1.10/1.30 (hskp19),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[814, 96])).
% 1.10/1.30 tff(816,plain,
% 1.10/1.30 (((~hskp19) | c3_1(a2432)) <=> ((~hskp19) | c3_1(a2432))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(817,axiom,((~hskp19) | c3_1(a2432)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 1.10/1.30 tff(818,plain,
% 1.10/1.30 ((~hskp19) | c3_1(a2432)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[817, 816])).
% 1.10/1.30 tff(819,plain,
% 1.10/1.30 ((~hskp19) | c3_1(a2432)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[818, 816])).
% 1.10/1.30 tff(820,plain,
% 1.10/1.30 ((~hskp19) | c3_1(a2432)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[819, 816])).
% 1.10/1.30 tff(821,plain,
% 1.10/1.30 ((~hskp19) | c3_1(a2432)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[820, 816])).
% 1.10/1.30 tff(822,plain,
% 1.10/1.30 ((~hskp19) | c3_1(a2432)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[821, 816])).
% 1.10/1.30 tff(823,plain,
% 1.10/1.30 (c3_1(a2432)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[822, 815])).
% 1.10/1.30 tff(824,plain,
% 1.10/1.30 (c1_1(a2432)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[305, 815])).
% 1.10/1.30 tff(825,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(826,plain,
% 1.10/1.30 ((hskp10 | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425))) <=> (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(827,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[826])).
% 1.10/1.30 tff(828,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.10/1.30 inference(transitivity,[status(thm)],[827, 825])).
% 1.10/1.30 tff(829,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(830,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp10 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[829, 828])).
% 1.10/1.30 tff(831,plain,
% 1.10/1.30 (~c2_1(a2432)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[830, 192, 96, 824, 823, 426, 412, 443, 433])).
% 1.10/1.30 tff(832,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(833,plain,
% 1.10/1.30 ((hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432))) <=> (hskp30 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(834,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[833])).
% 1.10/1.30 tff(835,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.10/1.30 inference(transitivity,[status(thm)],[834, 832])).
% 1.10/1.30 tff(836,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(837,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[836, 835])).
% 1.10/1.30 tff(838,plain,
% 1.10/1.30 (hskp30),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[837, 192, 824, 823, 426, 412, 564, 831, 433])).
% 1.10/1.30 tff(839,plain,
% 1.10/1.30 (c3_1(a2450)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[582, 838])).
% 1.10/1.30 tff(840,plain,
% 1.10/1.30 (c1_1(a2450)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[590, 838])).
% 1.10/1.30 tff(841,plain,
% 1.10/1.30 (~c2_1(a2450)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[654, 192, 96, 840, 839, 426, 412, 443, 433])).
% 1.10/1.30 tff(842,plain,
% 1.10/1.30 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.10/1.30 inference(bind,[status(th)],[])).
% 1.10/1.30 tff(843,plain,
% 1.10/1.30 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.30 inference(quant_intro,[status(thm)],[842])).
% 1.10/1.30 tff(844,plain,
% 1.10/1.30 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(845,plain,
% 1.10/1.30 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp20) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp20))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.10/1.30 inference(bind,[status(th)],[])).
% 1.10/1.30 tff(846,plain,
% 1.10/1.30 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.30 inference(quant_intro,[status(thm)],[845])).
% 1.10/1.30 tff(847,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(U)) | c0_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause190')).
% 1.10/1.30 tff(848,plain,
% 1.10/1.30 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[847, 846])).
% 1.10/1.30 tff(849,plain,
% 1.10/1.30 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[848, 844])).
% 1.10/1.30 tff(850,plain,(
% 1.10/1.30 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.30 inference(skolemize,[status(sab)],[849])).
% 1.10/1.30 tff(851,plain,
% 1.10/1.30 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[850, 843])).
% 1.10/1.30 tff(852,plain,
% 1.10/1.30 (~c0_1(a2432)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[297, 815])).
% 1.10/1.30 tff(853,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp20 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(854,plain,
% 1.10/1.30 ((hskp20 | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432))) <=> (hskp20 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(855,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[854])).
% 1.10/1.30 tff(856,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp20 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.10/1.30 inference(transitivity,[status(thm)],[855, 853])).
% 1.10/1.30 tff(857,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(858,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp20 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[857, 856])).
% 1.10/1.30 tff(859,plain,
% 1.10/1.30 (hskp20),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[858, 192, 824, 823, 852, 851, 831])).
% 1.10/1.30 tff(860,plain,
% 1.10/1.30 (~c2_1(a2435)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[802, 859])).
% 1.10/1.30 tff(861,plain,
% 1.10/1.30 (~c0_1(a2435)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[754, 859])).
% 1.10/1.30 tff(862,plain,
% 1.10/1.30 (c3_1(a2435)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[748, 859])).
% 1.10/1.30 tff(863,plain,
% 1.10/1.30 (c0_1(a2450)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[598, 838])).
% 1.10/1.30 tff(864,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2435)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(865,plain,
% 1.10/1.30 ((hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435))) <=> (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2435)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(866,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2435))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[865])).
% 1.10/1.30 tff(867,plain,
% 1.10/1.30 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2435)))),
% 1.10/1.30 inference(transitivity,[status(thm)],[866, 864])).
% 1.10/1.30 tff(868,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(869,plain,
% 1.10/1.30 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2435))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[868, 867])).
% 1.10/1.30 tff(870,plain,
% 1.10/1.30 (hskp12),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[869, 192, 863, 840, 839, 862, 861, 860, 766])).
% 1.10/1.30 tff(871,plain,
% 1.10/1.30 (~c1_1(a2417)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[217, 870])).
% 1.10/1.30 tff(872,plain,
% 1.10/1.30 (c3_1(a2417)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[231, 870])).
% 1.10/1.30 tff(873,plain,
% 1.10/1.30 (~c2_1(a2417)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[786, 192, 863, 840, 839, 426, 872, 418, 412, 871, 554])).
% 1.10/1.30 tff(874,plain,
% 1.10/1.30 (~c0_1(a2417)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[223, 870])).
% 1.10/1.30 tff(875,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[794, 192, 840, 839, 418, 412, 874, 871, 11, 873, 841, 433])).
% 1.10/1.30 tff(876,plain,(hskp10), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(877,plain,
% 1.10/1.30 (((~hskp10) | (~c3_1(a2414))) <=> ((~hskp10) | (~c3_1(a2414)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(878,plain,
% 1.10/1.30 (((~c3_1(a2414)) | (~hskp10)) <=> ((~hskp10) | (~c3_1(a2414)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(879,axiom,((~c3_1(a2414)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause117')).
% 1.10/1.30 tff(880,plain,
% 1.10/1.30 ((~hskp10) | (~c3_1(a2414))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[879, 878])).
% 1.10/1.30 tff(881,plain,
% 1.10/1.30 ((~hskp10) | (~c3_1(a2414))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[880, 877])).
% 1.10/1.30 tff(882,plain,
% 1.10/1.30 (~c3_1(a2414)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[881, 876])).
% 1.10/1.30 tff(883,plain,
% 1.10/1.30 (((~hskp10) | (~c1_1(a2414))) <=> ((~hskp10) | (~c1_1(a2414)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(884,plain,
% 1.10/1.30 (((~c1_1(a2414)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a2414)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(885,axiom,((~c1_1(a2414)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause116')).
% 1.10/1.30 tff(886,plain,
% 1.10/1.30 ((~hskp10) | (~c1_1(a2414))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[885, 884])).
% 1.10/1.30 tff(887,plain,
% 1.10/1.30 ((~hskp10) | (~c1_1(a2414))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[886, 883])).
% 1.10/1.30 tff(888,plain,
% 1.10/1.30 (~c1_1(a2414)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[887, 876])).
% 1.10/1.30 tff(889,assumption,(~hskp25), introduced(assumption)).
% 1.10/1.30 tff(890,assumption,(hskp6), introduced(assumption)).
% 1.10/1.30 tff(891,plain,
% 1.10/1.30 (((~hskp6) | (~c2_1(a2410))) <=> ((~hskp6) | (~c2_1(a2410)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(892,plain,
% 1.10/1.30 (((~c2_1(a2410)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a2410)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(893,axiom,((~c2_1(a2410)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 1.10/1.30 tff(894,plain,
% 1.10/1.30 ((~hskp6) | (~c2_1(a2410))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[893, 892])).
% 1.10/1.30 tff(895,plain,
% 1.10/1.30 ((~hskp6) | (~c2_1(a2410))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[894, 891])).
% 1.10/1.30 tff(896,plain,
% 1.10/1.30 (~c2_1(a2410)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[895, 890])).
% 1.10/1.30 tff(897,plain,
% 1.10/1.30 (((~hskp6) | c1_1(a2410)) <=> ((~hskp6) | c1_1(a2410))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(898,axiom,((~hskp6) | c1_1(a2410)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 1.10/1.30 tff(899,plain,
% 1.10/1.30 ((~hskp6) | c1_1(a2410)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[898, 897])).
% 1.10/1.30 tff(900,plain,
% 1.10/1.30 ((~hskp6) | c1_1(a2410)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[899, 897])).
% 1.10/1.30 tff(901,plain,
% 1.10/1.30 ((~hskp6) | c1_1(a2410)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[900, 897])).
% 1.10/1.30 tff(902,plain,
% 1.10/1.30 ((~hskp6) | c1_1(a2410)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[901, 897])).
% 1.10/1.30 tff(903,plain,
% 1.10/1.30 ((~hskp6) | c1_1(a2410)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[902, 897])).
% 1.10/1.30 tff(904,plain,
% 1.10/1.30 (c1_1(a2410)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[903, 890])).
% 1.10/1.30 tff(905,plain,
% 1.10/1.30 (((~hskp6) | c0_1(a2410)) <=> ((~hskp6) | c0_1(a2410))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(906,axiom,((~hskp6) | c0_1(a2410)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 1.10/1.30 tff(907,plain,
% 1.10/1.30 ((~hskp6) | c0_1(a2410)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[906, 905])).
% 1.10/1.30 tff(908,plain,
% 1.10/1.30 ((~hskp6) | c0_1(a2410)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[907, 905])).
% 1.10/1.30 tff(909,plain,
% 1.10/1.30 ((~hskp6) | c0_1(a2410)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[908, 905])).
% 1.10/1.30 tff(910,plain,
% 1.10/1.30 ((~hskp6) | c0_1(a2410)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[909, 905])).
% 1.10/1.30 tff(911,plain,
% 1.10/1.30 ((~hskp6) | c0_1(a2410)),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[910, 905])).
% 1.10/1.30 tff(912,plain,
% 1.10/1.30 (c0_1(a2410)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[911, 890])).
% 1.10/1.30 tff(913,plain,
% 1.10/1.30 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(914,plain,
% 1.10/1.30 ((hskp25 | hskp19 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410))) <=> (hskp25 | hskp19 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(915,plain,
% 1.10/1.30 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410))))),
% 1.10/1.30 inference(monotonicity,[status(thm)],[914])).
% 1.10/1.30 tff(916,plain,
% 1.10/1.30 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.10/1.30 inference(transitivity,[status(thm)],[915, 913])).
% 1.10/1.30 tff(917,plain,
% 1.10/1.30 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.10/1.30 inference(quant_inst,[status(thm)],[])).
% 1.10/1.30 tff(918,plain,
% 1.10/1.30 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[917, 916])).
% 1.10/1.30 tff(919,plain,
% 1.10/1.30 ($false),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[918, 192, 889, 43, 912, 904, 896, 106])).
% 1.10/1.30 tff(920,plain,((~hskp6) | hskp25 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.10/1.30 tff(921,plain,
% 1.10/1.30 (~hskp6),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[920, 889, 43])).
% 1.10/1.30 tff(922,assumption,(~hskp31), introduced(assumption)).
% 1.10/1.30 tff(923,plain,
% 1.10/1.30 (hskp27),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[190, 889, 922])).
% 1.10/1.30 tff(924,plain,
% 1.10/1.30 (((~hskp27) | (~c1_1(a2500))) <=> ((~hskp27) | (~c1_1(a2500)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(925,plain,
% 1.10/1.30 (((~c1_1(a2500)) | (~hskp27)) <=> ((~hskp27) | (~c1_1(a2500)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(926,axiom,((~c1_1(a2500)) | (~hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 1.10/1.30 tff(927,plain,
% 1.10/1.30 ((~hskp27) | (~c1_1(a2500))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[926, 925])).
% 1.10/1.30 tff(928,plain,
% 1.10/1.30 ((~hskp27) | (~c1_1(a2500))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[927, 924])).
% 1.10/1.30 tff(929,plain,
% 1.10/1.30 (~c1_1(a2500)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[928, 923])).
% 1.10/1.30 tff(930,plain,
% 1.10/1.30 (((~hskp27) | (~c0_1(a2500))) <=> ((~hskp27) | (~c0_1(a2500)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(931,plain,
% 1.10/1.30 (((~c0_1(a2500)) | (~hskp27)) <=> ((~hskp27) | (~c0_1(a2500)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(932,axiom,((~c0_1(a2500)) | (~hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause87')).
% 1.10/1.30 tff(933,plain,
% 1.10/1.30 ((~hskp27) | (~c0_1(a2500))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[932, 931])).
% 1.10/1.30 tff(934,plain,
% 1.10/1.30 ((~hskp27) | (~c0_1(a2500))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[933, 930])).
% 1.10/1.30 tff(935,plain,
% 1.10/1.30 (~c0_1(a2500)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[934, 923])).
% 1.10/1.30 tff(936,plain,
% 1.10/1.30 (((~hskp27) | (~c3_1(a2500))) <=> ((~hskp27) | (~c3_1(a2500)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(937,plain,
% 1.10/1.30 (((~c3_1(a2500)) | (~hskp27)) <=> ((~hskp27) | (~c3_1(a2500)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(938,axiom,((~c3_1(a2500)) | (~hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 1.10/1.30 tff(939,plain,
% 1.10/1.30 ((~hskp27) | (~c3_1(a2500))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[938, 937])).
% 1.10/1.30 tff(940,plain,
% 1.10/1.30 ((~hskp27) | (~c3_1(a2500))),
% 1.10/1.30 inference(modus_ponens,[status(thm)],[939, 936])).
% 1.10/1.30 tff(941,plain,
% 1.10/1.30 (~c3_1(a2500)),
% 1.10/1.30 inference(unit_resolution,[status(thm)],[940, 923])).
% 1.10/1.30 tff(942,plain,
% 1.10/1.30 (^[U: $i] : refl((hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.10/1.30 inference(bind,[status(th)],[])).
% 1.10/1.30 tff(943,plain,
% 1.10/1.30 (![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.10/1.30 inference(quant_intro,[status(thm)],[942])).
% 1.10/1.30 tff(944,plain,
% 1.10/1.30 (![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.10/1.30 inference(rewrite,[status(thm)],[])).
% 1.10/1.30 tff(945,plain,
% 1.10/1.30 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp1) <=> ((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp1))), rewrite(((hskp6 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp1) <=> (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp1) <=> (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.10/1.30 inference(bind,[status(th)],[])).
% 1.10/1.30 tff(946,plain,
% 1.10/1.30 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp1) <=> ![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.10/1.30 inference(quant_intro,[status(thm)],[945])).
% 1.10/1.30 tff(947,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp6) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 1.10/1.31 tff(948,plain,
% 1.10/1.31 (![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[947, 946])).
% 1.10/1.31 tff(949,plain,
% 1.10/1.31 (![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[948, 944])).
% 1.10/1.31 tff(950,plain,(
% 1.10/1.31 ![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.10/1.31 inference(skolemize,[status(sab)],[949])).
% 1.10/1.31 tff(951,plain,
% 1.10/1.31 (![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[950, 943])).
% 1.10/1.31 tff(952,assumption,(~c3_1(a2500)), introduced(assumption)).
% 1.10/1.31 tff(953,assumption,(~c1_1(a2500)), introduced(assumption)).
% 1.10/1.31 tff(954,assumption,(~c0_1(a2500)), introduced(assumption)).
% 1.10/1.31 tff(955,plain,
% 1.10/1.31 (^[U: $i] : refl((hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(956,plain,
% 1.10/1.31 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[955])).
% 1.10/1.31 tff(957,plain,
% 1.10/1.31 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(958,plain,
% 1.10/1.31 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1) <=> ((hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp1))), rewrite(((hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp1) <=> (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1) <=> (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(959,plain,
% 1.10/1.31 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1) <=> ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[958])).
% 1.10/1.31 tff(960,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp13) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 1.10/1.31 tff(961,plain,
% 1.10/1.31 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[960, 959])).
% 1.10/1.31 tff(962,plain,
% 1.10/1.31 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[961, 957])).
% 1.10/1.31 tff(963,plain,(
% 1.10/1.31 ![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.10/1.31 inference(skolemize,[status(sab)],[962])).
% 1.10/1.31 tff(964,plain,
% 1.10/1.31 (![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[963, 956])).
% 1.10/1.31 tff(965,plain,
% 1.10/1.31 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2500) | c3_1(a2500) | (~ndr1_0) | c2_1(a2500))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2500) | c3_1(a2500) | (~ndr1_0) | c2_1(a2500))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(966,plain,
% 1.10/1.31 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2500) | c0_1(a2500) | c2_1(a2500)) <=> (hskp13 | hskp1 | c0_1(a2500) | c3_1(a2500) | (~ndr1_0) | c2_1(a2500))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(967,plain,
% 1.10/1.31 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2500) | c0_1(a2500) | c2_1(a2500))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2500) | c3_1(a2500) | (~ndr1_0) | c2_1(a2500)))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[966])).
% 1.10/1.31 tff(968,plain,
% 1.10/1.31 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2500) | c0_1(a2500) | c2_1(a2500))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2500) | c3_1(a2500) | (~ndr1_0) | c2_1(a2500))),
% 1.10/1.31 inference(transitivity,[status(thm)],[967, 965])).
% 1.10/1.31 tff(969,plain,
% 1.10/1.31 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2500) | c0_1(a2500) | c2_1(a2500))),
% 1.10/1.31 inference(quant_inst,[status(thm)],[])).
% 1.10/1.31 tff(970,plain,
% 1.10/1.31 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2500) | c3_1(a2500) | (~ndr1_0) | c2_1(a2500)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[969, 968])).
% 1.10/1.31 tff(971,plain,
% 1.10/1.31 (hskp13 | hskp1 | c2_1(a2500)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[970, 192, 954, 952, 964])).
% 1.10/1.31 tff(972,plain,
% 1.10/1.31 (c2_1(a2500)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[971, 65, 22])).
% 1.10/1.31 tff(973,plain,
% 1.10/1.31 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(974,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[973])).
% 1.10/1.31 tff(975,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(976,plain,
% 1.10/1.31 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(977,plain,
% 1.10/1.31 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[976])).
% 1.10/1.31 tff(978,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 1.10/1.31 tff(979,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[978, 977])).
% 1.10/1.31 tff(980,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[979, 975])).
% 1.10/1.31 tff(981,plain,(
% 1.10/1.31 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(skolemize,[status(sab)],[980])).
% 1.10/1.31 tff(982,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[981, 974])).
% 1.10/1.31 tff(983,plain,
% 1.10/1.31 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c2_1(a2500)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c2_1(a2500)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(984,plain,
% 1.10/1.31 ((hskp16 | hskp12 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | (~c2_1(a2500))) <=> (hskp16 | hskp12 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c2_1(a2500)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(985,plain,
% 1.10/1.31 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | (~c2_1(a2500)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c2_1(a2500))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[984])).
% 1.10/1.31 tff(986,plain,
% 1.10/1.31 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | (~c2_1(a2500)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c2_1(a2500)))),
% 1.10/1.31 inference(transitivity,[status(thm)],[985, 983])).
% 1.10/1.31 tff(987,plain,
% 1.10/1.31 ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | (~c2_1(a2500)))),
% 1.10/1.31 inference(quant_inst,[status(thm)],[])).
% 1.10/1.31 tff(988,plain,
% 1.10/1.31 ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c2_1(a2500))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[987, 986])).
% 1.10/1.31 tff(989,plain,
% 1.10/1.31 (hskp16 | hskp12 | (~c2_1(a2500))),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[988, 192, 953, 952, 258])).
% 1.10/1.31 tff(990,plain,
% 1.10/1.31 (hskp12),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[989, 64, 972])).
% 1.10/1.31 tff(991,plain,
% 1.10/1.31 (~c0_1(a2417)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[223, 990])).
% 1.10/1.31 tff(992,plain,
% 1.10/1.31 (~c1_1(a2417)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[217, 990])).
% 1.10/1.31 tff(993,plain,
% 1.10/1.31 (c3_1(a2417)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[231, 990])).
% 1.10/1.31 tff(994,plain,
% 1.10/1.31 (hskp5),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[367, 43, 889])).
% 1.10/1.31 tff(995,plain,
% 1.10/1.31 (~c2_1(a2408)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[373, 994])).
% 1.10/1.31 tff(996,plain,
% 1.10/1.31 (c0_1(a2408)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[381, 994])).
% 1.10/1.31 tff(997,plain,
% 1.10/1.31 (~c1_1(a2408)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[388, 192, 889, 43, 996, 995, 106])).
% 1.10/1.31 tff(998,plain,
% 1.10/1.31 (^[V: $i, U: $i] : refl((hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(999,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[998])).
% 1.10/1.31 tff(1000,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(1001,plain,
% 1.10/1.31 (^[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) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(1002,plain,
% 1.10/1.31 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp1) <=> ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[1001])).
% 1.10/1.31 tff(1003,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 1.10/1.31 tff(1004,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 1.10/1.31 tff(1005,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1004, 1000])).
% 1.10/1.31 tff(1006,plain,(
% 1.10/1.31 ![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.31 inference(skolemize,[status(sab)],[1005])).
% 1.10/1.31 tff(1007,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1006, 999])).
% 1.10/1.31 tff(1008,assumption,(~c1_1(a2417)), introduced(assumption)).
% 1.10/1.31 tff(1009,plain,
% 1.10/1.31 (c3_1(a2408)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[396, 994])).
% 1.10/1.31 tff(1010,assumption,(c3_1(a2417)), introduced(assumption)).
% 1.10/1.31 tff(1011,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2417) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2417) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(1012,plain,
% 1.10/1.31 ((hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp1 | c1_1(a2417) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(1013,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2417) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2417)) | (~c3_1(a2417))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[1012])).
% 1.10/1.31 tff(1014,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2417) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.10/1.31 inference(transitivity,[status(thm)],[1013, 1011])).
% 1.10/1.31 tff(1015,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.10/1.31 inference(quant_inst,[status(thm)],[])).
% 1.10/1.31 tff(1016,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2417) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2417)) | (~c3_1(a2417))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 1.10/1.31 tff(1017,plain,
% 1.10/1.31 (~c2_1(a2417)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[1016, 192, 22, 1010, 1009, 1008, 995, 1007, 997])).
% 1.10/1.31 tff(1018,assumption,(c2_1(a2500)), introduced(assumption)).
% 1.10/1.31 tff(1019,assumption,(~c0_1(a2417)), introduced(assumption)).
% 1.10/1.31 tff(1020,assumption,(hskp10), introduced(assumption)).
% 1.10/1.31 tff(1021,plain,
% 1.10/1.31 (((~hskp10) | c0_1(a2414)) <=> ((~hskp10) | c0_1(a2414))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(1022,axiom,((~hskp10) | c0_1(a2414)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 1.10/1.31 tff(1023,plain,
% 1.10/1.31 ((~hskp10) | c0_1(a2414)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1022, 1021])).
% 1.10/1.31 tff(1024,plain,
% 1.10/1.31 ((~hskp10) | c0_1(a2414)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1023, 1021])).
% 1.10/1.31 tff(1025,plain,
% 1.10/1.31 ((~hskp10) | c0_1(a2414)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1024, 1021])).
% 1.10/1.31 tff(1026,plain,
% 1.10/1.31 ((~hskp10) | c0_1(a2414)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1025, 1021])).
% 1.10/1.31 tff(1027,plain,
% 1.10/1.31 ((~hskp10) | c0_1(a2414)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1026, 1021])).
% 1.10/1.31 tff(1028,plain,
% 1.10/1.31 (c0_1(a2414)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[1027, 1020])).
% 1.10/1.31 tff(1029,plain,
% 1.10/1.31 (~c3_1(a2414)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[881, 1020])).
% 1.10/1.31 tff(1030,plain,
% 1.10/1.31 (^[V: $i, U: $i] : refl((hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(1031,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[1030])).
% 1.10/1.31 tff(1032,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(1033,plain,
% 1.10/1.31 (^[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)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp29))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(1034,plain,
% 1.10/1.31 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp29) <=> ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[1033])).
% 1.10/1.31 tff(1035,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 1.10/1.31 tff(1036,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 1.10/1.31 tff(1037,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1036, 1032])).
% 1.10/1.31 tff(1038,plain,(
% 1.10/1.31 ![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(skolemize,[status(sab)],[1037])).
% 1.10/1.31 tff(1039,plain,
% 1.10/1.31 (![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1038, 1031])).
% 1.10/1.31 tff(1040,assumption,(~hskp29), introduced(assumption)).
% 1.10/1.31 tff(1041,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2500) | c1_1(a2500) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2500)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(1042,plain,
% 1.10/1.31 ((hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500))) <=> (hskp29 | c0_1(a2500) | c1_1(a2500) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2500)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(1043,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2500) | c1_1(a2500) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2500))))),
% 1.10/1.31 inference(monotonicity,[status(thm)],[1042])).
% 1.10/1.31 tff(1044,plain,
% 1.10/1.31 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2500)))),
% 1.10/1.31 inference(transitivity,[status(thm)],[1043, 1041])).
% 1.10/1.31 tff(1045,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))),
% 1.10/1.31 inference(quant_inst,[status(thm)],[])).
% 1.10/1.31 tff(1046,plain,
% 1.10/1.31 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2500))),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1045, 1044])).
% 1.10/1.31 tff(1047,plain,
% 1.10/1.31 ($false),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[1046, 192, 1040, 996, 1009, 954, 953, 1039, 1018, 997])).
% 1.10/1.31 tff(1048,plain,(hskp19 | hskp29 | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500)) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.10/1.31 tff(1049,plain,
% 1.10/1.31 (hskp29),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[1048, 43, 954, 953, 1018, 889])).
% 1.10/1.31 tff(1050,plain,
% 1.10/1.31 (((~hskp29) | c2_1(a2409)) <=> ((~hskp29) | c2_1(a2409))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(1051,axiom,((~hskp29) | c2_1(a2409)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 1.10/1.31 tff(1052,plain,
% 1.10/1.31 ((~hskp29) | c2_1(a2409)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1051, 1050])).
% 1.10/1.31 tff(1053,plain,
% 1.10/1.31 ((~hskp29) | c2_1(a2409)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1052, 1050])).
% 1.10/1.31 tff(1054,plain,
% 1.10/1.31 ((~hskp29) | c2_1(a2409)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1053, 1050])).
% 1.10/1.31 tff(1055,plain,
% 1.10/1.31 ((~hskp29) | c2_1(a2409)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1054, 1050])).
% 1.10/1.31 tff(1056,plain,
% 1.10/1.31 ((~hskp29) | c2_1(a2409)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1055, 1050])).
% 1.10/1.31 tff(1057,plain,
% 1.10/1.31 (c2_1(a2409)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[1056, 1049])).
% 1.10/1.31 tff(1058,plain,
% 1.10/1.31 (((~hskp29) | c3_1(a2409)) <=> ((~hskp29) | c3_1(a2409))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(1059,axiom,((~hskp29) | c3_1(a2409)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 1.10/1.31 tff(1060,plain,
% 1.10/1.31 ((~hskp29) | c3_1(a2409)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 1.10/1.31 tff(1061,plain,
% 1.10/1.31 ((~hskp29) | c3_1(a2409)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1060, 1058])).
% 1.10/1.31 tff(1062,plain,
% 1.10/1.31 ((~hskp29) | c3_1(a2409)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1061, 1058])).
% 1.10/1.31 tff(1063,plain,
% 1.10/1.31 ((~hskp29) | c3_1(a2409)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1062, 1058])).
% 1.10/1.31 tff(1064,plain,
% 1.10/1.31 ((~hskp29) | c3_1(a2409)),
% 1.10/1.31 inference(modus_ponens,[status(thm)],[1063, 1058])).
% 1.10/1.31 tff(1065,plain,
% 1.10/1.31 (c3_1(a2409)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[1064, 1049])).
% 1.10/1.31 tff(1066,plain,
% 1.10/1.31 (~c1_1(a2414)),
% 1.10/1.31 inference(unit_resolution,[status(thm)],[887, 1020])).
% 1.10/1.31 tff(1067,plain,
% 1.10/1.31 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(1068,plain,
% 1.10/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.10/1.31 inference(quant_intro,[status(thm)],[1067])).
% 1.10/1.31 tff(1069,plain,
% 1.10/1.31 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.10/1.31 inference(rewrite,[status(thm)],[])).
% 1.10/1.31 tff(1070,plain,
% 1.10/1.31 (^[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))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))))),
% 1.10/1.31 inference(bind,[status(th)],[])).
% 1.10/1.31 tff(1071,plain,
% 1.10/1.32 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.10/1.32 inference(quant_intro,[status(thm)],[1070])).
% 1.10/1.32 tff(1072,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | c3_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause202')).
% 1.10/1.32 tff(1073,plain,
% 1.10/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 1.10/1.32 tff(1074,plain,
% 1.10/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1073, 1069])).
% 1.10/1.32 tff(1075,plain,(
% 1.10/1.32 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.10/1.32 inference(skolemize,[status(sab)],[1074])).
% 1.10/1.32 tff(1076,plain,
% 1.10/1.32 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1075, 1068])).
% 1.10/1.32 tff(1077,assumption,(~c3_1(a2414)), introduced(assumption)).
% 1.10/1.32 tff(1078,assumption,(~c1_1(a2414)), introduced(assumption)).
% 1.10/1.32 tff(1079,assumption,(~hskp30), introduced(assumption)).
% 1.10/1.32 tff(1080,plain,
% 1.10/1.32 ((hskp30 | hskp26 | hskp19) <=> (hskp30 | hskp26 | hskp19)),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1081,plain,
% 1.10/1.32 (((hskp30 | hskp26) | hskp19) <=> (hskp30 | hskp26 | hskp19)),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1082,plain,
% 1.10/1.32 ((hskp30 | hskp26) <=> (hskp30 | hskp26)),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1083,plain,
% 1.10/1.32 (((hskp30 | hskp26) | hskp19) <=> ((hskp30 | hskp26) | hskp19)),
% 1.10/1.32 inference(monotonicity,[status(thm)],[1082])).
% 1.10/1.32 tff(1084,plain,
% 1.10/1.32 (((hskp30 | hskp26) | hskp19) <=> (hskp30 | hskp26 | hskp19)),
% 1.10/1.32 inference(transitivity,[status(thm)],[1083, 1081])).
% 1.10/1.32 tff(1085,axiom,((hskp30 | hskp26) | hskp19), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 1.10/1.32 tff(1086,plain,
% 1.10/1.32 (hskp30 | hskp26 | hskp19),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 1.10/1.32 tff(1087,plain,
% 1.10/1.32 (hskp30 | hskp26 | hskp19),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1086, 1080])).
% 1.10/1.32 tff(1088,plain,
% 1.10/1.32 (hskp30 | hskp26 | hskp19),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1087, 1080])).
% 1.10/1.32 tff(1089,plain,
% 1.10/1.32 (hskp30 | hskp26 | hskp19),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1088, 1080])).
% 1.10/1.32 tff(1090,plain,
% 1.10/1.32 (hskp30 | hskp26 | hskp19),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1089, 1080])).
% 1.10/1.32 tff(1091,plain,
% 1.10/1.32 (hskp26),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1090, 43, 1079])).
% 1.10/1.32 tff(1092,plain,
% 1.10/1.32 (((~hskp26) | (~c3_1(a2484))) <=> ((~hskp26) | (~c3_1(a2484)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1093,plain,
% 1.10/1.32 (((~c3_1(a2484)) | (~hskp26)) <=> ((~hskp26) | (~c3_1(a2484)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1094,axiom,((~c3_1(a2484)) | (~hskp26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 1.10/1.32 tff(1095,plain,
% 1.10/1.32 ((~hskp26) | (~c3_1(a2484))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 1.10/1.32 tff(1096,plain,
% 1.10/1.32 ((~hskp26) | (~c3_1(a2484))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1095, 1092])).
% 1.10/1.32 tff(1097,plain,
% 1.10/1.32 (~c3_1(a2484)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1096, 1091])).
% 1.10/1.32 tff(1098,assumption,(c0_1(a2414)), introduced(assumption)).
% 1.10/1.32 tff(1099,plain,
% 1.10/1.32 (((~hskp26) | c1_1(a2484)) <=> ((~hskp26) | c1_1(a2484))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1100,axiom,((~hskp26) | c1_1(a2484)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause52')).
% 1.10/1.32 tff(1101,plain,
% 1.10/1.32 ((~hskp26) | c1_1(a2484)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1100, 1099])).
% 1.10/1.32 tff(1102,plain,
% 1.10/1.32 ((~hskp26) | c1_1(a2484)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1101, 1099])).
% 1.10/1.32 tff(1103,plain,
% 1.10/1.32 ((~hskp26) | c1_1(a2484)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1102, 1099])).
% 1.10/1.32 tff(1104,plain,
% 1.10/1.32 ((~hskp26) | c1_1(a2484)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1103, 1099])).
% 1.10/1.32 tff(1105,plain,
% 1.10/1.32 ((~hskp26) | c1_1(a2484)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1104, 1099])).
% 1.10/1.32 tff(1106,plain,
% 1.10/1.32 (c1_1(a2484)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1105, 1091])).
% 1.10/1.32 tff(1107,plain,
% 1.10/1.32 (((~hskp26) | c0_1(a2484)) <=> ((~hskp26) | c0_1(a2484))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1108,axiom,((~hskp26) | c0_1(a2484)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause51')).
% 1.10/1.32 tff(1109,plain,
% 1.10/1.32 ((~hskp26) | c0_1(a2484)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 1.10/1.32 tff(1110,plain,
% 1.10/1.32 ((~hskp26) | c0_1(a2484)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1109, 1107])).
% 1.10/1.32 tff(1111,plain,
% 1.10/1.32 ((~hskp26) | c0_1(a2484)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1110, 1107])).
% 1.10/1.32 tff(1112,plain,
% 1.10/1.32 ((~hskp26) | c0_1(a2484)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1111, 1107])).
% 1.10/1.32 tff(1113,plain,
% 1.10/1.32 ((~hskp26) | c0_1(a2484)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1112, 1107])).
% 1.10/1.32 tff(1114,plain,
% 1.10/1.32 (c0_1(a2484)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1113, 1091])).
% 1.10/1.32 tff(1115,assumption,(c3_1(a2409)), introduced(assumption)).
% 1.10/1.32 tff(1116,assumption,(c2_1(a2409)), introduced(assumption)).
% 1.10/1.32 tff(1117,plain,
% 1.10/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2484) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2484)) | (~c0_1(a2484)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2484) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2484)) | (~c0_1(a2484)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1118,plain,
% 1.10/1.32 (((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2484) | (~c1_1(a2484)) | (~c0_1(a2484)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c3_1(a2484) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2484)) | (~c0_1(a2484)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1119,plain,
% 1.10/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2484) | (~c1_1(a2484)) | (~c0_1(a2484)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2484) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2484)) | (~c0_1(a2484))))),
% 1.10/1.32 inference(monotonicity,[status(thm)],[1118])).
% 1.10/1.32 tff(1120,plain,
% 1.10/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2484) | (~c1_1(a2484)) | (~c0_1(a2484)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2484) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2484)) | (~c0_1(a2484)))),
% 1.10/1.32 inference(transitivity,[status(thm)],[1119, 1117])).
% 1.10/1.32 tff(1121,plain,
% 1.10/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2484) | (~c1_1(a2484)) | (~c0_1(a2484)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.10/1.32 inference(quant_inst,[status(thm)],[])).
% 1.10/1.32 tff(1122,plain,
% 1.10/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2484) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2484)) | (~c0_1(a2484))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1121, 1120])).
% 1.10/1.32 tff(1123,plain,
% 1.10/1.32 (~c1_1(a2409)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1122, 192, 1116, 1115, 1114, 1106, 1098, 1097, 1078, 1077, 1076])).
% 1.10/1.32 tff(1124,plain,
% 1.10/1.32 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a2408) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a2408) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1125,plain,
% 1.10/1.32 ((hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp1 | c2_1(a2408) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1126,plain,
% 1.10/1.32 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a2408) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2408) | (~c3_1(a2408))))),
% 1.10/1.32 inference(monotonicity,[status(thm)],[1125])).
% 1.10/1.32 tff(1127,plain,
% 1.10/1.32 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a2408) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.10/1.32 inference(transitivity,[status(thm)],[1126, 1124])).
% 1.10/1.32 tff(1128,plain,
% 1.10/1.32 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.10/1.32 inference(quant_inst,[status(thm)],[])).
% 1.10/1.32 tff(1129,plain,
% 1.10/1.32 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a2408) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2408) | (~c3_1(a2408))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 1.10/1.32 tff(1130,plain,
% 1.10/1.32 ($false),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1129, 192, 22, 1116, 1115, 1009, 995, 1007, 1123, 997])).
% 1.10/1.32 tff(1131,plain,(hskp19 | hskp1 | (~c2_1(a2409)) | (~c3_1(a2409)) | (~c0_1(a2414)) | c1_1(a2414) | c3_1(a2414) | hskp25 | hskp30), inference(lemma,lemma(discharge,[]))).
% 1.10/1.32 tff(1132,plain,
% 1.10/1.32 (hskp30),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1131, 1066, 43, 1065, 22, 1057, 1029, 889, 1028])).
% 1.10/1.32 tff(1133,plain,
% 1.10/1.32 (c1_1(a2450)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[590, 1132])).
% 1.10/1.32 tff(1134,plain,
% 1.10/1.32 (c0_1(a2450)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[598, 1132])).
% 1.10/1.32 tff(1135,plain,
% 1.10/1.32 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1136,plain,
% 1.10/1.32 ((hskp25 | hskp19 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450))) <=> (hskp25 | hskp19 | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1137,plain,
% 1.10/1.32 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450))))),
% 1.10/1.32 inference(monotonicity,[status(thm)],[1136])).
% 1.10/1.32 tff(1138,plain,
% 1.10/1.32 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))),
% 1.10/1.32 inference(transitivity,[status(thm)],[1137, 1135])).
% 1.10/1.32 tff(1139,plain,
% 1.10/1.32 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)))),
% 1.10/1.32 inference(quant_inst,[status(thm)],[])).
% 1.10/1.32 tff(1140,plain,
% 1.10/1.32 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 1.10/1.32 tff(1141,plain,
% 1.10/1.32 (c2_1(a2450)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1140, 192, 889, 43, 1134, 1133, 106])).
% 1.10/1.32 tff(1142,plain,
% 1.10/1.32 (~hskp6),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[920, 43, 889])).
% 1.10/1.32 tff(1143,assumption,(hskp24), introduced(assumption)).
% 1.10/1.32 tff(1144,plain,
% 1.10/1.32 (((~hskp24) | (~c3_1(a2468))) <=> ((~hskp24) | (~c3_1(a2468)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1145,plain,
% 1.10/1.32 (((~c3_1(a2468)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a2468)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1146,axiom,((~c3_1(a2468)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 1.10/1.32 tff(1147,plain,
% 1.10/1.32 ((~hskp24) | (~c3_1(a2468))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1146, 1145])).
% 1.10/1.32 tff(1148,plain,
% 1.10/1.32 ((~hskp24) | (~c3_1(a2468))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1147, 1144])).
% 1.10/1.32 tff(1149,plain,
% 1.10/1.32 (~c3_1(a2468)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1148, 1143])).
% 1.10/1.32 tff(1150,plain,
% 1.10/1.32 (((~hskp24) | c1_1(a2468)) <=> ((~hskp24) | c1_1(a2468))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1151,axiom,((~hskp24) | c1_1(a2468)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 1.10/1.32 tff(1152,plain,
% 1.10/1.32 ((~hskp24) | c1_1(a2468)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 1.10/1.32 tff(1153,plain,
% 1.10/1.32 ((~hskp24) | c1_1(a2468)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1152, 1150])).
% 1.10/1.32 tff(1154,plain,
% 1.10/1.32 ((~hskp24) | c1_1(a2468)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1153, 1150])).
% 1.10/1.32 tff(1155,plain,
% 1.10/1.32 ((~hskp24) | c1_1(a2468)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1154, 1150])).
% 1.10/1.32 tff(1156,plain,
% 1.10/1.32 ((~hskp24) | c1_1(a2468)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1155, 1150])).
% 1.10/1.32 tff(1157,plain,
% 1.10/1.32 (c1_1(a2468)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1156, 1143])).
% 1.10/1.32 tff(1158,assumption,(~hskp6), introduced(assumption)).
% 1.10/1.32 tff(1159,plain,
% 1.10/1.32 (((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | c3_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | c2_1(a2468))) <=> ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp1 | c3_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | c2_1(a2468))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1160,plain,
% 1.10/1.32 ((hskp6 | hskp1 | (~ndr1_0) | c3_1(a2468) | c2_1(a2468) | (~c1_1(a2468))) <=> (hskp6 | hskp1 | c3_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | c2_1(a2468))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1161,plain,
% 1.10/1.32 (((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | (~ndr1_0) | c3_1(a2468) | c2_1(a2468) | (~c1_1(a2468)))) <=> ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | c3_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | c2_1(a2468)))),
% 1.10/1.32 inference(monotonicity,[status(thm)],[1160])).
% 1.10/1.32 tff(1162,plain,
% 1.10/1.32 (((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | (~ndr1_0) | c3_1(a2468) | c2_1(a2468) | (~c1_1(a2468)))) <=> ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp1 | c3_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | c2_1(a2468))),
% 1.10/1.32 inference(transitivity,[status(thm)],[1161, 1159])).
% 1.10/1.32 tff(1163,plain,
% 1.10/1.32 ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | (~ndr1_0) | c3_1(a2468) | c2_1(a2468) | (~c1_1(a2468)))),
% 1.10/1.32 inference(quant_inst,[status(thm)],[])).
% 1.10/1.32 tff(1164,plain,
% 1.10/1.32 ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp1 | c3_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | c2_1(a2468)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 1.10/1.32 tff(1165,plain,
% 1.10/1.32 (c2_1(a2468)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1164, 192, 1158, 22, 1157, 1149, 951])).
% 1.10/1.32 tff(1166,plain,
% 1.10/1.32 (((~hskp24) | (~c0_1(a2468))) <=> ((~hskp24) | (~c0_1(a2468)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1167,plain,
% 1.10/1.32 (((~c0_1(a2468)) | (~hskp24)) <=> ((~hskp24) | (~c0_1(a2468)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1168,axiom,((~c0_1(a2468)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 1.10/1.32 tff(1169,plain,
% 1.10/1.32 ((~hskp24) | (~c0_1(a2468))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1168, 1167])).
% 1.10/1.32 tff(1170,plain,
% 1.10/1.32 ((~hskp24) | (~c0_1(a2468))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1169, 1166])).
% 1.10/1.32 tff(1171,plain,
% 1.10/1.32 (~c0_1(a2468)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1170, 1143])).
% 1.10/1.32 tff(1172,plain,
% 1.10/1.32 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2468) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2468) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1173,plain,
% 1.10/1.32 ((hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468))) <=> (hskp19 | c0_1(a2468) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1174,plain,
% 1.10/1.32 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2468) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2468)) | (~c2_1(a2468))))),
% 1.10/1.32 inference(monotonicity,[status(thm)],[1173])).
% 1.10/1.32 tff(1175,plain,
% 1.10/1.32 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2468) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.10/1.32 inference(transitivity,[status(thm)],[1174, 1172])).
% 1.10/1.32 tff(1176,plain,
% 1.10/1.32 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.10/1.32 inference(quant_inst,[status(thm)],[])).
% 1.10/1.32 tff(1177,plain,
% 1.10/1.32 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2468) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2468)) | (~c2_1(a2468))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1176, 1175])).
% 1.10/1.32 tff(1178,plain,
% 1.10/1.32 ($false),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1177, 192, 43, 1157, 1098, 1171, 1078, 1077, 85, 1165])).
% 1.10/1.32 tff(1179,plain,((~hskp24) | hskp19 | (~c0_1(a2414)) | c1_1(a2414) | c3_1(a2414) | hskp6 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.10/1.32 tff(1180,plain,
% 1.10/1.32 (~hskp24),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1179, 1028, 43, 1066, 1029, 1142, 22])).
% 1.10/1.32 tff(1181,plain,
% 1.10/1.32 (^[U: $i] : refl((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.10/1.32 inference(bind,[status(th)],[])).
% 1.10/1.32 tff(1182,plain,
% 1.10/1.32 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.10/1.32 inference(quant_intro,[status(thm)],[1181])).
% 1.10/1.32 tff(1183,plain,
% 1.10/1.32 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1184,plain,
% 1.10/1.32 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp3))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp24) <=> ((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp24) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.10/1.32 inference(bind,[status(th)],[])).
% 1.10/1.32 tff(1185,plain,
% 1.10/1.32 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp24) <=> ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.10/1.32 inference(quant_intro,[status(thm)],[1184])).
% 1.10/1.32 tff(1186,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp3) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause167')).
% 1.10/1.32 tff(1187,plain,
% 1.10/1.32 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1186, 1185])).
% 1.10/1.32 tff(1188,plain,
% 1.10/1.32 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1187, 1183])).
% 1.10/1.32 tff(1189,plain,(
% 1.10/1.32 ![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.10/1.32 inference(skolemize,[status(sab)],[1188])).
% 1.10/1.32 tff(1190,plain,
% 1.10/1.32 (![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1189, 1182])).
% 1.10/1.32 tff(1191,plain,
% 1.10/1.32 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1192,plain,
% 1.10/1.32 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1193,plain,
% 1.10/1.32 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450))))),
% 1.10/1.32 inference(monotonicity,[status(thm)],[1192])).
% 1.10/1.32 tff(1194,plain,
% 1.10/1.32 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.10/1.32 inference(transitivity,[status(thm)],[1193, 1191])).
% 1.10/1.32 tff(1195,plain,
% 1.10/1.32 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)))),
% 1.10/1.32 inference(quant_inst,[status(thm)],[])).
% 1.10/1.32 tff(1196,plain,
% 1.10/1.32 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 1.10/1.32 tff(1197,plain,
% 1.10/1.32 (hskp24 | hskp3 | (~c2_1(a2450))),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1196, 192, 1134, 1133, 1190])).
% 1.10/1.32 tff(1198,plain,
% 1.10/1.32 (hskp3),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1197, 1180, 1141])).
% 1.10/1.32 tff(1199,plain,
% 1.10/1.32 (((~hskp3) | (~c3_1(a2405))) <=> ((~hskp3) | (~c3_1(a2405)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1200,plain,
% 1.10/1.32 (((~c3_1(a2405)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a2405)))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1201,axiom,((~c3_1(a2405)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 1.10/1.32 tff(1202,plain,
% 1.10/1.32 ((~hskp3) | (~c3_1(a2405))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 1.10/1.32 tff(1203,plain,
% 1.10/1.32 ((~hskp3) | (~c3_1(a2405))),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1202, 1199])).
% 1.10/1.32 tff(1204,plain,
% 1.10/1.32 (~c3_1(a2405)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1203, 1198])).
% 1.10/1.32 tff(1205,plain,
% 1.10/1.32 (((~hskp3) | c0_1(a2405)) <=> ((~hskp3) | c0_1(a2405))),
% 1.10/1.32 inference(rewrite,[status(thm)],[])).
% 1.10/1.32 tff(1206,axiom,((~hskp3) | c0_1(a2405)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 1.10/1.32 tff(1207,plain,
% 1.10/1.32 ((~hskp3) | c0_1(a2405)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1206, 1205])).
% 1.10/1.32 tff(1208,plain,
% 1.10/1.32 ((~hskp3) | c0_1(a2405)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1207, 1205])).
% 1.10/1.32 tff(1209,plain,
% 1.10/1.32 ((~hskp3) | c0_1(a2405)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1208, 1205])).
% 1.10/1.32 tff(1210,plain,
% 1.10/1.32 ((~hskp3) | c0_1(a2405)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1209, 1205])).
% 1.10/1.32 tff(1211,plain,
% 1.10/1.32 ((~hskp3) | c0_1(a2405)),
% 1.10/1.32 inference(modus_ponens,[status(thm)],[1210, 1205])).
% 1.10/1.32 tff(1212,plain,
% 1.10/1.32 (c0_1(a2405)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[1211, 1198])).
% 1.10/1.32 tff(1213,plain,
% 1.10/1.32 (c3_1(a2450)),
% 1.10/1.32 inference(unit_resolution,[status(thm)],[582, 1132])).
% 1.10/1.32 tff(1214,plain,
% 1.10/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2405) | (~ndr1_0) | (~c1_1(a2405)) | (~c0_1(a2405)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2405) | (~ndr1_0) | (~c1_1(a2405)) | (~c0_1(a2405)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1215,plain,
% 1.17/1.33 (((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2405) | (~c1_1(a2405)) | (~c0_1(a2405)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c1_1(a2414) | c3_1(a2414) | c3_1(a2405) | (~ndr1_0) | (~c1_1(a2405)) | (~c0_1(a2405)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1216,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2405) | (~c1_1(a2405)) | (~c0_1(a2405)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2405) | (~ndr1_0) | (~c1_1(a2405)) | (~c0_1(a2405)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[1215])).
% 1.17/1.33 tff(1217,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2405) | (~c1_1(a2405)) | (~c0_1(a2405)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2405) | (~ndr1_0) | (~c1_1(a2405)) | (~c0_1(a2405)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[1216, 1214])).
% 1.17/1.33 tff(1218,plain,
% 1.17/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2405) | (~c1_1(a2405)) | (~c0_1(a2405)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(1219,plain,
% 1.17/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2405) | (~ndr1_0) | (~c1_1(a2405)) | (~c0_1(a2405)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 1.17/1.33 tff(1220,plain,
% 1.17/1.33 (~c1_1(a2405)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1219, 192, 1133, 1213, 1028, 1212, 1066, 1029, 1204, 1076, 1141])).
% 1.17/1.33 tff(1221,assumption,(~c2_1(a2417)), introduced(assumption)).
% 1.17/1.33 tff(1222,plain,
% 1.17/1.33 (((~hskp3) | c2_1(a2405)) <=> ((~hskp3) | c2_1(a2405))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1223,axiom,((~hskp3) | c2_1(a2405)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 1.17/1.33 tff(1224,plain,
% 1.17/1.33 ((~hskp3) | c2_1(a2405)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 1.17/1.33 tff(1225,plain,
% 1.17/1.33 ((~hskp3) | c2_1(a2405)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1224, 1222])).
% 1.17/1.33 tff(1226,plain,
% 1.17/1.33 ((~hskp3) | c2_1(a2405)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1225, 1222])).
% 1.17/1.33 tff(1227,plain,
% 1.17/1.33 ((~hskp3) | c2_1(a2405)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1226, 1222])).
% 1.17/1.33 tff(1228,plain,
% 1.17/1.33 ((~hskp3) | c2_1(a2405)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1227, 1222])).
% 1.17/1.33 tff(1229,plain,
% 1.17/1.33 (c2_1(a2405)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1228, 1198])).
% 1.17/1.33 tff(1230,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c1_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)) | c2_1(a2417) | (~c2_1(a2500)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c1_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)) | c2_1(a2417) | (~c2_1(a2500)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1231,plain,
% 1.17/1.33 (((~ndr1_0) | c1_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c1_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)) | c2_1(a2417) | (~c2_1(a2500)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1232,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c1_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)) | c2_1(a2417) | (~c2_1(a2500))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[1231])).
% 1.17/1.33 tff(1233,plain,
% 1.17/1.33 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c1_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)) | c2_1(a2417) | (~c2_1(a2500)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[1232, 1230])).
% 1.17/1.33 tff(1234,plain,
% 1.17/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(1235,plain,
% 1.17/1.33 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c1_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)) | c2_1(a2417) | (~c2_1(a2500))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1234, 1233])).
% 1.17/1.33 tff(1236,plain,
% 1.17/1.33 ($false),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1235, 192, 1212, 1229, 954, 953, 1019, 1008, 21, 1018, 1221, 1220])).
% 1.17/1.33 tff(1237,plain,((~hskp10) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | (~c2_1(a2500)) | c2_1(a2417) | hskp19 | hskp1 | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.17/1.33 tff(1238,plain,
% 1.17/1.33 (~hskp10),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1237, 1017, 953, 1019, 1008, 1018, 954, 43, 22, 889])).
% 1.17/1.33 tff(1239,plain,
% 1.17/1.33 (hskp16 | hskp10 | c2_1(a2417)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[245, 192, 1010, 1008, 137])).
% 1.17/1.33 tff(1240,plain,
% 1.17/1.33 (hskp16),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1239, 1238, 1017])).
% 1.17/1.33 tff(1241,plain,
% 1.17/1.33 (~c2_1(a2425)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[417, 1240])).
% 1.17/1.33 tff(1242,plain,
% 1.17/1.33 (c0_1(a2425)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[425, 1240])).
% 1.17/1.33 tff(1243,plain,
% 1.17/1.33 (~c1_1(a2425)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[459, 192, 889, 43, 1242, 1241, 106])).
% 1.17/1.33 tff(1244,plain,
% 1.17/1.33 (~c3_1(a2425)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[411, 1240])).
% 1.17/1.33 tff(1245,plain,
% 1.17/1.33 ($false),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[432, 192, 1238, 1242, 1241, 1244, 95, 1243])).
% 1.17/1.33 tff(1246,plain,(hskp19 | hskp25 | (~c3_1(a2417)) | c1_1(a2417) | c1_1(a2500) | c0_1(a2417) | (~c2_1(a2500)) | c0_1(a2500) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.17/1.33 tff(1247,plain,
% 1.17/1.33 (hskp19),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1246, 993, 889, 992, 953, 991, 972, 954, 22])).
% 1.17/1.33 tff(1248,plain,
% 1.17/1.33 (~c0_1(a2432)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[297, 1247])).
% 1.17/1.33 tff(1249,plain,
% 1.17/1.33 (c1_1(a2432)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[305, 1247])).
% 1.17/1.33 tff(1250,plain,
% 1.17/1.33 (c3_1(a2432)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[822, 1247])).
% 1.17/1.33 tff(1251,assumption,(~c0_1(a2432)), introduced(assumption)).
% 1.17/1.33 tff(1252,assumption,(c1_1(a2432)), introduced(assumption)).
% 1.17/1.33 tff(1253,plain,
% 1.17/1.33 (hskp16 | c2_1(a2432)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[353, 192, 65, 1252, 1251, 75])).
% 1.17/1.33 tff(1254,plain,
% 1.17/1.33 (c2_1(a2432)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1253, 64])).
% 1.17/1.33 tff(1255,assumption,(c3_1(a2432)), introduced(assumption)).
% 1.17/1.33 tff(1256,plain,
% 1.17/1.33 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1257,plain,
% 1.17/1.33 ((hskp15 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432))) <=> (hskp15 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1258,plain,
% 1.17/1.33 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[1257])).
% 1.17/1.33 tff(1259,plain,
% 1.17/1.33 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[1258, 1256])).
% 1.17/1.33 tff(1260,plain,
% 1.17/1.33 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(1261,plain,
% 1.17/1.33 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 1.17/1.33 tff(1262,plain,
% 1.17/1.33 (hskp15 | (~c2_1(a2432))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1261, 192, 1255, 1251, 475])).
% 1.17/1.33 tff(1263,plain,
% 1.17/1.33 (hskp15),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1262, 1254])).
% 1.17/1.33 tff(1264,plain,
% 1.17/1.33 (~c2_1(a2422)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[528, 1263])).
% 1.17/1.33 tff(1265,plain,
% 1.17/1.33 (c1_1(a2422)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[522, 1263])).
% 1.17/1.33 tff(1266,plain,
% 1.17/1.33 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1267,plain,
% 1.17/1.33 ((hskp16 | hskp13 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422))) <=> (hskp16 | hskp13 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1268,plain,
% 1.17/1.33 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422)))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[1267])).
% 1.17/1.33 tff(1269,plain,
% 1.17/1.33 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))),
% 1.17/1.33 inference(transitivity,[status(thm)],[1268, 1266])).
% 1.17/1.33 tff(1270,plain,
% 1.17/1.33 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(1271,plain,
% 1.17/1.33 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1270, 1269])).
% 1.17/1.33 tff(1272,plain,
% 1.17/1.33 (c0_1(a2422)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1271, 192, 64, 65, 1265, 1264, 75])).
% 1.17/1.33 tff(1273,plain,
% 1.17/1.33 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.17/1.33 inference(bind,[status(th)],[])).
% 1.17/1.33 tff(1274,plain,
% 1.17/1.33 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.33 inference(quant_intro,[status(thm)],[1273])).
% 1.17/1.33 tff(1275,plain,
% 1.17/1.33 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1276,plain,
% 1.17/1.33 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp2))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.17/1.33 inference(bind,[status(th)],[])).
% 1.17/1.33 tff(1277,plain,
% 1.17/1.33 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.33 inference(quant_intro,[status(thm)],[1276])).
% 1.17/1.33 tff(1278,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause186')).
% 1.17/1.33 tff(1279,plain,
% 1.17/1.33 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 1.17/1.33 tff(1280,plain,
% 1.17/1.33 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1279, 1275])).
% 1.17/1.33 tff(1281,plain,(
% 1.17/1.33 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.33 inference(skolemize,[status(sab)],[1280])).
% 1.17/1.33 tff(1282,plain,
% 1.17/1.33 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1281, 1274])).
% 1.17/1.33 tff(1283,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c2_1(a2500)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1284,plain,
% 1.17/1.33 ((hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500))) <=> (hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c2_1(a2500)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1285,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c2_1(a2500))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[1284])).
% 1.17/1.33 tff(1286,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c2_1(a2500)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[1285, 1283])).
% 1.17/1.33 tff(1287,plain,
% 1.17/1.33 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(1288,plain,
% 1.17/1.33 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c2_1(a2500))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1287, 1286])).
% 1.17/1.33 tff(1289,plain,
% 1.17/1.33 (hskp2 | (~c0_1(a2422))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1288, 192, 1265, 953, 952, 1264, 1282, 1018])).
% 1.17/1.33 tff(1290,plain,
% 1.17/1.33 (hskp2),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1289, 1272])).
% 1.17/1.33 tff(1291,plain,
% 1.17/1.33 (((~hskp2) | (~c3_1(a2404))) <=> ((~hskp2) | (~c3_1(a2404)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1292,plain,
% 1.17/1.33 (((~c3_1(a2404)) | (~hskp2)) <=> ((~hskp2) | (~c3_1(a2404)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1293,axiom,((~c3_1(a2404)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 1.17/1.33 tff(1294,plain,
% 1.17/1.33 ((~hskp2) | (~c3_1(a2404))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 1.17/1.33 tff(1295,plain,
% 1.17/1.33 ((~hskp2) | (~c3_1(a2404))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1294, 1291])).
% 1.17/1.33 tff(1296,plain,
% 1.17/1.33 (~c3_1(a2404)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1295, 1290])).
% 1.17/1.33 tff(1297,plain,
% 1.17/1.33 (((~hskp2) | (~c2_1(a2404))) <=> ((~hskp2) | (~c2_1(a2404)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1298,plain,
% 1.17/1.33 (((~c2_1(a2404)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a2404)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1299,axiom,((~c2_1(a2404)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause130')).
% 1.17/1.33 tff(1300,plain,
% 1.17/1.33 ((~hskp2) | (~c2_1(a2404))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1299, 1298])).
% 1.17/1.33 tff(1301,plain,
% 1.17/1.33 ((~hskp2) | (~c2_1(a2404))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1300, 1297])).
% 1.17/1.33 tff(1302,plain,
% 1.17/1.33 (~c2_1(a2404)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1301, 1290])).
% 1.17/1.33 tff(1303,plain,
% 1.17/1.33 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1304,plain,
% 1.17/1.33 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2404) | c0_1(a2404) | c2_1(a2404)) <=> (hskp13 | hskp1 | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1305,plain,
% 1.17/1.33 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2404) | c0_1(a2404) | c2_1(a2404))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404)))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[1304])).
% 1.17/1.33 tff(1306,plain,
% 1.17/1.33 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2404) | c0_1(a2404) | c2_1(a2404))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404))),
% 1.17/1.33 inference(transitivity,[status(thm)],[1305, 1303])).
% 1.17/1.33 tff(1307,plain,
% 1.17/1.33 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2404) | c0_1(a2404) | c2_1(a2404))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(1308,plain,
% 1.17/1.33 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404)),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1307, 1306])).
% 1.17/1.33 tff(1309,plain,
% 1.17/1.33 (c0_1(a2404)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1308, 192, 65, 22, 1302, 1296, 964])).
% 1.17/1.33 tff(1310,plain,
% 1.17/1.33 (c3_1(a2422)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[514, 1263])).
% 1.17/1.33 tff(1311,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | c0_1(a2432) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp20 | c0_1(a2432) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1312,plain,
% 1.17/1.33 ((hskp20 | (~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432))) <=> (hskp20 | c0_1(a2432) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1313,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | c0_1(a2432) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2432)) | (~c1_1(a2432))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[1312])).
% 1.17/1.33 tff(1314,plain,
% 1.17/1.33 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp20 | c0_1(a2432) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[1313, 1311])).
% 1.17/1.33 tff(1315,plain,
% 1.17/1.33 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c3_1(a2432)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(1316,plain,
% 1.17/1.33 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp20 | c0_1(a2432) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2432)) | (~c1_1(a2432))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1315, 1314])).
% 1.17/1.33 tff(1317,plain,
% 1.17/1.33 (hskp20),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1316, 192, 1252, 1255, 1265, 1310, 1251, 1264, 851])).
% 1.17/1.33 tff(1318,plain,
% 1.17/1.33 (~c2_1(a2435)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[802, 1317])).
% 1.17/1.33 tff(1319,plain,
% 1.17/1.33 (~c0_1(a2435)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[754, 1317])).
% 1.17/1.33 tff(1320,plain,
% 1.17/1.33 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1321,plain,
% 1.17/1.33 ((hskp16 | hskp13 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435))) <=> (hskp16 | hskp13 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1322,plain,
% 1.17/1.33 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[1321])).
% 1.17/1.33 tff(1323,plain,
% 1.17/1.33 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[1322, 1320])).
% 1.17/1.33 tff(1324,plain,
% 1.17/1.33 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(1325,plain,
% 1.17/1.33 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 1.17/1.33 tff(1326,plain,
% 1.17/1.33 (~c1_1(a2435)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[1325, 192, 64, 65, 1319, 1318, 75])).
% 1.17/1.33 tff(1327,plain,
% 1.17/1.33 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 1.17/1.33 inference(bind,[status(th)],[])).
% 1.17/1.33 tff(1328,plain,
% 1.17/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.17/1.33 inference(quant_intro,[status(thm)],[1327])).
% 1.17/1.33 tff(1329,plain,
% 1.17/1.33 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(1330,plain,
% 1.17/1.33 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 1.17/1.34 inference(bind,[status(th)],[])).
% 1.17/1.34 tff(1331,plain,
% 1.17/1.34 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.17/1.34 inference(quant_intro,[status(thm)],[1330])).
% 1.17/1.34 tff(1332,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause197')).
% 1.17/1.34 tff(1333,plain,
% 1.17/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 1.17/1.34 tff(1334,plain,
% 1.17/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1333, 1329])).
% 1.17/1.34 tff(1335,plain,(
% 1.17/1.34 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.17/1.34 inference(skolemize,[status(sab)],[1334])).
% 1.17/1.34 tff(1336,plain,
% 1.17/1.34 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1335, 1328])).
% 1.17/1.34 tff(1337,plain,
% 1.17/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1338,plain,
% 1.17/1.34 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1339,plain,
% 1.17/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[1338])).
% 1.17/1.34 tff(1340,plain,
% 1.17/1.34 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.17/1.34 inference(transitivity,[status(thm)],[1339, 1337])).
% 1.17/1.34 tff(1341,plain,
% 1.17/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(1342,plain,
% 1.17/1.34 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1341, 1340])).
% 1.17/1.34 tff(1343,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1342, 192, 1265, 1310, 1319, 1318, 1264, 1302, 1296, 1336, 1326, 1309])).
% 1.17/1.34 tff(1344,plain,(hskp16 | hskp13 | hskp1 | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)) | (~c1_1(a2432)) | (~c3_1(a2432)) | c0_1(a2432)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(1345,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1344, 1250, 1249, 22, 953, 952, 972, 65, 64, 1248])).
% 1.17/1.34 tff(1346,plain,(hskp16 | hskp1 | c1_1(a2500) | c3_1(a2500) | hskp13 | hskp25 | c0_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(1347,plain,
% 1.17/1.34 (hskp16),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1346, 65, 953, 952, 22, 889, 954])).
% 1.17/1.34 tff(1348,plain,
% 1.17/1.34 (~c3_1(a2425)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[411, 1347])).
% 1.17/1.34 tff(1349,plain,
% 1.17/1.34 (~c2_1(a2425)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[417, 1347])).
% 1.17/1.34 tff(1350,plain,
% 1.17/1.34 (c0_1(a2425)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[425, 1347])).
% 1.17/1.34 tff(1351,assumption,(c0_1(a2425)), introduced(assumption)).
% 1.17/1.34 tff(1352,plain,
% 1.17/1.34 (hskp19 | (~c1_1(a2425))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[459, 192, 889, 1351, 707, 106])).
% 1.17/1.34 tff(1353,plain,
% 1.17/1.34 (~c1_1(a2425)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1352, 43])).
% 1.17/1.34 tff(1354,plain,
% 1.17/1.34 (hskp10 | c1_1(a2425)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[432, 192, 1351, 707, 706, 95])).
% 1.17/1.34 tff(1355,plain,
% 1.17/1.34 (hskp10),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1354, 1353])).
% 1.17/1.34 tff(1356,plain,
% 1.17/1.34 (c0_1(a2414)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1027, 1355])).
% 1.17/1.34 tff(1357,plain,
% 1.17/1.34 (~c3_1(a2414)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[881, 1355])).
% 1.17/1.34 tff(1358,plain,
% 1.17/1.34 (~c1_1(a2414)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[887, 1355])).
% 1.17/1.34 tff(1359,plain,
% 1.17/1.34 (hskp30),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1131, 1358, 43, 1065, 22, 1057, 1357, 889, 1356])).
% 1.17/1.34 tff(1360,plain,
% 1.17/1.34 (c1_1(a2450)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[590, 1359])).
% 1.17/1.34 tff(1361,plain,
% 1.17/1.34 (c0_1(a2450)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[598, 1359])).
% 1.17/1.34 tff(1362,plain,
% 1.17/1.34 (c2_1(a2450)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1140, 192, 889, 43, 1361, 1360, 106])).
% 1.17/1.34 tff(1363,plain,
% 1.17/1.34 (~hskp24),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1179, 1356, 43, 1358, 1357, 1142, 22])).
% 1.17/1.34 tff(1364,plain,
% 1.17/1.34 (hskp3 | (~c2_1(a2450))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1196, 192, 1363, 1361, 1360, 1190])).
% 1.17/1.34 tff(1365,plain,
% 1.17/1.34 (hskp3),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1364, 1362])).
% 1.17/1.34 tff(1366,plain,
% 1.17/1.34 (~c3_1(a2405)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1203, 1365])).
% 1.17/1.34 tff(1367,plain,
% 1.17/1.34 (c2_1(a2405)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1228, 1365])).
% 1.17/1.34 tff(1368,plain,
% 1.17/1.34 (c0_1(a2405)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1211, 1365])).
% 1.17/1.34 tff(1369,plain,
% 1.17/1.34 (hskp30),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1131, 1358, 1116, 1115, 22, 43, 1357, 889, 1356])).
% 1.17/1.34 tff(1370,plain,
% 1.17/1.34 (c1_1(a2450)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[590, 1369])).
% 1.17/1.34 tff(1371,plain,
% 1.17/1.34 (c0_1(a2450)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[598, 1369])).
% 1.17/1.34 tff(1372,plain,
% 1.17/1.34 (c2_1(a2450)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1140, 192, 889, 43, 1371, 1370, 106])).
% 1.17/1.34 tff(1373,assumption,(~c3_1(a2405)), introduced(assumption)).
% 1.17/1.34 tff(1374,assumption,(c2_1(a2405)), introduced(assumption)).
% 1.17/1.34 tff(1375,assumption,(c0_1(a2405)), introduced(assumption)).
% 1.17/1.34 tff(1376,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1377,plain,
% 1.17/1.34 ((hskp20 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c3_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405))) <=> (hskp20 | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1378,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c3_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[1377])).
% 1.17/1.34 tff(1379,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c3_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.17/1.34 inference(transitivity,[status(thm)],[1378, 1376])).
% 1.17/1.34 tff(1380,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | (hskp20 | (~ndr1_0) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c3_1(a2405) | (~c0_1(a2405)) | (~c2_1(a2405)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(1381,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c0_1(V)) | (~c2_1(V)))) | hskp20 | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c2_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 1.17/1.34 tff(1382,plain,
% 1.17/1.34 (hskp20),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1381, 192, 1371, 1370, 1375, 1374, 1373, 665, 1372])).
% 1.17/1.34 tff(1383,plain,
% 1.17/1.34 (~c2_1(a2435)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[802, 1382])).
% 1.17/1.34 tff(1384,plain,
% 1.17/1.34 (~c0_1(a2435)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[754, 1382])).
% 1.17/1.34 tff(1385,plain,
% 1.17/1.34 (c3_1(a2435)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[748, 1382])).
% 1.17/1.34 tff(1386,plain,
% 1.17/1.34 (c3_1(a2450)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[582, 1369])).
% 1.17/1.34 tff(1387,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[869, 192, 308, 1371, 1370, 1386, 1385, 1384, 1383, 766])).
% 1.17/1.34 tff(1388,plain,(hskp19 | hskp12 | (~c0_1(a2405)) | (~c2_1(a2405)) | c3_1(a2405) | hskp25 | (~c2_1(a2409)) | (~c3_1(a2409)) | hskp1 | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(1389,plain,
% 1.17/1.34 (hskp12),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1388, 1368, 43, 1367, 1366, 889, 1057, 1065, 22, 1351, 707, 706])).
% 1.17/1.34 tff(1390,plain,
% 1.17/1.34 (~c0_1(a2417)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[223, 1389])).
% 1.17/1.34 tff(1391,plain,
% 1.17/1.34 (c3_1(a2417)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[231, 1389])).
% 1.17/1.34 tff(1392,plain,
% 1.17/1.34 (~c1_1(a2417)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[217, 1389])).
% 1.17/1.34 tff(1393,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1246, 1392, 1391, 889, 43, 953, 1390, 1018, 954, 22])).
% 1.17/1.34 tff(1394,plain,(hskp19 | hskp25 | c1_1(a2500) | (~c2_1(a2500)) | c0_1(a2500) | hskp1 | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(1395,plain,
% 1.17/1.34 (hskp19),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1394, 972, 953, 889, 954, 22, 1350, 1349, 1348])).
% 1.17/1.34 tff(1396,plain,
% 1.17/1.34 (~c0_1(a2432)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[297, 1395])).
% 1.17/1.34 tff(1397,plain,
% 1.17/1.34 (c3_1(a2432)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[822, 1395])).
% 1.17/1.34 tff(1398,plain,
% 1.17/1.34 (c1_1(a2432)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[305, 1395])).
% 1.17/1.34 tff(1399,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)) | (~c2_1(a2500)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1400,plain,
% 1.17/1.34 ((hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500))) <=> (hskp4 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)) | (~c2_1(a2500)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1401,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)) | (~c2_1(a2500))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[1400])).
% 1.17/1.34 tff(1402,plain,
% 1.17/1.34 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)) | (~c2_1(a2500)))),
% 1.17/1.34 inference(transitivity,[status(thm)],[1401, 1399])).
% 1.17/1.34 tff(1403,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(1404,plain,
% 1.17/1.34 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)) | (~c2_1(a2500))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 1.17/1.34 tff(1405,plain,
% 1.17/1.34 (hskp4),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1404, 192, 1398, 1397, 954, 953, 1396, 982, 972])).
% 1.17/1.34 tff(1406,plain,
% 1.17/1.34 (((~hskp4) | (~c1_1(a2407))) <=> ((~hskp4) | (~c1_1(a2407)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1407,plain,
% 1.17/1.34 (((~c1_1(a2407)) | (~hskp4)) <=> ((~hskp4) | (~c1_1(a2407)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1408,axiom,((~c1_1(a2407)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause126')).
% 1.17/1.34 tff(1409,plain,
% 1.17/1.34 ((~hskp4) | (~c1_1(a2407))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 1.17/1.34 tff(1410,plain,
% 1.17/1.34 ((~hskp4) | (~c1_1(a2407))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1409, 1406])).
% 1.17/1.34 tff(1411,plain,
% 1.17/1.34 (~c1_1(a2407)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1410, 1405])).
% 1.17/1.34 tff(1412,plain,
% 1.17/1.34 (((~hskp4) | (~c2_1(a2407))) <=> ((~hskp4) | (~c2_1(a2407)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1413,plain,
% 1.17/1.34 (((~c2_1(a2407)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a2407)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1414,axiom,((~c2_1(a2407)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause127')).
% 1.17/1.34 tff(1415,plain,
% 1.17/1.34 ((~hskp4) | (~c2_1(a2407))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 1.17/1.34 tff(1416,plain,
% 1.17/1.34 ((~hskp4) | (~c2_1(a2407))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1415, 1412])).
% 1.17/1.34 tff(1417,plain,
% 1.17/1.34 (~c2_1(a2407)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1416, 1405])).
% 1.17/1.34 tff(1418,assumption,(~c2_1(a2407)), introduced(assumption)).
% 1.17/1.34 tff(1419,assumption,(~c1_1(a2407)), introduced(assumption)).
% 1.17/1.34 tff(1420,assumption,(~c0_1(a2407)), introduced(assumption)).
% 1.17/1.34 tff(1421,plain,
% 1.17/1.34 (^[U: $i] : refl((hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.17/1.34 inference(bind,[status(th)],[])).
% 1.17/1.34 tff(1422,plain,
% 1.17/1.34 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.17/1.34 inference(quant_intro,[status(thm)],[1421])).
% 1.17/1.34 tff(1423,plain,
% 1.17/1.34 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1424,plain,
% 1.17/1.34 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp12))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.17/1.34 inference(bind,[status(th)],[])).
% 1.17/1.34 tff(1425,plain,
% 1.17/1.34 (![U: $i] : (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.17/1.34 inference(quant_intro,[status(thm)],[1424])).
% 1.17/1.34 tff(1426,axiom,(![U: $i] : (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause136')).
% 1.17/1.34 tff(1427,plain,
% 1.17/1.34 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1426, 1425])).
% 1.17/1.34 tff(1428,plain,
% 1.17/1.34 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1427, 1423])).
% 1.17/1.34 tff(1429,plain,(
% 1.17/1.34 ![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.17/1.34 inference(skolemize,[status(sab)],[1428])).
% 1.17/1.34 tff(1430,plain,
% 1.17/1.34 (![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1429, 1422])).
% 1.17/1.34 tff(1431,plain,
% 1.17/1.34 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c0_1(a2407) | c1_1(a2407) | (~ndr1_0) | (~c3_1(a2407)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2407) | c1_1(a2407) | (~ndr1_0) | (~c3_1(a2407)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1432,plain,
% 1.17/1.34 ((hskp12 | (~ndr1_0) | c1_1(a2407) | c0_1(a2407) | (~c3_1(a2407))) <=> (hskp12 | c0_1(a2407) | c1_1(a2407) | (~ndr1_0) | (~c3_1(a2407)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1433,plain,
% 1.17/1.34 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2407) | c0_1(a2407) | (~c3_1(a2407)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c0_1(a2407) | c1_1(a2407) | (~ndr1_0) | (~c3_1(a2407))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[1432])).
% 1.17/1.34 tff(1434,plain,
% 1.17/1.34 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2407) | c0_1(a2407) | (~c3_1(a2407)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2407) | c1_1(a2407) | (~ndr1_0) | (~c3_1(a2407)))),
% 1.17/1.34 inference(transitivity,[status(thm)],[1433, 1431])).
% 1.17/1.34 tff(1435,plain,
% 1.17/1.34 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2407) | c0_1(a2407) | (~c3_1(a2407)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(1436,plain,
% 1.17/1.34 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2407) | c1_1(a2407) | (~ndr1_0) | (~c3_1(a2407))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1435, 1434])).
% 1.17/1.34 tff(1437,plain,
% 1.17/1.34 (hskp12 | c0_1(a2407) | (~c3_1(a2407))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1436, 192, 1419, 1430])).
% 1.17/1.34 tff(1438,plain,
% 1.17/1.34 (~c3_1(a2407)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1437, 1420, 308])).
% 1.17/1.34 tff(1439,plain,
% 1.17/1.34 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2407) | c2_1(a2407) | (~ndr1_0) | c3_1(a2407))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2407) | c2_1(a2407) | (~ndr1_0) | c3_1(a2407))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1440,plain,
% 1.17/1.34 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2407) | c0_1(a2407) | c2_1(a2407)) <=> (hskp13 | hskp1 | c0_1(a2407) | c2_1(a2407) | (~ndr1_0) | c3_1(a2407))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1441,plain,
% 1.17/1.34 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2407) | c0_1(a2407) | c2_1(a2407))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2407) | c2_1(a2407) | (~ndr1_0) | c3_1(a2407)))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[1440])).
% 1.17/1.34 tff(1442,plain,
% 1.17/1.34 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2407) | c0_1(a2407) | c2_1(a2407))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2407) | c2_1(a2407) | (~ndr1_0) | c3_1(a2407))),
% 1.17/1.34 inference(transitivity,[status(thm)],[1441, 1439])).
% 1.17/1.34 tff(1443,plain,
% 1.17/1.34 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2407) | c0_1(a2407) | c2_1(a2407))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(1444,plain,
% 1.17/1.34 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2407) | c2_1(a2407) | (~ndr1_0) | c3_1(a2407)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1443, 1442])).
% 1.17/1.34 tff(1445,plain,
% 1.17/1.34 (c0_1(a2407) | c3_1(a2407)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1444, 192, 65, 22, 1418, 964])).
% 1.17/1.34 tff(1446,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1445, 1438, 1420])).
% 1.17/1.34 tff(1447,plain,(c0_1(a2407) | hskp13 | hskp1 | c2_1(a2407) | hskp12 | c1_1(a2407)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(1448,plain,
% 1.17/1.34 (c0_1(a2407)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1447, 308, 22, 1418, 65, 1419])).
% 1.17/1.34 tff(1449,plain,
% 1.17/1.34 (hskp16),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[989, 308, 972])).
% 1.17/1.34 tff(1450,plain,
% 1.17/1.34 (~c2_1(a2425)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[417, 1449])).
% 1.17/1.34 tff(1451,assumption,(hskp22), introduced(assumption)).
% 1.17/1.34 tff(1452,plain,
% 1.17/1.34 (((~hskp22) | (~c2_1(a2453))) <=> ((~hskp22) | (~c2_1(a2453)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1453,plain,
% 1.17/1.34 (((~c2_1(a2453)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a2453)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1454,axiom,((~c2_1(a2453)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 1.17/1.34 tff(1455,plain,
% 1.17/1.34 ((~hskp22) | (~c2_1(a2453))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 1.17/1.34 tff(1456,plain,
% 1.17/1.34 ((~hskp22) | (~c2_1(a2453))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1455, 1452])).
% 1.17/1.34 tff(1457,plain,
% 1.17/1.34 (~c2_1(a2453)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1456, 1451])).
% 1.17/1.34 tff(1458,plain,
% 1.17/1.34 (((~hskp22) | (~c0_1(a2453))) <=> ((~hskp22) | (~c0_1(a2453)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1459,plain,
% 1.17/1.34 (((~c0_1(a2453)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a2453)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1460,axiom,((~c0_1(a2453)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 1.17/1.34 tff(1461,plain,
% 1.17/1.34 ((~hskp22) | (~c0_1(a2453))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1460, 1459])).
% 1.17/1.34 tff(1462,plain,
% 1.17/1.34 ((~hskp22) | (~c0_1(a2453))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1461, 1458])).
% 1.17/1.34 tff(1463,plain,
% 1.17/1.34 (~c0_1(a2453)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1462, 1451])).
% 1.17/1.34 tff(1464,plain,
% 1.17/1.34 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2453) | c2_1(a2453) | (~ndr1_0) | c3_1(a2453))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2453) | c2_1(a2453) | (~ndr1_0) | c3_1(a2453))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1465,plain,
% 1.17/1.34 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2453) | c0_1(a2453) | c2_1(a2453)) <=> (hskp13 | hskp1 | c0_1(a2453) | c2_1(a2453) | (~ndr1_0) | c3_1(a2453))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1466,plain,
% 1.17/1.34 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2453) | c0_1(a2453) | c2_1(a2453))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2453) | c2_1(a2453) | (~ndr1_0) | c3_1(a2453)))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[1465])).
% 1.17/1.34 tff(1467,plain,
% 1.17/1.34 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2453) | c0_1(a2453) | c2_1(a2453))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2453) | c2_1(a2453) | (~ndr1_0) | c3_1(a2453))),
% 1.17/1.34 inference(transitivity,[status(thm)],[1466, 1464])).
% 1.17/1.34 tff(1468,plain,
% 1.17/1.34 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2453) | c0_1(a2453) | c2_1(a2453))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(1469,plain,
% 1.17/1.34 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2453) | c2_1(a2453) | (~ndr1_0) | c3_1(a2453)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1468, 1467])).
% 1.17/1.34 tff(1470,plain,
% 1.17/1.34 (c3_1(a2453)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1469, 192, 65, 22, 1463, 1457, 964])).
% 1.17/1.34 tff(1471,plain,
% 1.17/1.34 (((~hskp22) | (~c1_1(a2453))) <=> ((~hskp22) | (~c1_1(a2453)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1472,plain,
% 1.17/1.34 (((~c1_1(a2453)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a2453)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1473,axiom,((~c1_1(a2453)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 1.17/1.34 tff(1474,plain,
% 1.17/1.34 ((~hskp22) | (~c1_1(a2453))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1473, 1472])).
% 1.17/1.34 tff(1475,plain,
% 1.17/1.34 ((~hskp22) | (~c1_1(a2453))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1474, 1471])).
% 1.17/1.34 tff(1476,plain,
% 1.17/1.34 (~c1_1(a2453)),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1475, 1451])).
% 1.17/1.34 tff(1477,plain,
% 1.17/1.34 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c0_1(a2453) | c1_1(a2453) | (~ndr1_0) | (~c3_1(a2453)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2453) | c1_1(a2453) | (~ndr1_0) | (~c3_1(a2453)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1478,plain,
% 1.17/1.34 ((hskp12 | (~ndr1_0) | c1_1(a2453) | c0_1(a2453) | (~c3_1(a2453))) <=> (hskp12 | c0_1(a2453) | c1_1(a2453) | (~ndr1_0) | (~c3_1(a2453)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1479,plain,
% 1.17/1.34 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2453) | c0_1(a2453) | (~c3_1(a2453)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c0_1(a2453) | c1_1(a2453) | (~ndr1_0) | (~c3_1(a2453))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[1478])).
% 1.17/1.34 tff(1480,plain,
% 1.17/1.34 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2453) | c0_1(a2453) | (~c3_1(a2453)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2453) | c1_1(a2453) | (~ndr1_0) | (~c3_1(a2453)))),
% 1.17/1.34 inference(transitivity,[status(thm)],[1479, 1477])).
% 1.17/1.34 tff(1481,plain,
% 1.17/1.34 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2453) | c0_1(a2453) | (~c3_1(a2453)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(1482,plain,
% 1.17/1.34 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2453) | c1_1(a2453) | (~ndr1_0) | (~c3_1(a2453))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[1481, 1480])).
% 1.17/1.34 tff(1483,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1482, 192, 308, 1463, 1476, 1430, 1470])).
% 1.17/1.34 tff(1484,plain,((~hskp22) | hskp12 | hskp13 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(1485,plain,
% 1.17/1.34 (~hskp22),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[1484, 308, 65, 22])).
% 1.17/1.34 tff(1486,plain,
% 1.17/1.34 (^[U: $i] : refl((hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))),
% 1.17/1.34 inference(bind,[status(th)],[])).
% 1.17/1.34 tff(1487,plain,
% 1.17/1.34 (![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.17/1.34 inference(quant_intro,[status(thm)],[1486])).
% 1.17/1.34 tff(1488,plain,
% 1.17/1.34 (![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(1489,plain,
% 1.17/1.34 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp22) <=> ((hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp22))), rewrite(((hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp22) <=> (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp22) <=> (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(1490,plain,
% 1.17/1.35 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp22) <=> ![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[1489])).
% 1.17/1.35 tff(1491,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp5) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 1.17/1.35 tff(1492,plain,
% 1.17/1.35 (![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 1.17/1.35 tff(1493,plain,
% 1.17/1.35 (![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1492, 1488])).
% 1.17/1.35 tff(1494,plain,(
% 1.17/1.35 ![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.17/1.35 inference(skolemize,[status(sab)],[1493])).
% 1.17/1.35 tff(1495,plain,
% 1.17/1.35 (![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1494, 1487])).
% 1.17/1.35 tff(1496,plain,
% 1.17/1.35 (((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))) <=> ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp5 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1497,plain,
% 1.17/1.35 ((hskp22 | hskp5 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407))) <=> (hskp22 | hskp5 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1498,plain,
% 1.17/1.35 (((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407)))) <=> ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[1497])).
% 1.17/1.35 tff(1499,plain,
% 1.17/1.35 (((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407)))) <=> ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp5 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[1498, 1496])).
% 1.17/1.35 tff(1500,plain,
% 1.17/1.35 ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(1501,plain,
% 1.17/1.35 ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp5 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 1.17/1.35 tff(1502,plain,
% 1.17/1.35 (hskp22 | hskp5 | c2_1(a2407) | (~c0_1(a2407))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1501, 192, 1419, 1495])).
% 1.17/1.35 tff(1503,plain,
% 1.17/1.35 (hskp5),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1502, 1485, 1448, 1418])).
% 1.17/1.35 tff(1504,plain,
% 1.17/1.35 (c0_1(a2408)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[381, 1503])).
% 1.17/1.35 tff(1505,plain,
% 1.17/1.35 (c0_1(a2425)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[425, 1449])).
% 1.17/1.35 tff(1506,plain,
% 1.17/1.35 (~c3_1(a2425)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[411, 1449])).
% 1.17/1.35 tff(1507,assumption,(hskp0), introduced(assumption)).
% 1.17/1.35 tff(1508,plain,
% 1.17/1.35 (((~hskp0) | (~c1_1(a2402))) <=> ((~hskp0) | (~c1_1(a2402)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1509,plain,
% 1.17/1.35 (((~c1_1(a2402)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a2402)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1510,axiom,((~c1_1(a2402)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause134')).
% 1.17/1.35 tff(1511,plain,
% 1.17/1.35 ((~hskp0) | (~c1_1(a2402))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 1.17/1.35 tff(1512,plain,
% 1.17/1.35 ((~hskp0) | (~c1_1(a2402))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1511, 1508])).
% 1.17/1.35 tff(1513,plain,
% 1.17/1.35 (~c1_1(a2402)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1512, 1507])).
% 1.17/1.35 tff(1514,plain,
% 1.17/1.35 (((~hskp0) | c3_1(a2402)) <=> ((~hskp0) | c3_1(a2402))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1515,axiom,((~hskp0) | c3_1(a2402)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause86')).
% 1.17/1.35 tff(1516,plain,
% 1.17/1.35 ((~hskp0) | c3_1(a2402)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1515, 1514])).
% 1.17/1.35 tff(1517,plain,
% 1.17/1.35 ((~hskp0) | c3_1(a2402)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1516, 1514])).
% 1.17/1.35 tff(1518,plain,
% 1.17/1.35 ((~hskp0) | c3_1(a2402)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1517, 1514])).
% 1.17/1.35 tff(1519,plain,
% 1.17/1.35 ((~hskp0) | c3_1(a2402)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1518, 1514])).
% 1.17/1.35 tff(1520,plain,
% 1.17/1.35 ((~hskp0) | c3_1(a2402)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1519, 1514])).
% 1.17/1.35 tff(1521,plain,
% 1.17/1.35 (c3_1(a2402)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1520, 1507])).
% 1.17/1.35 tff(1522,plain,
% 1.17/1.35 (((~hskp0) | c0_1(a2402)) <=> ((~hskp0) | c0_1(a2402))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1523,axiom,((~hskp0) | c0_1(a2402)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause85')).
% 1.17/1.35 tff(1524,plain,
% 1.17/1.35 ((~hskp0) | c0_1(a2402)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1523, 1522])).
% 1.17/1.35 tff(1525,plain,
% 1.17/1.35 ((~hskp0) | c0_1(a2402)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1524, 1522])).
% 1.17/1.35 tff(1526,plain,
% 1.17/1.35 ((~hskp0) | c0_1(a2402)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1525, 1522])).
% 1.17/1.35 tff(1527,plain,
% 1.17/1.35 ((~hskp0) | c0_1(a2402)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1526, 1522])).
% 1.17/1.35 tff(1528,plain,
% 1.17/1.35 ((~hskp0) | c0_1(a2402)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1527, 1522])).
% 1.17/1.35 tff(1529,plain,
% 1.17/1.35 (c0_1(a2402)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1528, 1507])).
% 1.17/1.35 tff(1530,plain,
% 1.17/1.35 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | (~c2_1(a2500)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1531,plain,
% 1.17/1.35 ((hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500))) <=> (hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | (~c2_1(a2500)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1532,plain,
% 1.17/1.35 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | (~c2_1(a2500))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[1531])).
% 1.17/1.35 tff(1533,plain,
% 1.17/1.35 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | (~c2_1(a2500)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[1532, 1530])).
% 1.17/1.35 tff(1534,plain,
% 1.17/1.35 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(1535,plain,
% 1.17/1.35 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | (~c2_1(a2500))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 1.17/1.35 tff(1536,plain,
% 1.17/1.35 ($false),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1535, 192, 1040, 1529, 1521, 954, 953, 1513, 1039, 1018])).
% 1.17/1.35 tff(1537,plain,((~hskp0) | hskp29 | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500))), inference(lemma,lemma(discharge,[]))).
% 1.17/1.35 tff(1538,plain,
% 1.17/1.35 (~hskp0),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1537, 1040, 954, 953, 1018])).
% 1.17/1.35 tff(1539,plain,
% 1.17/1.35 (^[U: $i] : refl((hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(1540,plain,
% 1.17/1.35 (![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[1539])).
% 1.17/1.35 tff(1541,plain,
% 1.17/1.35 (![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1542,plain,
% 1.17/1.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp29) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp29))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp29) | hskp0) <=> ((hskp29 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp0))), rewrite(((hskp29 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp0) <=> (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp29) | hskp0) <=> (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(1543,plain,
% 1.17/1.35 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp29) | hskp0) <=> ![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[1542])).
% 1.17/1.35 tff(1544,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp29) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause142')).
% 1.17/1.35 tff(1545,plain,
% 1.17/1.35 (![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1544, 1543])).
% 1.17/1.35 tff(1546,plain,
% 1.17/1.35 (![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1545, 1541])).
% 1.17/1.35 tff(1547,plain,(
% 1.17/1.35 ![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.17/1.35 inference(skolemize,[status(sab)],[1546])).
% 1.17/1.35 tff(1548,plain,
% 1.17/1.35 (![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1547, 1540])).
% 1.17/1.35 tff(1549,plain,
% 1.17/1.35 (hskp19),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1048, 1040, 954, 953, 1018, 889])).
% 1.17/1.35 tff(1550,plain,
% 1.17/1.35 (~c0_1(a2432)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[297, 1549])).
% 1.17/1.35 tff(1551,plain,
% 1.17/1.35 (c1_1(a2432)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[305, 1549])).
% 1.17/1.35 tff(1552,plain,
% 1.17/1.35 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1553,plain,
% 1.17/1.35 ((hskp29 | hskp0 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432))) <=> (hskp29 | hskp0 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1554,plain,
% 1.17/1.35 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[1553])).
% 1.17/1.35 tff(1555,plain,
% 1.17/1.35 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[1554, 1552])).
% 1.17/1.35 tff(1556,plain,
% 1.17/1.35 ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2432) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(1557,plain,
% 1.17/1.35 ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c0_1(a2432) | (~ndr1_0) | c2_1(a2432) | (~c1_1(a2432))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 1.17/1.35 tff(1558,plain,
% 1.17/1.35 (hskp0 | c2_1(a2432)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1557, 192, 1040, 1551, 1550, 1548])).
% 1.17/1.35 tff(1559,plain,
% 1.17/1.35 (c2_1(a2432)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1558, 1538])).
% 1.17/1.35 tff(1560,plain,
% 1.17/1.35 (hskp11 | (~c2_1(a2432))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[314, 192, 308, 1551, 1550, 278])).
% 1.17/1.35 tff(1561,plain,
% 1.17/1.35 (hskp11),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1560, 1559])).
% 1.17/1.35 tff(1562,plain,
% 1.17/1.35 (~c2_1(a2416)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[143, 1561])).
% 1.17/1.35 tff(1563,plain,
% 1.17/1.35 (~c1_1(a2416)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[149, 1561])).
% 1.17/1.35 tff(1564,plain,
% 1.17/1.35 (c3_1(a2432)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[822, 1549])).
% 1.17/1.35 tff(1565,plain,
% 1.17/1.35 (hskp15 | (~c2_1(a2432))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1261, 192, 1564, 1550, 475])).
% 1.17/1.35 tff(1566,plain,
% 1.17/1.35 (hskp15),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1565, 1559])).
% 1.17/1.35 tff(1567,plain,
% 1.17/1.35 (~c2_1(a2422)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[528, 1566])).
% 1.17/1.35 tff(1568,plain,
% 1.17/1.35 (c3_1(a2422)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[514, 1566])).
% 1.17/1.35 tff(1569,plain,
% 1.17/1.35 (c1_1(a2422)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[522, 1566])).
% 1.17/1.35 tff(1570,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1571,plain,
% 1.17/1.35 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2416) | c1_1(a2416) | c0_1(a2416)) <=> (c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1572,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2416) | c1_1(a2416) | c0_1(a2416))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[1571])).
% 1.17/1.35 tff(1573,plain,
% 1.17/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2416) | c1_1(a2416) | c0_1(a2416))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[1572, 1570])).
% 1.17/1.35 tff(1574,plain,
% 1.17/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2416) | c1_1(a2416) | c0_1(a2416))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(1575,plain,
% 1.17/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 1.17/1.35 tff(1576,plain,
% 1.17/1.35 (c0_1(a2416)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1575, 192, 1351, 1569, 1568, 707, 706, 1567, 1563, 1562, 1336])).
% 1.17/1.35 tff(1577,plain,
% 1.17/1.35 (c3_1(a2416)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[157, 1561])).
% 1.17/1.35 tff(1578,plain,
% 1.17/1.35 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2416) | (~ndr1_0) | (~c0_1(a2416)) | (~c3_1(a2416)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2416) | (~ndr1_0) | (~c0_1(a2416)) | (~c3_1(a2416)) | (~c2_1(a2500)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1579,plain,
% 1.17/1.35 ((hskp29 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | (~c0_1(a2416)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500))) <=> (hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2416) | (~ndr1_0) | (~c0_1(a2416)) | (~c3_1(a2416)) | (~c2_1(a2500)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1580,plain,
% 1.17/1.35 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | (~c0_1(a2416)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2416) | (~ndr1_0) | (~c0_1(a2416)) | (~c3_1(a2416)) | (~c2_1(a2500))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[1579])).
% 1.17/1.35 tff(1581,plain,
% 1.17/1.35 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | (~c0_1(a2416)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2416) | (~ndr1_0) | (~c0_1(a2416)) | (~c3_1(a2416)) | (~c2_1(a2500)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[1580, 1578])).
% 1.17/1.35 tff(1582,plain,
% 1.17/1.35 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2416) | (~c3_1(a2416)) | (~c0_1(a2416)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(1583,plain,
% 1.17/1.35 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2500) | c1_1(a2500) | c1_1(a2416) | (~ndr1_0) | (~c0_1(a2416)) | (~c3_1(a2416)) | (~c2_1(a2500))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1582, 1581])).
% 1.17/1.35 tff(1584,plain,
% 1.17/1.35 ($false),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1583, 192, 1040, 1577, 954, 953, 1563, 1039, 1018, 1576])).
% 1.17/1.35 tff(1585,plain,(hskp29 | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500)) | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425) | hskp12 | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.17/1.35 tff(1586,plain,
% 1.17/1.35 (hskp29),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1585, 1505, 953, 972, 954, 1450, 1506, 308, 889])).
% 1.17/1.35 tff(1587,plain,
% 1.17/1.35 (c3_1(a2409)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1064, 1586])).
% 1.17/1.35 tff(1588,plain,
% 1.17/1.35 (c2_1(a2409)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1056, 1586])).
% 1.17/1.35 tff(1589,assumption,(~hskp3), introduced(assumption)).
% 1.17/1.35 tff(1590,plain,
% 1.17/1.35 (^[U: $i] : refl((hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(1591,plain,
% 1.17/1.35 (![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[1590])).
% 1.17/1.35 tff(1592,plain,
% 1.17/1.35 (![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1593,plain,
% 1.17/1.35 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp28) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp28))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp28) <=> (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp28) <=> (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(1594,plain,
% 1.17/1.35 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp28) <=> ![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[1593])).
% 1.17/1.35 tff(1595,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 1.17/1.35 tff(1596,plain,
% 1.17/1.35 (![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 1.17/1.35 tff(1597,plain,
% 1.17/1.35 (![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1596, 1592])).
% 1.17/1.35 tff(1598,plain,(
% 1.17/1.35 ![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.17/1.35 inference(skolemize,[status(sab)],[1597])).
% 1.17/1.35 tff(1599,plain,
% 1.17/1.35 (![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1598, 1591])).
% 1.17/1.35 tff(1600,plain,
% 1.17/1.35 (((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp3 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0))) <=> ((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp28 | hskp3 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1601,plain,
% 1.17/1.35 ((hskp28 | hskp3 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | c0_1(a2500)) <=> (hskp28 | hskp3 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1602,plain,
% 1.17/1.35 (((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp3 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | c0_1(a2500))) <=> ((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp3 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0)))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[1601])).
% 1.17/1.35 tff(1603,plain,
% 1.17/1.35 (((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp3 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | c0_1(a2500))) <=> ((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp28 | hskp3 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0))),
% 1.17/1.35 inference(transitivity,[status(thm)],[1602, 1600])).
% 1.17/1.35 tff(1604,plain,
% 1.17/1.35 ((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp28 | hskp3 | (~ndr1_0) | c3_1(a2500) | c1_1(a2500) | c0_1(a2500))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(1605,plain,
% 1.17/1.35 ((~![U: $i] : (hskp28 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp28 | hskp3 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 1.17/1.35 tff(1606,plain,
% 1.17/1.35 (hskp28 | hskp3),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1605, 192, 954, 953, 952, 1599])).
% 1.17/1.35 tff(1607,plain,
% 1.17/1.35 (hskp28),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1606, 1589])).
% 1.17/1.35 tff(1608,plain,
% 1.17/1.35 (((~hskp28) | c2_1(a2406)) <=> ((~hskp28) | c2_1(a2406))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1609,axiom,((~hskp28) | c2_1(a2406)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause49')).
% 1.17/1.35 tff(1610,plain,
% 1.17/1.35 ((~hskp28) | c2_1(a2406)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 1.17/1.35 tff(1611,plain,
% 1.17/1.35 ((~hskp28) | c2_1(a2406)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1610, 1608])).
% 1.17/1.35 tff(1612,plain,
% 1.17/1.35 ((~hskp28) | c2_1(a2406)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1611, 1608])).
% 1.17/1.35 tff(1613,plain,
% 1.17/1.35 ((~hskp28) | c2_1(a2406)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1612, 1608])).
% 1.17/1.35 tff(1614,plain,
% 1.17/1.35 ((~hskp28) | c2_1(a2406)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1613, 1608])).
% 1.17/1.35 tff(1615,plain,
% 1.17/1.35 (c2_1(a2406)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1614, 1607])).
% 1.17/1.35 tff(1616,plain,
% 1.17/1.35 (((~hskp28) | c1_1(a2406)) <=> ((~hskp28) | c1_1(a2406))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(1617,axiom,((~hskp28) | c1_1(a2406)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 1.17/1.35 tff(1618,plain,
% 1.17/1.35 ((~hskp28) | c1_1(a2406)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 1.17/1.35 tff(1619,plain,
% 1.17/1.35 ((~hskp28) | c1_1(a2406)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1618, 1616])).
% 1.17/1.35 tff(1620,plain,
% 1.17/1.35 ((~hskp28) | c1_1(a2406)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1619, 1616])).
% 1.17/1.35 tff(1621,plain,
% 1.17/1.35 ((~hskp28) | c1_1(a2406)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1620, 1616])).
% 1.17/1.35 tff(1622,plain,
% 1.17/1.35 ((~hskp28) | c1_1(a2406)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[1621, 1616])).
% 1.17/1.35 tff(1623,plain,
% 1.17/1.35 (c1_1(a2406)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[1622, 1607])).
% 1.17/1.35 tff(1624,assumption,(c2_1(a2406)), introduced(assumption)).
% 1.17/1.35 tff(1625,assumption,(c1_1(a2406)), introduced(assumption)).
% 1.17/1.35 tff(1626,plain,
% 1.17/1.35 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | c0_1(a2406))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | c0_1(a2406))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1627,plain,
% 1.17/1.36 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a2406) | (~c2_1(a2406)) | (~c1_1(a2406))) <=> (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | c0_1(a2406))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1628,plain,
% 1.17/1.36 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2406) | (~c2_1(a2406)) | (~c1_1(a2406)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | c0_1(a2406)))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[1627])).
% 1.17/1.36 tff(1629,plain,
% 1.17/1.36 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2406) | (~c2_1(a2406)) | (~c1_1(a2406)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | c0_1(a2406))),
% 1.17/1.36 inference(transitivity,[status(thm)],[1628, 1626])).
% 1.17/1.36 tff(1630,plain,
% 1.17/1.36 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2406) | (~c2_1(a2406)) | (~c1_1(a2406)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(1631,plain,
% 1.17/1.36 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | c0_1(a2406)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1630, 1629])).
% 1.17/1.36 tff(1632,plain,
% 1.17/1.36 (hskp11 | c0_1(a2406)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1631, 192, 308, 1625, 1624, 278])).
% 1.17/1.36 tff(1633,plain,
% 1.17/1.36 (c0_1(a2406)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1632, 307])).
% 1.17/1.36 tff(1634,plain,
% 1.17/1.36 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | (~c0_1(a2406)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | (~c0_1(a2406)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1635,plain,
% 1.17/1.36 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | (~c0_1(a2406)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(1636,plain,
% 1.17/1.36 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2406)) | (~c1_1(a2406)) | (~c0_1(a2406))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1635, 1634])).
% 1.17/1.36 tff(1637,plain,
% 1.17/1.36 (hskp24 | (~c0_1(a2406))),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1636, 192, 1589, 1625, 1624, 1190])).
% 1.17/1.36 tff(1638,plain,
% 1.17/1.36 (hskp24),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1637, 1633])).
% 1.17/1.36 tff(1639,plain,
% 1.17/1.36 (~c0_1(a2468)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1170, 1638])).
% 1.17/1.36 tff(1640,plain,
% 1.17/1.36 (c1_1(a2468)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1156, 1638])).
% 1.17/1.36 tff(1641,plain,
% 1.17/1.36 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1642,plain,
% 1.17/1.36 ((hskp12 | hskp11 | (~ndr1_0) | c0_1(a2468) | (~c2_1(a2468)) | (~c1_1(a2468))) <=> (hskp12 | hskp11 | c0_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1643,plain,
% 1.17/1.36 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2468) | (~c2_1(a2468)) | (~c1_1(a2468)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | c0_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | (~c2_1(a2468))))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[1642])).
% 1.17/1.36 tff(1644,plain,
% 1.17/1.36 (((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2468) | (~c2_1(a2468)) | (~c1_1(a2468)))) <=> ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.17/1.36 inference(transitivity,[status(thm)],[1643, 1641])).
% 1.17/1.36 tff(1645,plain,
% 1.17/1.36 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp12 | hskp11 | (~ndr1_0) | c0_1(a2468) | (~c2_1(a2468)) | (~c1_1(a2468)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(1646,plain,
% 1.17/1.36 ((~![U: $i] : (hskp12 | hskp11 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp12 | hskp11 | c0_1(a2468) | (~ndr1_0) | (~c1_1(a2468)) | (~c2_1(a2468))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 1.17/1.36 tff(1647,plain,
% 1.17/1.36 (~c2_1(a2468)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1646, 192, 308, 307, 1640, 1639, 278])).
% 1.17/1.36 tff(1648,plain,
% 1.17/1.36 (~c3_1(a2468)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1148, 1638])).
% 1.17/1.36 tff(1649,plain,
% 1.17/1.36 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2468) | c3_1(a2468) | (~ndr1_0) | c2_1(a2468))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2468) | c3_1(a2468) | (~ndr1_0) | c2_1(a2468))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1650,plain,
% 1.17/1.36 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2468) | c0_1(a2468) | c2_1(a2468)) <=> (hskp13 | hskp1 | c0_1(a2468) | c3_1(a2468) | (~ndr1_0) | c2_1(a2468))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1651,plain,
% 1.17/1.36 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2468) | c0_1(a2468) | c2_1(a2468))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2468) | c3_1(a2468) | (~ndr1_0) | c2_1(a2468)))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[1650])).
% 1.17/1.36 tff(1652,plain,
% 1.17/1.36 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2468) | c0_1(a2468) | c2_1(a2468))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2468) | c3_1(a2468) | (~ndr1_0) | c2_1(a2468))),
% 1.17/1.36 inference(transitivity,[status(thm)],[1651, 1649])).
% 1.17/1.36 tff(1653,plain,
% 1.17/1.36 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2468) | c0_1(a2468) | c2_1(a2468))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(1654,plain,
% 1.17/1.36 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2468) | c3_1(a2468) | (~ndr1_0) | c2_1(a2468)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1653, 1652])).
% 1.17/1.36 tff(1655,plain,
% 1.17/1.36 ($false),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1654, 192, 65, 22, 1639, 1648, 964, 1647])).
% 1.17/1.36 tff(1656,plain,(hskp11 | hskp13 | hskp1 | hskp12 | hskp3 | (~c1_1(a2406)) | (~c2_1(a2406))), inference(lemma,lemma(discharge,[]))).
% 1.17/1.36 tff(1657,plain,
% 1.17/1.36 (hskp11),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1656, 1589, 22, 308, 65, 1623, 1615])).
% 1.17/1.36 tff(1658,plain,
% 1.17/1.36 (~c1_1(a2416)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[149, 1657])).
% 1.17/1.36 tff(1659,plain,
% 1.17/1.36 (c3_1(a2416)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[157, 1657])).
% 1.17/1.36 tff(1660,plain,
% 1.17/1.36 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c1_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c3_1(a2416)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c1_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c3_1(a2416)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1661,plain,
% 1.17/1.36 ((hskp12 | (~ndr1_0) | c1_1(a2416) | c0_1(a2416) | (~c3_1(a2416))) <=> (hskp12 | c1_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c3_1(a2416)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1662,plain,
% 1.17/1.36 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2416) | c0_1(a2416) | (~c3_1(a2416)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c1_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c3_1(a2416))))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[1661])).
% 1.17/1.36 tff(1663,plain,
% 1.17/1.36 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2416) | c0_1(a2416) | (~c3_1(a2416)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c1_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c3_1(a2416)))),
% 1.17/1.36 inference(transitivity,[status(thm)],[1662, 1660])).
% 1.17/1.36 tff(1664,plain,
% 1.17/1.36 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2416) | c0_1(a2416) | (~c3_1(a2416)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(1665,plain,
% 1.17/1.36 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c1_1(a2416) | (~ndr1_0) | c0_1(a2416) | (~c3_1(a2416))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1664, 1663])).
% 1.17/1.36 tff(1666,plain,
% 1.17/1.36 (c0_1(a2416)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1665, 192, 308, 1659, 1658, 1430])).
% 1.17/1.36 tff(1667,plain,
% 1.17/1.36 (hskp29),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1583, 192, 1659, 954, 953, 1658, 1039, 972, 1666])).
% 1.17/1.36 tff(1668,plain,
% 1.17/1.36 (c2_1(a2409)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1056, 1667])).
% 1.17/1.36 tff(1669,plain,
% 1.17/1.36 (((~hskp29) | c0_1(a2409)) <=> ((~hskp29) | c0_1(a2409))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1670,axiom,((~hskp29) | c0_1(a2409)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 1.17/1.36 tff(1671,plain,
% 1.17/1.36 ((~hskp29) | c0_1(a2409)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 1.17/1.36 tff(1672,plain,
% 1.17/1.36 ((~hskp29) | c0_1(a2409)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1671, 1669])).
% 1.17/1.36 tff(1673,plain,
% 1.17/1.36 ((~hskp29) | c0_1(a2409)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1672, 1669])).
% 1.17/1.36 tff(1674,plain,
% 1.17/1.36 ((~hskp29) | c0_1(a2409)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1673, 1669])).
% 1.17/1.36 tff(1675,plain,
% 1.17/1.36 ((~hskp29) | c0_1(a2409)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1674, 1669])).
% 1.17/1.36 tff(1676,plain,
% 1.17/1.36 (c0_1(a2409)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1675, 1667])).
% 1.17/1.36 tff(1677,assumption,(~c1_1(a2409)), introduced(assumption)).
% 1.17/1.36 tff(1678,plain,
% 1.17/1.36 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.17/1.36 inference(bind,[status(th)],[])).
% 1.17/1.36 tff(1679,plain,
% 1.17/1.36 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.36 inference(quant_intro,[status(thm)],[1678])).
% 1.17/1.36 tff(1680,plain,
% 1.17/1.36 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1681,plain,
% 1.17/1.36 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp3))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.17/1.36 inference(bind,[status(th)],[])).
% 1.17/1.36 tff(1682,plain,
% 1.17/1.36 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.36 inference(quant_intro,[status(thm)],[1681])).
% 1.17/1.36 tff(1683,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause185')).
% 1.17/1.36 tff(1684,plain,
% 1.17/1.36 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 1.17/1.36 tff(1685,plain,
% 1.17/1.36 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1684, 1680])).
% 1.17/1.36 tff(1686,plain,(
% 1.17/1.36 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.36 inference(skolemize,[status(sab)],[1685])).
% 1.17/1.36 tff(1687,plain,
% 1.17/1.36 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1686, 1679])).
% 1.17/1.36 tff(1688,assumption,(c0_1(a2409)), introduced(assumption)).
% 1.17/1.36 tff(1689,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c2_1(a2500)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1690,plain,
% 1.17/1.36 ((hskp3 | (~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500))) <=> (hskp3 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c2_1(a2500)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1691,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c2_1(a2500))))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[1690])).
% 1.17/1.36 tff(1692,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c2_1(a2500)))),
% 1.17/1.36 inference(transitivity,[status(thm)],[1691, 1689])).
% 1.17/1.36 tff(1693,plain,
% 1.17/1.36 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(1694,plain,
% 1.17/1.36 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c2_1(a2500))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 1.17/1.36 tff(1695,plain,
% 1.17/1.36 ($false),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1694, 192, 1589, 1688, 1116, 953, 952, 1687, 1018, 1677])).
% 1.17/1.36 tff(1696,plain,(c1_1(a2409) | hskp3 | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500))), inference(lemma,lemma(discharge,[]))).
% 1.17/1.36 tff(1697,plain,
% 1.17/1.36 (c1_1(a2409)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1696, 1589, 1676, 1668, 953, 952, 972])).
% 1.17/1.36 tff(1698,plain,
% 1.17/1.36 (c3_1(a2409)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1064, 1667])).
% 1.17/1.36 tff(1699,assumption,(c1_1(a2409)), introduced(assumption)).
% 1.17/1.36 tff(1700,assumption,(hskp21), introduced(assumption)).
% 1.17/1.36 tff(1701,plain,
% 1.17/1.36 (((~hskp21) | (~c1_1(a2437))) <=> ((~hskp21) | (~c1_1(a2437)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1702,plain,
% 1.17/1.36 (((~c1_1(a2437)) | (~hskp21)) <=> ((~hskp21) | (~c1_1(a2437)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1703,axiom,((~c1_1(a2437)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 1.17/1.36 tff(1704,plain,
% 1.17/1.36 ((~hskp21) | (~c1_1(a2437))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 1.17/1.36 tff(1705,plain,
% 1.17/1.36 ((~hskp21) | (~c1_1(a2437))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1704, 1701])).
% 1.17/1.36 tff(1706,plain,
% 1.17/1.36 (~c1_1(a2437)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1705, 1700])).
% 1.17/1.36 tff(1707,plain,
% 1.17/1.36 (((~hskp21) | c2_1(a2437)) <=> ((~hskp21) | c2_1(a2437))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1708,axiom,((~hskp21) | c2_1(a2437)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 1.17/1.36 tff(1709,plain,
% 1.17/1.36 ((~hskp21) | c2_1(a2437)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 1.17/1.36 tff(1710,plain,
% 1.17/1.36 ((~hskp21) | c2_1(a2437)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1709, 1707])).
% 1.17/1.36 tff(1711,plain,
% 1.17/1.36 ((~hskp21) | c2_1(a2437)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1710, 1707])).
% 1.17/1.36 tff(1712,plain,
% 1.17/1.36 ((~hskp21) | c2_1(a2437)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1711, 1707])).
% 1.17/1.36 tff(1713,plain,
% 1.17/1.36 ((~hskp21) | c2_1(a2437)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1712, 1707])).
% 1.17/1.36 tff(1714,plain,
% 1.17/1.36 (c2_1(a2437)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1713, 1700])).
% 1.17/1.36 tff(1715,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2437) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c2_1(a2437)) | (~c3_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2437) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c2_1(a2437)) | (~c3_1(a2437)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1716,plain,
% 1.17/1.36 (((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2437) | (~c2_1(a2437)) | (~c3_1(a2437))) <=> (c1_1(a2437) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c2_1(a2437)) | (~c3_1(a2437)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1717,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2437) | (~c2_1(a2437)) | (~c3_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2437) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c2_1(a2437)) | (~c3_1(a2437))))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[1716])).
% 1.17/1.36 tff(1718,plain,
% 1.17/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2437) | (~c2_1(a2437)) | (~c3_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2437) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c2_1(a2437)) | (~c3_1(a2437)))),
% 1.17/1.36 inference(transitivity,[status(thm)],[1717, 1715])).
% 1.17/1.36 tff(1719,plain,
% 1.17/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2437) | (~c2_1(a2437)) | (~c3_1(a2437)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(1720,plain,
% 1.17/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2437) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c2_1(a2437)) | (~c3_1(a2437))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1719, 1718])).
% 1.17/1.36 tff(1721,plain,
% 1.17/1.36 (~c3_1(a2437)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1720, 192, 1688, 1115, 1714, 1351, 1706, 707, 706, 554, 1699])).
% 1.17/1.36 tff(1722,plain,
% 1.17/1.36 (((~hskp21) | c0_1(a2437)) <=> ((~hskp21) | c0_1(a2437))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1723,axiom,((~hskp21) | c0_1(a2437)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 1.17/1.36 tff(1724,plain,
% 1.17/1.36 ((~hskp21) | c0_1(a2437)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1723, 1722])).
% 1.17/1.36 tff(1725,plain,
% 1.17/1.36 ((~hskp21) | c0_1(a2437)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1724, 1722])).
% 1.17/1.36 tff(1726,plain,
% 1.17/1.36 ((~hskp21) | c0_1(a2437)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1725, 1722])).
% 1.17/1.36 tff(1727,plain,
% 1.17/1.36 ((~hskp21) | c0_1(a2437)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1726, 1722])).
% 1.17/1.36 tff(1728,plain,
% 1.17/1.36 ((~hskp21) | c0_1(a2437)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1727, 1722])).
% 1.17/1.36 tff(1729,plain,
% 1.17/1.36 (c0_1(a2437)),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1728, 1700])).
% 1.17/1.36 tff(1730,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c3_1(a2437))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c3_1(a2437))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1731,plain,
% 1.17/1.36 ((hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2437) | c3_1(a2437) | (~c2_1(a2437))) <=> (hskp3 | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c3_1(a2437))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1732,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2437) | c3_1(a2437) | (~c2_1(a2437)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c3_1(a2437)))),
% 1.17/1.36 inference(monotonicity,[status(thm)],[1731])).
% 1.17/1.36 tff(1733,plain,
% 1.17/1.36 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2437) | c3_1(a2437) | (~c2_1(a2437)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c3_1(a2437))),
% 1.17/1.36 inference(transitivity,[status(thm)],[1732, 1730])).
% 1.17/1.36 tff(1734,plain,
% 1.17/1.36 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2437) | c3_1(a2437) | (~c2_1(a2437)))),
% 1.17/1.36 inference(quant_inst,[status(thm)],[])).
% 1.17/1.36 tff(1735,plain,
% 1.17/1.36 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c3_1(a2437)),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 1.17/1.36 tff(1736,plain,
% 1.17/1.36 ($false),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1735, 192, 1589, 1729, 1714, 1706, 1687, 1721])).
% 1.17/1.36 tff(1737,plain,((~hskp21) | hskp3 | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425) | (~c1_1(a2409))), inference(lemma,lemma(discharge,[]))).
% 1.17/1.36 tff(1738,plain,
% 1.17/1.36 (~hskp21),
% 1.17/1.36 inference(unit_resolution,[status(thm)],[1737, 1589, 1676, 1698, 1505, 1450, 1506, 1697])).
% 1.17/1.36 tff(1739,plain,
% 1.17/1.36 (^[U: $i] : refl((hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 1.17/1.36 inference(bind,[status(th)],[])).
% 1.17/1.36 tff(1740,plain,
% 1.17/1.36 (![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.17/1.36 inference(quant_intro,[status(thm)],[1739])).
% 1.17/1.36 tff(1741,plain,
% 1.17/1.36 (![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1742,plain,
% 1.17/1.36 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp21) <=> (hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) <=> (hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp17) <=> ((hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17))), rewrite(((hskp21 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp17) <=> (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp17) <=> (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 1.17/1.36 inference(bind,[status(th)],[])).
% 1.17/1.36 tff(1743,plain,
% 1.17/1.36 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp17) <=> ![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.17/1.36 inference(quant_intro,[status(thm)],[1742])).
% 1.17/1.36 tff(1744,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp21) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 1.17/1.36 tff(1745,plain,
% 1.17/1.36 (![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1744, 1743])).
% 1.17/1.36 tff(1746,plain,
% 1.17/1.36 (![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1745, 1741])).
% 1.17/1.36 tff(1747,plain,(
% 1.17/1.36 ![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.17/1.36 inference(skolemize,[status(sab)],[1746])).
% 1.17/1.36 tff(1748,plain,
% 1.17/1.36 (![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 1.17/1.36 inference(modus_ponens,[status(thm)],[1747, 1740])).
% 1.17/1.36 tff(1749,plain,
% 1.17/1.36 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)))),
% 1.17/1.36 inference(bind,[status(th)],[])).
% 1.17/1.36 tff(1750,plain,
% 1.17/1.36 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.17/1.36 inference(quant_intro,[status(thm)],[1749])).
% 1.17/1.36 tff(1751,plain,
% 1.17/1.36 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.17/1.36 inference(rewrite,[status(thm)],[])).
% 1.17/1.36 tff(1752,plain,
% 1.17/1.36 (^[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)) | c1_1(V) | c0_1(V) | c3_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)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))))),
% 1.21/1.37 inference(bind,[status(th)],[])).
% 1.21/1.37 tff(1753,plain,
% 1.21/1.37 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.21/1.37 inference(quant_intro,[status(thm)],[1752])).
% 1.21/1.37 tff(1754,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)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 1.21/1.37 tff(1755,plain,
% 1.21/1.37 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1754, 1753])).
% 1.21/1.37 tff(1756,plain,
% 1.21/1.37 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1755, 1751])).
% 1.21/1.37 tff(1757,plain,(
% 1.21/1.37 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.21/1.37 inference(skolemize,[status(sab)],[1756])).
% 1.21/1.37 tff(1758,plain,
% 1.21/1.37 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1757, 1750])).
% 1.21/1.37 tff(1759,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1760,plain,
% 1.21/1.37 ((hskp2 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c0_1(a2500) | c3_1(a2500)) <=> (hskp2 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1761,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c0_1(a2500) | c3_1(a2500))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[1760])).
% 1.21/1.37 tff(1762,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c0_1(a2500) | c3_1(a2500))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[1761, 1759])).
% 1.21/1.37 tff(1763,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | (hskp2 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c1_1(a2500) | c0_1(a2500) | c3_1(a2500))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(1764,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | c3_1(V))) | hskp2 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1763, 1762])).
% 1.21/1.37 tff(1765,plain,
% 1.21/1.37 (hskp2 | (~c1_1(a2409))),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1764, 192, 1676, 1668, 954, 953, 952, 1758])).
% 1.21/1.37 tff(1766,plain,
% 1.21/1.37 (hskp2),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1765, 1697])).
% 1.21/1.37 tff(1767,plain,
% 1.21/1.37 (~c3_1(a2404)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1295, 1766])).
% 1.21/1.37 tff(1768,plain,
% 1.21/1.37 (~c2_1(a2404)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1301, 1766])).
% 1.21/1.37 tff(1769,plain,
% 1.21/1.37 (c0_1(a2404)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1308, 192, 65, 22, 1768, 1767, 964])).
% 1.21/1.37 tff(1770,plain,
% 1.21/1.37 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1771,plain,
% 1.21/1.37 ((hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409))) <=> (hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1772,plain,
% 1.21/1.37 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[1771])).
% 1.21/1.37 tff(1773,plain,
% 1.21/1.37 (((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)))) <=> ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[1772, 1770])).
% 1.21/1.37 tff(1774,plain,
% 1.21/1.37 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(1775,plain,
% 1.21/1.37 ((~![U: $i] : (hskp24 | hskp3 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp24 | hskp3 | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1774, 1773])).
% 1.21/1.37 tff(1776,plain,
% 1.21/1.37 (hskp24 | (~c1_1(a2409))),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1775, 192, 1589, 1676, 1668, 1190])).
% 1.21/1.37 tff(1777,plain,
% 1.21/1.37 (hskp24),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1776, 1697])).
% 1.21/1.37 tff(1778,plain,
% 1.21/1.37 (~c3_1(a2468)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1148, 1777])).
% 1.21/1.37 tff(1779,plain,
% 1.21/1.37 (~c0_1(a2468)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1170, 1777])).
% 1.21/1.37 tff(1780,plain,
% 1.21/1.37 (c2_1(a2468)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1654, 192, 65, 22, 1779, 1778, 964])).
% 1.21/1.37 tff(1781,plain,
% 1.21/1.37 (((~hskp2) | (~c1_1(a2404))) <=> ((~hskp2) | (~c1_1(a2404)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1782,plain,
% 1.21/1.37 (((~c1_1(a2404)) | (~hskp2)) <=> ((~hskp2) | (~c1_1(a2404)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1783,axiom,((~c1_1(a2404)) | (~hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 1.21/1.37 tff(1784,plain,
% 1.21/1.37 ((~hskp2) | (~c1_1(a2404))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1783, 1782])).
% 1.21/1.37 tff(1785,plain,
% 1.21/1.37 ((~hskp2) | (~c1_1(a2404))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1784, 1781])).
% 1.21/1.37 tff(1786,plain,
% 1.21/1.37 (~c1_1(a2404)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1785, 1766])).
% 1.21/1.37 tff(1787,plain,
% 1.21/1.37 (c1_1(a2468)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1156, 1777])).
% 1.21/1.37 tff(1788,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2468) | c1_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2468) | c1_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1789,plain,
% 1.21/1.37 ((hskp19 | (~ndr1_0) | c3_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468))) <=> (hskp19 | c0_1(a2468) | c1_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1790,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2468) | c1_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2468)) | (~c2_1(a2468))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[1789])).
% 1.21/1.37 tff(1791,plain,
% 1.21/1.37 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2468) | c1_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[1790, 1788])).
% 1.21/1.37 tff(1792,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c0_1(a2468) | (~c1_1(a2468)) | (~c2_1(a2468)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(1793,plain,
% 1.21/1.37 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2468) | c1_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2468)) | (~c2_1(a2468))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1792, 1791])).
% 1.21/1.37 tff(1794,plain,
% 1.21/1.37 (hskp19 | (~c0_1(a2404)) | (~c2_1(a2468))),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1793, 192, 1787, 1779, 1786, 1767, 85])).
% 1.21/1.37 tff(1795,plain,
% 1.21/1.37 (hskp19),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1794, 1780, 1769])).
% 1.21/1.37 tff(1796,plain,
% 1.21/1.37 (~c0_1(a2432)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[297, 1795])).
% 1.21/1.37 tff(1797,plain,
% 1.21/1.37 (c3_1(a2432)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[822, 1795])).
% 1.21/1.37 tff(1798,plain,
% 1.21/1.37 (c1_1(a2432)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[305, 1795])).
% 1.21/1.37 tff(1799,plain,
% 1.21/1.37 (((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp17 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp17 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1800,plain,
% 1.21/1.37 ((hskp21 | hskp17 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432))) <=> (hskp21 | hskp17 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1801,plain,
% 1.21/1.37 (((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp17 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp17 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[1800])).
% 1.21/1.37 tff(1802,plain,
% 1.21/1.37 (((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp17 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp17 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[1801, 1799])).
% 1.21/1.37 tff(1803,plain,
% 1.21/1.37 ((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp21 | hskp17 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(1804,plain,
% 1.21/1.37 ((~![U: $i] : (hskp21 | hskp17 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp21 | hskp17 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1803, 1802])).
% 1.21/1.37 tff(1805,plain,
% 1.21/1.37 (hskp21 | hskp17),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1804, 192, 1798, 1797, 1796, 1748])).
% 1.21/1.37 tff(1806,plain,
% 1.21/1.37 (hskp17),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1805, 1738])).
% 1.21/1.37 tff(1807,plain,
% 1.21/1.37 (((~hskp17) | (~c1_1(a2427))) <=> ((~hskp17) | (~c1_1(a2427)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1808,plain,
% 1.21/1.37 (((~c1_1(a2427)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a2427)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1809,axiom,((~c1_1(a2427)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 1.21/1.37 tff(1810,plain,
% 1.21/1.37 ((~hskp17) | (~c1_1(a2427))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1809, 1808])).
% 1.21/1.37 tff(1811,plain,
% 1.21/1.37 ((~hskp17) | (~c1_1(a2427))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1810, 1807])).
% 1.21/1.37 tff(1812,plain,
% 1.21/1.37 (~c1_1(a2427)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1811, 1806])).
% 1.21/1.37 tff(1813,plain,
% 1.21/1.37 (((~hskp17) | c3_1(a2427)) <=> ((~hskp17) | c3_1(a2427))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1814,axiom,((~hskp17) | c3_1(a2427)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 1.21/1.37 tff(1815,plain,
% 1.21/1.37 ((~hskp17) | c3_1(a2427)),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1814, 1813])).
% 1.21/1.37 tff(1816,plain,
% 1.21/1.37 ((~hskp17) | c3_1(a2427)),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1815, 1813])).
% 1.21/1.37 tff(1817,plain,
% 1.21/1.37 ((~hskp17) | c3_1(a2427)),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1816, 1813])).
% 1.21/1.37 tff(1818,plain,
% 1.21/1.37 ((~hskp17) | c3_1(a2427)),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1817, 1813])).
% 1.21/1.37 tff(1819,plain,
% 1.21/1.37 ((~hskp17) | c3_1(a2427)),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1818, 1813])).
% 1.21/1.37 tff(1820,plain,
% 1.21/1.37 (c3_1(a2427)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1819, 1806])).
% 1.21/1.37 tff(1821,plain,
% 1.21/1.37 (((~hskp17) | c2_1(a2427)) <=> ((~hskp17) | c2_1(a2427))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1822,axiom,((~hskp17) | c2_1(a2427)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 1.21/1.37 tff(1823,plain,
% 1.21/1.37 ((~hskp17) | c2_1(a2427)),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1822, 1821])).
% 1.21/1.37 tff(1824,plain,
% 1.21/1.37 ((~hskp17) | c2_1(a2427)),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1823, 1821])).
% 1.21/1.37 tff(1825,plain,
% 1.21/1.37 ((~hskp17) | c2_1(a2427)),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1824, 1821])).
% 1.21/1.37 tff(1826,plain,
% 1.21/1.37 ((~hskp17) | c2_1(a2427)),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1825, 1821])).
% 1.21/1.37 tff(1827,plain,
% 1.21/1.37 ((~hskp17) | c2_1(a2427)),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1826, 1821])).
% 1.21/1.37 tff(1828,plain,
% 1.21/1.37 (c2_1(a2427)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1827, 1806])).
% 1.21/1.37 tff(1829,plain,
% 1.21/1.37 (^[U: $i] : refl((hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))),
% 1.21/1.37 inference(bind,[status(th)],[])).
% 1.21/1.37 tff(1830,plain,
% 1.21/1.37 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.21/1.37 inference(quant_intro,[status(thm)],[1829])).
% 1.21/1.37 tff(1831,plain,
% 1.21/1.37 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1832,plain,
% 1.21/1.37 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp30))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) <=> (hskp30 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp21) <=> ((hskp30 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp21))), rewrite(((hskp30 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | hskp21) <=> (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp21) <=> (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))))),
% 1.21/1.37 inference(bind,[status(th)],[])).
% 1.21/1.37 tff(1833,plain,
% 1.21/1.37 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp21) <=> ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.21/1.37 inference(quant_intro,[status(thm)],[1832])).
% 1.21/1.37 tff(1834,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | hskp30) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 1.21/1.37 tff(1835,plain,
% 1.21/1.37 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1834, 1833])).
% 1.21/1.37 tff(1836,plain,
% 1.21/1.37 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1835, 1831])).
% 1.21/1.37 tff(1837,plain,(
% 1.21/1.37 ![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.21/1.37 inference(skolemize,[status(sab)],[1836])).
% 1.21/1.37 tff(1838,plain,
% 1.21/1.37 (![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1837, 1830])).
% 1.21/1.37 tff(1839,plain,
% 1.21/1.37 (((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp21 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))) <=> ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp30 | hskp21 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1840,plain,
% 1.21/1.37 ((hskp30 | hskp21 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407))) <=> (hskp30 | hskp21 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1841,plain,
% 1.21/1.37 (((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp21 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407)))) <=> ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp21 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[1840])).
% 1.21/1.37 tff(1842,plain,
% 1.21/1.37 (((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp21 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407)))) <=> ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp30 | hskp21 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[1841, 1839])).
% 1.21/1.37 tff(1843,plain,
% 1.21/1.37 ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp30 | hskp21 | (~ndr1_0) | c1_1(a2407) | c2_1(a2407) | (~c0_1(a2407)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(1844,plain,
% 1.21/1.37 ((~![U: $i] : (hskp30 | hskp21 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp30 | hskp21 | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 1.21/1.37 tff(1845,plain,
% 1.21/1.37 (hskp30 | hskp21 | c2_1(a2407) | (~c0_1(a2407))),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1844, 192, 1419, 1838])).
% 1.21/1.37 tff(1846,plain,
% 1.21/1.37 (hskp30),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1845, 1738, 1448, 1418])).
% 1.21/1.37 tff(1847,plain,
% 1.21/1.37 (c3_1(a2450)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[582, 1846])).
% 1.21/1.37 tff(1848,plain,
% 1.21/1.37 (c1_1(a2450)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[590, 1846])).
% 1.21/1.37 tff(1849,plain,
% 1.21/1.37 (c0_1(a2450)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[598, 1846])).
% 1.21/1.37 tff(1850,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1851,plain,
% 1.21/1.37 (((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427))) <=> (c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1852,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427))))),
% 1.21/1.37 inference(monotonicity,[status(thm)],[1851])).
% 1.21/1.37 tff(1853,plain,
% 1.21/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.21/1.37 inference(transitivity,[status(thm)],[1852, 1850])).
% 1.21/1.37 tff(1854,plain,
% 1.21/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.21/1.37 inference(quant_inst,[status(thm)],[])).
% 1.21/1.37 tff(1855,plain,
% 1.21/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 1.21/1.37 tff(1856,plain,
% 1.21/1.37 ($false),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1855, 192, 1849, 1848, 1847, 1828, 1820, 1505, 1812, 1450, 1506, 554])).
% 1.21/1.37 tff(1857,plain,(hskp3 | c2_1(a2407) | c1_1(a2407) | hskp13 | hskp1 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | hskp12), inference(lemma,lemma(discharge,[]))).
% 1.21/1.37 tff(1858,plain,
% 1.21/1.37 (hskp3),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1857, 308, 1419, 65, 22, 954, 953, 952, 1418])).
% 1.21/1.37 tff(1859,plain,
% 1.21/1.37 (~c3_1(a2405)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1203, 1858])).
% 1.21/1.37 tff(1860,plain,
% 1.21/1.37 (c2_1(a2405)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1228, 1858])).
% 1.21/1.37 tff(1861,plain,
% 1.21/1.37 (c0_1(a2405)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1211, 1858])).
% 1.21/1.37 tff(1862,plain,
% 1.21/1.37 (hskp19),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1388, 308, 1861, 1860, 1859, 889, 1588, 1587, 22, 1505, 1450, 1506])).
% 1.21/1.37 tff(1863,plain,
% 1.21/1.37 (c1_1(a2432)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[305, 1862])).
% 1.21/1.37 tff(1864,plain,
% 1.21/1.37 (~c0_1(a2432)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[297, 1862])).
% 1.21/1.37 tff(1865,plain,
% 1.21/1.37 (c3_1(a2432)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[822, 1862])).
% 1.21/1.37 tff(1866,plain,
% 1.21/1.37 (c0_1(a2409)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[1675, 1586])).
% 1.21/1.37 tff(1867,plain,
% 1.21/1.37 (~c2_1(a2408)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[373, 1503])).
% 1.21/1.37 tff(1868,plain,
% 1.21/1.37 (c3_1(a2408)),
% 1.21/1.37 inference(unit_resolution,[status(thm)],[396, 1503])).
% 1.21/1.37 tff(1869,assumption,(~c2_1(a2432)), introduced(assumption)).
% 1.21/1.37 tff(1870,plain,
% 1.21/1.37 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))))),
% 1.21/1.37 inference(bind,[status(th)],[])).
% 1.21/1.37 tff(1871,plain,
% 1.21/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.21/1.37 inference(quant_intro,[status(thm)],[1870])).
% 1.21/1.37 tff(1872,plain,
% 1.21/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.21/1.37 inference(rewrite,[status(thm)],[])).
% 1.21/1.37 tff(1873,plain,
% 1.21/1.37 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~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))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~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))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c1_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)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_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))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c1_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))))),
% 1.21/1.37 inference(bind,[status(th)],[])).
% 1.21/1.37 tff(1874,plain,
% 1.21/1.37 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.21/1.37 inference(quant_intro,[status(thm)],[1873])).
% 1.21/1.37 tff(1875,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause201')).
% 1.21/1.37 tff(1876,plain,
% 1.21/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1875, 1874])).
% 1.21/1.37 tff(1877,plain,
% 1.21/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.21/1.37 inference(modus_ponens,[status(thm)],[1876, 1872])).
% 1.21/1.37 tff(1878,plain,(
% 1.21/1.37 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.21/1.37 inference(skolemize,[status(sab)],[1877])).
% 1.21/1.37 tff(1879,plain,
% 1.21/1.37 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1878, 1871])).
% 1.21/1.38 tff(1880,assumption,(c0_1(a2407)), introduced(assumption)).
% 1.21/1.38 tff(1881,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2425) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2425) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1882,plain,
% 1.21/1.38 (((~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432))) <=> (c0_1(a2432) | c2_1(a2425) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1883,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2425) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[1882])).
% 1.21/1.38 tff(1884,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2425) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[1883, 1881])).
% 1.21/1.38 tff(1885,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(1886,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2425) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1885, 1884])).
% 1.21/1.38 tff(1887,plain,
% 1.21/1.38 (~c1_1(a2425)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1886, 192, 1252, 1351, 1880, 1251, 707, 1419, 1418, 1879, 1869])).
% 1.21/1.38 tff(1888,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1889,plain,
% 1.21/1.38 (((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432))) <=> (c0_1(a2432) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1890,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[1889])).
% 1.21/1.38 tff(1891,plain,
% 1.21/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[1890, 1888])).
% 1.21/1.38 tff(1892,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(1893,plain,
% 1.21/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1892, 1891])).
% 1.21/1.38 tff(1894,plain,
% 1.21/1.38 (~c1_1(a2408)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1893, 192, 1252, 1351, 767, 1251, 707, 611, 1879, 1887, 1869])).
% 1.21/1.38 tff(1895,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2432) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2432)) | c2_1(a2432))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2432) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2432)) | c2_1(a2432))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1896,plain,
% 1.21/1.38 ((hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432))) <=> (hskp12 | c0_1(a2432) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2432)) | c2_1(a2432))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1897,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2432) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2432)) | c2_1(a2432)))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[1896])).
% 1.21/1.38 tff(1898,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2432) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2432)) | c2_1(a2432))),
% 1.21/1.38 inference(transitivity,[status(thm)],[1897, 1895])).
% 1.21/1.38 tff(1899,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(1900,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2432) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2432)) | c2_1(a2432)),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1899, 1898])).
% 1.21/1.38 tff(1901,plain,
% 1.21/1.38 (~c1_1(a2409)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1900, 192, 308, 1688, 1115, 1255, 1251, 766, 1869])).
% 1.21/1.38 tff(1902,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1129, 192, 22, 1116, 1115, 612, 611, 1007, 1901, 1894])).
% 1.21/1.38 tff(1903,plain,(c2_1(a2432) | hskp1 | (~c2_1(a2409)) | (~c3_1(a2409)) | (~c3_1(a2408)) | c2_1(a2408) | hskp12 | (~c0_1(a2409)) | (~c3_1(a2432)) | c0_1(a2432) | (~c1_1(a2432)) | (~c0_1(a2425)) | (~c0_1(a2408)) | c2_1(a2425) | (~c0_1(a2407)) | c1_1(a2407) | c2_1(a2407)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(1904,plain,
% 1.21/1.38 (c2_1(a2432)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1903, 1588, 22, 1587, 1868, 1867, 308, 1866, 1865, 1864, 1863, 1505, 1504, 1450, 1448, 1419, 1418])).
% 1.21/1.38 tff(1905,plain,
% 1.21/1.38 (hskp15 | (~c2_1(a2432))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1261, 192, 1865, 1864, 475])).
% 1.21/1.38 tff(1906,plain,
% 1.21/1.38 (hskp15),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1905, 1904])).
% 1.21/1.38 tff(1907,plain,
% 1.21/1.38 (~c2_1(a2422)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[528, 1906])).
% 1.21/1.38 tff(1908,plain,
% 1.21/1.38 (c3_1(a2422)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[514, 1906])).
% 1.21/1.38 tff(1909,plain,
% 1.21/1.38 (c1_1(a2422)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[522, 1906])).
% 1.21/1.38 tff(1910,plain,
% 1.21/1.38 (hskp20),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1316, 192, 1863, 1865, 1909, 1908, 1864, 1907, 851])).
% 1.21/1.38 tff(1911,plain,
% 1.21/1.38 (~c2_1(a2435)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[802, 1910])).
% 1.21/1.38 tff(1912,plain,
% 1.21/1.38 (~c0_1(a2435)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[754, 1910])).
% 1.21/1.38 tff(1913,plain,
% 1.21/1.38 (c3_1(a2435)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[748, 1910])).
% 1.21/1.38 tff(1914,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2435)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1915,plain,
% 1.21/1.38 ((hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435))) <=> (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2435)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1916,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2435))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[1915])).
% 1.21/1.38 tff(1917,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2435)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[1916, 1914])).
% 1.21/1.38 tff(1918,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(1919,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2435))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.21/1.38 tff(1920,plain,
% 1.21/1.38 (~c1_1(a2409)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1919, 192, 308, 1866, 1587, 1913, 1912, 1911, 766])).
% 1.21/1.38 tff(1921,plain,
% 1.21/1.38 (hskp11 | (~c2_1(a2432))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[314, 192, 308, 1863, 1864, 278])).
% 1.21/1.38 tff(1922,plain,
% 1.21/1.38 (hskp11),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1921, 1904])).
% 1.21/1.38 tff(1923,plain,
% 1.21/1.38 (~c2_1(a2416)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[143, 1922])).
% 1.21/1.38 tff(1924,plain,
% 1.21/1.38 (~c1_1(a2416)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[149, 1922])).
% 1.21/1.38 tff(1925,plain,
% 1.21/1.38 (c3_1(a2416)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[157, 1922])).
% 1.21/1.38 tff(1926,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c3_1(a2416)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1927,plain,
% 1.21/1.38 ((hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416))) <=> (hskp1 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c3_1(a2416)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1928,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c3_1(a2416))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[1927])).
% 1.21/1.38 tff(1929,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c3_1(a2416)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[1928, 1926])).
% 1.21/1.38 tff(1930,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(1931,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | (~c3_1(a2416))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1930, 1929])).
% 1.21/1.38 tff(1932,plain,
% 1.21/1.38 ($false),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1931, 192, 22, 1588, 1587, 1925, 1924, 1923, 1007, 1920])).
% 1.21/1.38 tff(1933,plain,(hskp12 | hskp1 | c1_1(a2407) | c2_1(a2407) | hskp25 | hskp13 | c1_1(a2500) | c0_1(a2500) | c3_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.38 tff(1934,plain,
% 1.21/1.38 (hskp12),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1933, 1418, 1419, 22, 889, 65, 953, 954, 952])).
% 1.21/1.38 tff(1935,plain,
% 1.21/1.38 (~c0_1(a2417)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[223, 1934])).
% 1.21/1.38 tff(1936,plain,
% 1.21/1.38 (~c1_1(a2417)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[217, 1934])).
% 1.21/1.38 tff(1937,plain,
% 1.21/1.38 (c3_1(a2417)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[231, 1934])).
% 1.21/1.38 tff(1938,plain,
% 1.21/1.38 (hskp19),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1246, 1937, 889, 1936, 953, 1935, 972, 954, 22])).
% 1.21/1.38 tff(1939,plain,
% 1.21/1.38 (~c0_1(a2432)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[297, 1938])).
% 1.21/1.38 tff(1940,plain,
% 1.21/1.38 (c3_1(a2432)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[822, 1938])).
% 1.21/1.38 tff(1941,plain,
% 1.21/1.38 (c1_1(a2432)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[305, 1938])).
% 1.21/1.38 tff(1942,plain,
% 1.21/1.38 (hskp4),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1404, 192, 1941, 1940, 954, 953, 1939, 982, 972])).
% 1.21/1.38 tff(1943,plain,
% 1.21/1.38 (((~hskp4) | c0_1(a2407)) <=> ((~hskp4) | c0_1(a2407))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1944,axiom,((~hskp4) | c0_1(a2407)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 1.21/1.38 tff(1945,plain,
% 1.21/1.38 ((~hskp4) | c0_1(a2407)),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1944, 1943])).
% 1.21/1.38 tff(1946,plain,
% 1.21/1.38 ((~hskp4) | c0_1(a2407)),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1945, 1943])).
% 1.21/1.38 tff(1947,plain,
% 1.21/1.38 ((~hskp4) | c0_1(a2407)),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1946, 1943])).
% 1.21/1.38 tff(1948,plain,
% 1.21/1.38 ((~hskp4) | c0_1(a2407)),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1947, 1943])).
% 1.21/1.38 tff(1949,plain,
% 1.21/1.38 ((~hskp4) | c0_1(a2407)),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1948, 1943])).
% 1.21/1.38 tff(1950,plain,
% 1.21/1.38 (c0_1(a2407)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1949, 1942])).
% 1.21/1.38 tff(1951,plain,
% 1.21/1.38 (hskp16),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1344, 1941, 22, 953, 952, 972, 65, 1940, 1939])).
% 1.21/1.38 tff(1952,plain,
% 1.21/1.38 (~c3_1(a2425)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[411, 1951])).
% 1.21/1.38 tff(1953,plain,
% 1.21/1.38 (~c2_1(a2425)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[417, 1951])).
% 1.21/1.38 tff(1954,plain,
% 1.21/1.38 (c0_1(a2425)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[425, 1951])).
% 1.21/1.38 tff(1955,assumption,(~hskp5), introduced(assumption)).
% 1.21/1.38 tff(1956,plain,
% 1.21/1.38 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(1957,plain,
% 1.21/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[1956])).
% 1.21/1.38 tff(1958,plain,
% 1.21/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1959,plain,
% 1.21/1.38 (^[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) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.21/1.38 inference(bind,[status(th)],[])).
% 1.21/1.38 tff(1960,plain,
% 1.21/1.38 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.38 inference(quant_intro,[status(thm)],[1959])).
% 1.21/1.38 tff(1961,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause179')).
% 1.21/1.38 tff(1962,plain,
% 1.21/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1961, 1960])).
% 1.21/1.38 tff(1963,plain,
% 1.21/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1962, 1958])).
% 1.21/1.38 tff(1964,plain,(
% 1.21/1.38 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.38 inference(skolemize,[status(sab)],[1963])).
% 1.21/1.38 tff(1965,plain,
% 1.21/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1964, 1957])).
% 1.21/1.38 tff(1966,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c2_1(a2500)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1967,plain,
% 1.21/1.38 ((hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500))) <=> (hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c2_1(a2500)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1968,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c2_1(a2500))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[1967])).
% 1.21/1.38 tff(1969,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c2_1(a2500)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[1968, 1966])).
% 1.21/1.38 tff(1970,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))),
% 1.21/1.38 inference(quant_inst,[status(thm)],[])).
% 1.21/1.38 tff(1971,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c2_1(a2500))),
% 1.21/1.38 inference(modus_ponens,[status(thm)],[1970, 1969])).
% 1.21/1.38 tff(1972,plain,
% 1.21/1.38 (hskp5 | (~c2_1(a2417))),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1971, 192, 1010, 954, 953, 1019, 1965, 1018])).
% 1.21/1.38 tff(1973,plain,
% 1.21/1.38 (~c2_1(a2417)),
% 1.21/1.38 inference(unit_resolution,[status(thm)],[1972, 1955])).
% 1.21/1.38 tff(1974,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c2_1(a2500)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1975,plain,
% 1.21/1.38 ((hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500))) <=> (hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c2_1(a2500)))),
% 1.21/1.38 inference(rewrite,[status(thm)],[])).
% 1.21/1.38 tff(1976,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c2_1(a2500))))),
% 1.21/1.38 inference(monotonicity,[status(thm)],[1975])).
% 1.21/1.38 tff(1977,plain,
% 1.21/1.38 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c2_1(a2500)))),
% 1.21/1.38 inference(transitivity,[status(thm)],[1976, 1974])).
% 1.21/1.38 tff(1978,plain,
% 1.21/1.38 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(1979,plain,
% 1.21/1.39 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c2_1(a2500))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[1978, 1977])).
% 1.21/1.39 tff(1980,plain,
% 1.21/1.39 (hskp5 | (~c2_1(a2432))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1979, 192, 1255, 954, 953, 1251, 1965, 1018])).
% 1.21/1.39 tff(1981,plain,
% 1.21/1.39 (~c2_1(a2432)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1980, 1955])).
% 1.21/1.39 tff(1982,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(1983,plain,
% 1.21/1.39 (((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(1984,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[1983])).
% 1.21/1.39 tff(1985,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[1984, 1982])).
% 1.21/1.39 tff(1986,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(1987,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[1986, 1985])).
% 1.21/1.39 tff(1988,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1987, 192, 1252, 1255, 1351, 707, 706, 1019, 1008, 1336, 1981, 1973])).
% 1.21/1.39 tff(1989,plain,(hskp5 | (~c1_1(a2432)) | (~c3_1(a2432)) | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | c0_1(a2500) | c1_1(a2500) | c0_1(a2432) | (~c2_1(a2500)) | (~c3_1(a2417))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(1990,plain,
% 1.21/1.39 (hskp5),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1989, 1941, 1940, 1954, 1953, 1952, 1935, 1936, 954, 953, 1939, 972, 1937])).
% 1.21/1.39 tff(1991,plain,
% 1.21/1.39 (c0_1(a2408)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[381, 1990])).
% 1.21/1.39 tff(1992,plain,
% 1.21/1.39 (~c2_1(a2408)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[373, 1990])).
% 1.21/1.39 tff(1993,plain,
% 1.21/1.39 (c3_1(a2408)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[396, 1990])).
% 1.21/1.39 tff(1994,plain,
% 1.21/1.39 (~c1_1(a2408)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1893, 192, 1252, 1351, 767, 1251, 707, 611, 1879, 1869, 1887])).
% 1.21/1.39 tff(1995,plain,
% 1.21/1.39 (c1_1(a2408) | (~c2_1(a2417))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1016, 192, 22, 1010, 612, 1008, 611, 1007])).
% 1.21/1.39 tff(1996,plain,
% 1.21/1.39 (~c2_1(a2417)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1995, 1994])).
% 1.21/1.39 tff(1997,plain,
% 1.21/1.39 (hskp20 | c2_1(a2432)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[858, 192, 1252, 1255, 1251, 851])).
% 1.21/1.39 tff(1998,plain,
% 1.21/1.39 (hskp20),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1997, 1869])).
% 1.21/1.39 tff(1999,plain,
% 1.21/1.39 (~c2_1(a2435)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[802, 1998])).
% 1.21/1.39 tff(2000,plain,
% 1.21/1.39 (~c0_1(a2435)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[754, 1998])).
% 1.21/1.39 tff(2001,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2002,plain,
% 1.21/1.39 (((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2003,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[2002])).
% 1.21/1.39 tff(2004,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))),
% 1.21/1.39 inference(transitivity,[status(thm)],[2003, 2001])).
% 1.21/1.39 tff(2005,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(2006,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2005, 2004])).
% 1.21/1.39 tff(2007,plain,
% 1.21/1.39 (c1_1(a2435)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2006, 192, 1252, 1255, 1351, 2000, 1999, 707, 706, 1336, 1869])).
% 1.21/1.39 tff(2008,plain,
% 1.21/1.39 (c3_1(a2435)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[748, 1998])).
% 1.21/1.39 tff(2009,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2010,plain,
% 1.21/1.39 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2011,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[2010])).
% 1.21/1.39 tff(2012,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[2011, 2009])).
% 1.21/1.39 tff(2013,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(2014,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2013, 2012])).
% 1.21/1.39 tff(2015,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2014, 192, 2008, 1351, 1999, 707, 706, 1019, 1008, 1336, 2007, 1996])).
% 1.21/1.39 tff(2016,plain,(c2_1(a2432) | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | hskp1 | (~c3_1(a2417)) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2432)) | (~c3_1(a2432)) | (~c0_1(a2408)) | c0_1(a2432) | (~c0_1(a2407)) | c1_1(a2407) | c2_1(a2407)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(2017,plain,
% 1.21/1.39 (c2_1(a2432)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2016, 1954, 1953, 1952, 1935, 1936, 22, 1937, 1993, 1992, 1941, 1940, 1991, 1939, 1950, 1419, 1418])).
% 1.21/1.39 tff(2018,plain,
% 1.21/1.39 (hskp15 | (~c2_1(a2432))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1261, 192, 1940, 1939, 475])).
% 1.21/1.39 tff(2019,plain,
% 1.21/1.39 (hskp15),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2018, 2017])).
% 1.21/1.39 tff(2020,plain,
% 1.21/1.39 (~c2_1(a2422)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[528, 2019])).
% 1.21/1.39 tff(2021,plain,
% 1.21/1.39 (c3_1(a2422)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[514, 2019])).
% 1.21/1.39 tff(2022,plain,
% 1.21/1.39 (c1_1(a2422)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[522, 2019])).
% 1.21/1.39 tff(2023,plain,
% 1.21/1.39 (hskp20),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1316, 192, 1941, 1940, 2022, 2021, 1939, 2020, 851])).
% 1.21/1.39 tff(2024,plain,
% 1.21/1.39 (~c2_1(a2435)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[802, 2023])).
% 1.21/1.39 tff(2025,plain,
% 1.21/1.39 (~c0_1(a2435)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[754, 2023])).
% 1.21/1.39 tff(2026,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)) | c1_1(a2435))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2027,plain,
% 1.21/1.39 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)) | c1_1(a2435))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2028,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)) | c1_1(a2435)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[2027])).
% 1.21/1.39 tff(2029,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)) | c1_1(a2435))),
% 1.21/1.39 inference(transitivity,[status(thm)],[2028, 2026])).
% 1.21/1.39 tff(2030,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(2031,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)) | c1_1(a2435)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2030, 2029])).
% 1.21/1.39 tff(2032,plain,
% 1.21/1.39 (c1_1(a2435)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2031, 192, 1954, 2022, 2021, 2025, 2024, 1953, 1952, 2020, 1336])).
% 1.21/1.39 tff(2033,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2034,plain,
% 1.21/1.39 (((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2035,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[2034])).
% 1.21/1.39 tff(2036,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[2035, 2033])).
% 1.21/1.39 tff(2037,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(2038,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 1.21/1.39 tff(2039,plain,
% 1.21/1.39 ((~c1_1(a2408)) | (~c1_1(a2435))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2038, 192, 1991, 1950, 2025, 2024, 1992, 1419, 1418, 1879])).
% 1.21/1.39 tff(2040,plain,
% 1.21/1.39 (~c1_1(a2408)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2039, 2032])).
% 1.21/1.39 tff(2041,plain,
% 1.21/1.39 (c1_1(a2408) | (~c2_1(a2417))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[1016, 192, 22, 1937, 1993, 1936, 1992, 1007])).
% 1.21/1.39 tff(2042,plain,
% 1.21/1.39 (~c2_1(a2417)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2041, 2040])).
% 1.21/1.39 tff(2043,plain,
% 1.21/1.39 (c3_1(a2435)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[748, 2023])).
% 1.21/1.39 tff(2044,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2014, 192, 2043, 1954, 2024, 1953, 1952, 1935, 1936, 1336, 2032, 2042])).
% 1.21/1.39 tff(2045,plain,(c2_1(a2407) | hskp1 | c1_1(a2407) | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | hskp13 | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(2046,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2045, 1417, 1411, 22, 954, 953, 952, 65, 889])).
% 1.21/1.39 tff(2047,plain,(hskp13 | hskp1 | c0_1(a2500) | c1_1(a2500) | c3_1(a2500) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(2048,plain,
% 1.21/1.39 (hskp13),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2047, 22, 954, 953, 952, 889])).
% 1.21/1.39 tff(2049,plain,
% 1.21/1.39 (~c0_1(a2418)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[321, 2048])).
% 1.21/1.39 tff(2050,plain,
% 1.21/1.39 (c2_1(a2418)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[329, 2048])).
% 1.21/1.39 tff(2051,plain,
% 1.21/1.39 (c1_1(a2418)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[337, 2048])).
% 1.21/1.39 tff(2052,assumption,(c1_1(a2418)), introduced(assumption)).
% 1.21/1.39 tff(2053,assumption,(~c0_1(a2418)), introduced(assumption)).
% 1.21/1.39 tff(2054,assumption,(c2_1(a2418)), introduced(assumption)).
% 1.21/1.39 tff(2055,assumption,(~c2_1(a2500)), introduced(assumption)).
% 1.21/1.39 tff(2056,assumption,(hskp15), introduced(assumption)).
% 1.21/1.39 tff(2057,plain,
% 1.21/1.39 (~c2_1(a2422)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[528, 2056])).
% 1.21/1.39 tff(2058,plain,
% 1.21/1.39 (c3_1(a2422)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[514, 2056])).
% 1.21/1.39 tff(2059,plain,
% 1.21/1.39 (c1_1(a2422)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[522, 2056])).
% 1.21/1.39 tff(2060,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2500) | c3_1(a2500) | c2_1(a2422) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2500) | c3_1(a2500) | c2_1(a2422) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2061,plain,
% 1.21/1.39 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500)) <=> (c0_1(a2500) | c3_1(a2500) | c2_1(a2422) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2062,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2500) | c3_1(a2500) | c2_1(a2422) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500)))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[2061])).
% 1.21/1.39 tff(2063,plain,
% 1.21/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2500) | c3_1(a2500) | c2_1(a2422) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))),
% 1.21/1.39 inference(transitivity,[status(thm)],[2062, 2060])).
% 1.21/1.39 tff(2064,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(2065,plain,
% 1.21/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2500) | c3_1(a2500) | c2_1(a2422) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500)),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2064, 2063])).
% 1.21/1.39 tff(2066,plain,
% 1.21/1.39 ($false),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2065, 192, 2059, 2058, 2052, 2054, 954, 952, 2057, 2053, 63, 2055])).
% 1.21/1.39 tff(2067,plain,((~hskp15) | (~c1_1(a2418)) | (~c2_1(a2418)) | c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | c2_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.39 tff(2068,plain,
% 1.21/1.39 (~hskp15),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2067, 2055, 2054, 954, 952, 2053, 2052])).
% 1.21/1.39 tff(2069,plain,
% 1.21/1.39 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2418) | (~ndr1_0) | (~c3_1(a2418)) | (~c2_1(a2418)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2418) | (~ndr1_0) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2070,plain,
% 1.21/1.39 ((hskp15 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418))) <=> (hskp15 | c0_1(a2418) | (~ndr1_0) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2071,plain,
% 1.21/1.39 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2418) | (~ndr1_0) | (~c3_1(a2418)) | (~c2_1(a2418))))),
% 1.21/1.39 inference(monotonicity,[status(thm)],[2070])).
% 1.21/1.39 tff(2072,plain,
% 1.21/1.39 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2418) | (~ndr1_0) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.21/1.39 inference(transitivity,[status(thm)],[2071, 2069])).
% 1.21/1.39 tff(2073,plain,
% 1.21/1.39 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.21/1.39 inference(quant_inst,[status(thm)],[])).
% 1.21/1.39 tff(2074,plain,
% 1.21/1.39 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2418) | (~ndr1_0) | (~c3_1(a2418)) | (~c2_1(a2418))),
% 1.21/1.39 inference(modus_ponens,[status(thm)],[2073, 2072])).
% 1.21/1.39 tff(2075,plain,
% 1.21/1.39 (hskp15 | (~c3_1(a2418))),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2074, 192, 2054, 2053, 475])).
% 1.21/1.39 tff(2076,plain,
% 1.21/1.39 (~c3_1(a2418)),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[2075, 2068])).
% 1.21/1.39 tff(2077,plain,
% 1.21/1.39 (~hskp23),
% 1.21/1.39 inference(unit_resolution,[status(thm)],[506, 2068])).
% 1.21/1.39 tff(2078,plain,
% 1.21/1.39 (^[U: $i] : refl((hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.21/1.39 inference(bind,[status(th)],[])).
% 1.21/1.39 tff(2079,plain,
% 1.21/1.39 (![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.21/1.39 inference(quant_intro,[status(thm)],[2078])).
% 1.21/1.39 tff(2080,plain,
% 1.21/1.39 (![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.21/1.39 inference(rewrite,[status(thm)],[])).
% 1.21/1.39 tff(2081,plain,
% 1.21/1.39 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp6))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) | hskp23) <=> ((hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp23))), rewrite(((hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp23) <=> (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) | hskp23) <=> (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.21/1.40 inference(bind,[status(th)],[])).
% 1.21/1.40 tff(2082,plain,
% 1.21/1.40 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) | hskp23) <=> ![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.21/1.40 inference(quant_intro,[status(thm)],[2081])).
% 1.21/1.40 tff(2083,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp6) | hskp23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause166')).
% 1.21/1.40 tff(2084,plain,
% 1.21/1.40 (![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2083, 2082])).
% 1.21/1.40 tff(2085,plain,
% 1.21/1.40 (![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2084, 2080])).
% 1.21/1.40 tff(2086,plain,(
% 1.21/1.40 ![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.21/1.40 inference(skolemize,[status(sab)],[2085])).
% 1.21/1.40 tff(2087,plain,
% 1.21/1.40 (![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2086, 2079])).
% 1.21/1.40 tff(2088,plain,
% 1.21/1.40 (((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | (~ndr1_0) | c3_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2089,plain,
% 1.21/1.40 ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2090,plain,
% 1.21/1.40 ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | (~ndr1_0) | c3_1(a2418) | (~c2_1(a2418)) | (~c1_1(a2418))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 1.21/1.40 tff(2091,plain,
% 1.21/1.40 (hskp23 | hskp6 | c3_1(a2418)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2090, 192, 2052, 2054, 2087])).
% 1.21/1.40 tff(2092,plain,
% 1.21/1.40 (hskp6),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2091, 2077, 2076])).
% 1.21/1.40 tff(2093,plain,
% 1.21/1.40 (hskp19),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[920, 2092, 889])).
% 1.21/1.40 tff(2094,plain,
% 1.21/1.40 (~c0_1(a2432)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[297, 2093])).
% 1.21/1.40 tff(2095,plain,
% 1.21/1.40 (c3_1(a2432)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[822, 2093])).
% 1.21/1.40 tff(2096,plain,
% 1.21/1.40 (~c2_1(a2432)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1261, 192, 2068, 2095, 2094, 475])).
% 1.21/1.40 tff(2097,plain,
% 1.21/1.40 (c1_1(a2432)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[305, 2093])).
% 1.21/1.40 tff(2098,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2099,plain,
% 1.21/1.40 (((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500)) <=> (c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2100,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500)))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2099])).
% 1.21/1.40 tff(2101,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2100, 2098])).
% 1.21/1.40 tff(2102,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2500) | c0_1(a2500) | c3_1(a2500))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2103,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500)),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 1.21/1.40 tff(2104,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2103, 192, 2097, 2095, 2052, 2054, 954, 952, 2053, 63, 2055, 2096])).
% 1.21/1.40 tff(2105,plain,(c2_1(a2500) | (~c1_1(a2418)) | (~c2_1(a2418)) | c0_1(a2500) | c3_1(a2500) | c0_1(a2418) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(2106,plain,
% 1.21/1.40 (c2_1(a2500)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2105, 2051, 2050, 954, 952, 2049, 889])).
% 1.21/1.40 tff(2107,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1246, 218, 232, 889, 43, 953, 224, 1018, 954, 22])).
% 1.21/1.40 tff(2108,plain,((~hskp12) | hskp25 | hskp19 | c1_1(a2500) | (~c2_1(a2500)) | c0_1(a2500) | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(2109,plain,
% 1.21/1.40 (~hskp12),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2108, 43, 889, 953, 2106, 954, 22])).
% 1.21/1.40 tff(2110,plain,
% 1.21/1.40 (hskp16),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[989, 2109, 2106])).
% 1.21/1.40 tff(2111,plain,
% 1.21/1.40 (~c3_1(a2425)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[411, 2110])).
% 1.21/1.40 tff(2112,plain,
% 1.21/1.40 (c0_1(a2425)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[425, 2110])).
% 1.21/1.40 tff(2113,plain,
% 1.21/1.40 (~c2_1(a2425)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[417, 2110])).
% 1.21/1.40 tff(2114,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1394, 2113, 2112, 953, 889, 954, 22, 2106, 43, 2111])).
% 1.21/1.40 tff(2115,plain,(hskp19 | c1_1(a2500) | hskp25 | c0_1(a2500) | hskp1 | c3_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(2116,plain,
% 1.21/1.40 (hskp19),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2115, 22, 889, 954, 953, 952])).
% 1.21/1.40 tff(2117,plain,
% 1.21/1.40 (c3_1(a2432)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[822, 2116])).
% 1.21/1.40 tff(2118,plain,
% 1.21/1.40 (~c0_1(a2432)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[297, 2116])).
% 1.21/1.40 tff(2119,plain,
% 1.21/1.40 (c1_1(a2432)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[305, 2116])).
% 1.21/1.40 tff(2120,plain,
% 1.21/1.40 (hskp4),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1404, 192, 2119, 2117, 954, 953, 2118, 982, 2106])).
% 1.21/1.40 tff(2121,plain,
% 1.21/1.40 (~c2_1(a2407)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1416, 2120])).
% 1.21/1.40 tff(2122,plain,
% 1.21/1.40 (~c1_1(a2407)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1410, 2120])).
% 1.21/1.40 tff(2123,plain,
% 1.21/1.40 (c0_1(a2407)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1949, 2120])).
% 1.21/1.40 tff(2124,plain,
% 1.21/1.40 (~c2_1(a2432)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1262, 498])).
% 1.21/1.40 tff(2125,plain,
% 1.21/1.40 (~c3_1(a2418)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2075, 498])).
% 1.21/1.40 tff(2126,plain,
% 1.21/1.40 (~hskp23),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[506, 498])).
% 1.21/1.40 tff(2127,plain,
% 1.21/1.40 (hskp6),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2091, 2126, 2125])).
% 1.21/1.40 tff(2128,plain,
% 1.21/1.40 (~c2_1(a2410)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[895, 2127])).
% 1.21/1.40 tff(2129,plain,
% 1.21/1.40 (c1_1(a2410)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[903, 2127])).
% 1.21/1.40 tff(2130,plain,
% 1.21/1.40 (c0_1(a2410)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[911, 2127])).
% 1.21/1.40 tff(2131,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2132,plain,
% 1.21/1.40 (((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432))) <=> (c0_1(a2432) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2133,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2132])).
% 1.21/1.40 tff(2134,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2133, 2131])).
% 1.21/1.40 tff(2135,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2136,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2135, 2134])).
% 1.21/1.40 tff(2137,plain,
% 1.21/1.40 ($false),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2136, 192, 1252, 2130, 2129, 1880, 1251, 2128, 1419, 1418, 1879, 2124])).
% 1.21/1.40 tff(2138,plain,(hskp15 | (~c1_1(a2432)) | (~c0_1(a2407)) | c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | (~c1_1(a2418)) | (~c2_1(a2418)) | (~c3_1(a2432)) | c0_1(a2418)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.40 tff(2139,plain,
% 1.21/1.40 (hskp15),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2138, 2119, 2123, 2118, 2122, 2121, 2051, 2050, 2117, 2049])).
% 1.21/1.40 tff(2140,plain,
% 1.21/1.40 (c1_1(a2422)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[522, 2139])).
% 1.21/1.40 tff(2141,plain,
% 1.21/1.40 (~c2_1(a2422)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[528, 2139])).
% 1.21/1.40 tff(2142,plain,
% 1.21/1.40 (c3_1(a2422)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[514, 2139])).
% 1.21/1.40 tff(2143,plain,
% 1.21/1.40 (hskp20),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1316, 192, 2119, 2117, 2140, 2142, 2118, 2141, 851])).
% 1.21/1.40 tff(2144,plain,
% 1.21/1.40 (c3_1(a2435)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[748, 2143])).
% 1.21/1.40 tff(2145,plain,
% 1.21/1.40 (~c2_1(a2435)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[802, 2143])).
% 1.21/1.40 tff(2146,plain,
% 1.21/1.40 (~c0_1(a2435)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[754, 2143])).
% 1.21/1.40 tff(2147,assumption,(~c0_1(a2435)), introduced(assumption)).
% 1.21/1.40 tff(2148,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | (~c1_1(a2435)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2149,plain,
% 1.21/1.40 (((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | (~c1_1(a2435)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2150,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | (~c1_1(a2435))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2149])).
% 1.21/1.40 tff(2151,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | (~c1_1(a2435)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2150, 2148])).
% 1.21/1.40 tff(2152,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2153,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2407)) | (~c1_1(a2435))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2152, 2151])).
% 1.21/1.40 tff(2154,plain,
% 1.21/1.40 (~c1_1(a2435)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2153, 192, 912, 904, 1880, 2147, 722, 896, 1419, 1418, 1879])).
% 1.21/1.40 tff(2155,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2156,plain,
% 1.21/1.40 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2410) | c3_1(a2410) | (~c1_1(a2410)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2157,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2410) | c3_1(a2410) | (~c1_1(a2410)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2156])).
% 1.21/1.40 tff(2158,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2410) | c3_1(a2410) | (~c1_1(a2410)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2157, 2155])).
% 1.21/1.40 tff(2159,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2410) | c3_1(a2410) | (~c1_1(a2410)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2160,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 1.21/1.40 tff(2161,plain,
% 1.21/1.40 (c3_1(a2410)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2160, 192, 567, 566, 904, 2147, 722, 565, 896, 11, 2154])).
% 1.21/1.40 tff(2162,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c2_1(a2500)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2163,plain,
% 1.21/1.40 ((hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500))) <=> (hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c2_1(a2500)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2164,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c2_1(a2500))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2163])).
% 1.21/1.40 tff(2165,plain,
% 1.21/1.40 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c2_1(a2500)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2164, 2162])).
% 1.21/1.40 tff(2166,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2167,plain,
% 1.21/1.40 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c1_1(a2500) | c3_1(a2500) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c2_1(a2500))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 1.21/1.40 tff(2168,plain,
% 1.21/1.40 (hskp2),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2167, 192, 912, 904, 953, 952, 896, 1282, 1018])).
% 1.21/1.40 tff(2169,plain,
% 1.21/1.40 (~c3_1(a2404)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1295, 2168])).
% 1.21/1.40 tff(2170,plain,
% 1.21/1.40 (~c2_1(a2404)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[1301, 2168])).
% 1.21/1.40 tff(2171,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2418) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | c0_1(a2404) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | c0_1(a2404) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2172,plain,
% 1.21/1.40 (((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404)) <=> (c0_1(a2418) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | c0_1(a2404) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2173,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2418) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | c0_1(a2404) | (~c2_1(a2418)) | (~c1_1(a2418))))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2172])).
% 1.21/1.40 tff(2174,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | c0_1(a2404) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2173, 2171])).
% 1.21/1.40 tff(2175,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2176,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | c0_1(a2404) | (~c2_1(a2418)) | (~c1_1(a2418))),
% 1.21/1.40 inference(modus_ponens,[status(thm)],[2175, 2174])).
% 1.21/1.40 tff(2177,plain,
% 1.21/1.40 (c0_1(a2404)),
% 1.21/1.40 inference(unit_resolution,[status(thm)],[2176, 192, 2052, 2054, 904, 2053, 896, 2170, 2169, 63, 2161])).
% 1.21/1.40 tff(2178,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | (~c0_1(a2404)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | (~c0_1(a2404)) | c1_1(a2435))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2179,plain,
% 1.21/1.40 (((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | (~c0_1(a2404)) | c1_1(a2435))),
% 1.21/1.40 inference(rewrite,[status(thm)],[])).
% 1.21/1.40 tff(2180,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | (~c0_1(a2404)) | c1_1(a2435)))),
% 1.21/1.40 inference(monotonicity,[status(thm)],[2179])).
% 1.21/1.40 tff(2181,plain,
% 1.21/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | (~c0_1(a2404)) | c1_1(a2435))),
% 1.21/1.40 inference(transitivity,[status(thm)],[2180, 2178])).
% 1.21/1.40 tff(2182,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2410)) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.21/1.40 inference(quant_inst,[status(thm)],[])).
% 1.21/1.40 tff(2183,plain,
% 1.21/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c3_1(a2410)) | (~c0_1(a2404)) | c1_1(a2435)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 1.21/1.41 tff(2184,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2183, 192, 904, 2147, 722, 896, 2170, 2169, 1336, 2154, 2161, 2177])).
% 1.21/1.41 tff(2185,plain,((~hskp6) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2418)) | (~c2_1(a2418)) | c0_1(a2418) | c1_1(a2500) | c3_1(a2500) | (~c2_1(a2500)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2422) | (~c0_1(a2407)) | c1_1(a2407) | c2_1(a2407)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(2186,plain,
% 1.21/1.41 (~hskp6),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2185, 2146, 2145, 2051, 2050, 2049, 953, 952, 2106, 2140, 2142, 2141, 2123, 2122, 2121])).
% 1.21/1.41 tff(2187,plain,
% 1.21/1.41 (^[U: $i] : refl((hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 1.21/1.41 inference(bind,[status(th)],[])).
% 1.21/1.41 tff(2188,plain,
% 1.21/1.41 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.21/1.41 inference(quant_intro,[status(thm)],[2187])).
% 1.21/1.41 tff(2189,plain,
% 1.21/1.41 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2190,plain,
% 1.21/1.41 (^[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)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp11) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp11))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp11) <=> (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp11) <=> (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 1.21/1.41 inference(bind,[status(th)],[])).
% 1.21/1.41 tff(2191,plain,
% 1.21/1.41 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp11) <=> ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.21/1.41 inference(quant_intro,[status(thm)],[2190])).
% 1.21/1.41 tff(2192,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause141')).
% 1.21/1.41 tff(2193,plain,
% 1.21/1.41 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 1.21/1.41 tff(2194,plain,
% 1.21/1.41 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2193, 2189])).
% 1.21/1.41 tff(2195,plain,(
% 1.21/1.41 ![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.21/1.41 inference(skolemize,[status(sab)],[2194])).
% 1.21/1.41 tff(2196,plain,
% 1.21/1.41 (![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2195, 2188])).
% 1.21/1.41 tff(2197,plain,
% 1.21/1.41 (hskp12),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[989, 64, 1018])).
% 1.21/1.41 tff(2198,plain,
% 1.21/1.41 (~c1_1(a2417)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[217, 2197])).
% 1.21/1.41 tff(2199,plain,
% 1.21/1.41 (~c0_1(a2417)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[223, 2197])).
% 1.21/1.41 tff(2200,plain,
% 1.21/1.41 (c3_1(a2417)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[231, 2197])).
% 1.21/1.41 tff(2201,assumption,(c3_1(a2435)), introduced(assumption)).
% 1.21/1.41 tff(2202,plain,
% 1.21/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2417) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2417) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2203,plain,
% 1.21/1.41 ((hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416))) <=> (hskp1 | c1_1(a2417) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2204,plain,
% 1.21/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2417) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c2_1(a2417)) | (~c3_1(a2417))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[2203])).
% 1.21/1.41 tff(2205,plain,
% 1.21/1.41 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2417) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[2204, 2202])).
% 1.21/1.41 tff(2206,plain,
% 1.21/1.41 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c2_1(a2416) | c1_1(a2416) | (~c3_1(a2416)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(2207,plain,
% 1.21/1.41 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2417) | c1_1(a2416) | c2_1(a2416) | (~ndr1_0) | (~c3_1(a2416)) | (~c2_1(a2417)) | (~c3_1(a2417))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2206, 2205])).
% 1.21/1.41 tff(2208,plain,
% 1.21/1.41 (~c2_1(a2417)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2207, 192, 22, 1010, 158, 1008, 150, 144, 1007])).
% 1.21/1.41 tff(2209,plain,
% 1.21/1.41 (hskp10),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[198, 192, 64, 158, 150, 144, 137])).
% 1.21/1.41 tff(2210,plain,
% 1.21/1.41 (~c1_1(a2414)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[887, 2209])).
% 1.21/1.41 tff(2211,plain,
% 1.21/1.41 (c0_1(a2414)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1027, 2209])).
% 1.21/1.41 tff(2212,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | (~c2_1(a2500)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | (~c2_1(a2500)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2213,plain,
% 1.21/1.41 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | (~c2_1(a2500)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2214,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | (~c2_1(a2500))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[2213])).
% 1.21/1.41 tff(2215,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | (~c2_1(a2500)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[2214, 2212])).
% 1.21/1.41 tff(2216,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2500) | c0_1(a2500) | (~c2_1(a2500)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(2217,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | (~c2_1(a2500))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2216, 2215])).
% 1.21/1.41 tff(2218,plain,
% 1.21/1.41 (~c2_1(a2414)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2217, 192, 2211, 954, 953, 1019, 1008, 2210, 21, 1018, 2208])).
% 1.21/1.41 tff(2219,plain,
% 1.21/1.41 (~c3_1(a2414)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[881, 2209])).
% 1.21/1.41 tff(2220,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2221,plain,
% 1.21/1.41 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2222,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[2221])).
% 1.21/1.41 tff(2223,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[2222, 2220])).
% 1.21/1.41 tff(2224,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(2225,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2224, 2223])).
% 1.21/1.41 tff(2226,plain,
% 1.21/1.41 (~c1_1(a2435)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2225, 192, 2201, 2211, 722, 1019, 1008, 2219, 1336, 2208, 2218])).
% 1.21/1.41 tff(2227,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2228,plain,
% 1.21/1.41 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2229,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[2228])).
% 1.21/1.41 tff(2230,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.21/1.41 inference(transitivity,[status(thm)],[2229, 2227])).
% 1.21/1.41 tff(2231,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(2232,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 1.21/1.41 tff(2233,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2232, 192, 567, 566, 2211, 2147, 722, 565, 2219, 1336, 2226, 2218])).
% 1.21/1.41 tff(2234,plain,((~hskp11) | (~c1_1(a2422)) | (~c3_1(a2422)) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | (~c3_1(a2435)) | c0_1(a2417) | c1_1(a2417) | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500)) | hskp16 | hskp1 | (~c3_1(a2417))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(2235,plain,
% 1.21/1.41 (~hskp11),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2234, 2199, 566, 2147, 722, 565, 2201, 567, 2198, 954, 953, 1018, 64, 22, 2200])).
% 1.21/1.41 tff(2236,plain,
% 1.21/1.41 (((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2417)))) <=> ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp6 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2417)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2237,plain,
% 1.21/1.41 ((hskp11 | hskp6 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417))) <=> (hskp11 | hskp6 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2417)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2238,plain,
% 1.21/1.41 (((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)))) <=> ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2417))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[2237])).
% 1.21/1.41 tff(2239,plain,
% 1.21/1.41 (((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)))) <=> ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp6 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2417)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[2238, 2236])).
% 1.21/1.41 tff(2240,plain,
% 1.21/1.41 ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp11 | hskp6 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(2241,plain,
% 1.21/1.41 ((~![U: $i] : (hskp11 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp11 | hskp6 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2417))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2240, 2239])).
% 1.21/1.41 tff(2242,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2241, 192, 2235, 1158, 2200, 2199, 2198, 2196])).
% 1.21/1.41 tff(2243,plain,(hskp16 | hskp6 | (~c3_1(a2422)) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | (~c3_1(a2435)) | (~c1_1(a2422)) | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500)) | hskp1 | c3_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(2244,plain,
% 1.21/1.41 (hskp16),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2243, 2186, 2142, 2146, 2145, 2141, 2144, 2140, 954, 953, 2106, 22, 952])).
% 1.21/1.41 tff(2245,plain,
% 1.21/1.41 (~c3_1(a2425)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[411, 2244])).
% 1.21/1.41 tff(2246,plain,
% 1.21/1.41 (~c2_1(a2425)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[417, 2244])).
% 1.21/1.41 tff(2247,plain,
% 1.21/1.41 (((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)))) <=> ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp1 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2248,plain,
% 1.21/1.41 ((hskp6 | hskp1 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425))) <=> (hskp6 | hskp1 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2249,plain,
% 1.21/1.41 (((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)))) <=> ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[2248])).
% 1.21/1.41 tff(2250,plain,
% 1.21/1.41 (((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)))) <=> ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp1 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[2249, 2247])).
% 1.21/1.41 tff(2251,plain,
% 1.21/1.41 ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp6 | hskp1 | (~ndr1_0) | c3_1(a2425) | c2_1(a2425) | (~c1_1(a2425)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(2252,plain,
% 1.21/1.41 ((~![U: $i] : (hskp6 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp6 | hskp1 | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2251, 2250])).
% 1.21/1.41 tff(2253,plain,
% 1.21/1.41 (~c1_1(a2425)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2252, 192, 2186, 22, 2246, 2245, 951])).
% 1.21/1.41 tff(2254,plain,
% 1.21/1.41 (c0_1(a2425)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[425, 2244])).
% 1.21/1.41 tff(2255,plain,
% 1.21/1.41 (c1_1(a2435)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2031, 192, 2254, 2140, 2142, 2146, 2145, 2246, 2245, 2141, 1336])).
% 1.21/1.41 tff(2256,plain,
% 1.21/1.41 (hskp29),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1585, 308, 953, 1018, 954, 707, 706, 1351, 889])).
% 1.21/1.41 tff(2257,plain,
% 1.21/1.41 (c3_1(a2409)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1064, 2256])).
% 1.21/1.41 tff(2258,plain,
% 1.21/1.41 (c0_1(a2409)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1675, 2256])).
% 1.21/1.41 tff(2259,plain,
% 1.21/1.41 (~c1_1(a2409)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1919, 192, 308, 2258, 2257, 2201, 2147, 722, 766])).
% 1.21/1.41 tff(2260,plain,
% 1.21/1.41 (hskp12 | hskp11),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[344, 192, 2052, 2054, 2053, 278])).
% 1.21/1.41 tff(2261,plain,
% 1.21/1.41 (hskp11),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2260, 308])).
% 1.21/1.41 tff(2262,plain,
% 1.21/1.41 (~c2_1(a2416)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[143, 2261])).
% 1.21/1.41 tff(2263,plain,
% 1.21/1.41 (~c1_1(a2416)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[149, 2261])).
% 1.21/1.41 tff(2264,plain,
% 1.21/1.41 (c3_1(a2416)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[157, 2261])).
% 1.21/1.41 tff(2265,plain,
% 1.21/1.41 (c2_1(a2409)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1056, 2256])).
% 1.21/1.41 tff(2266,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1931, 192, 22, 2265, 2257, 2264, 2263, 2262, 1007, 2259])).
% 1.21/1.41 tff(2267,plain,(hskp12 | hskp1 | (~c3_1(a2435)) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2418)) | (~c2_1(a2418)) | c0_1(a2418) | c1_1(a2500) | (~c2_1(a2500)) | c0_1(a2500) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(2268,plain,
% 1.21/1.41 (hskp12),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2267, 22, 2144, 2146, 2145, 2051, 2050, 2049, 953, 2106, 954, 2246, 2245, 2254, 889])).
% 1.21/1.41 tff(2269,plain,
% 1.21/1.41 (~c1_1(a2417)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[217, 2268])).
% 1.21/1.41 tff(2270,plain,
% 1.21/1.41 (~c0_1(a2417)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[223, 2268])).
% 1.21/1.41 tff(2271,plain,
% 1.21/1.41 (c3_1(a2417)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[231, 2268])).
% 1.21/1.41 tff(2272,plain,
% 1.21/1.41 (hskp5),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1989, 2271, 2117, 2254, 2246, 2245, 2119, 2270, 954, 953, 2118, 2106, 2269])).
% 1.21/1.41 tff(2273,plain,
% 1.21/1.41 (~c2_1(a2408)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[373, 2272])).
% 1.21/1.41 tff(2274,plain,
% 1.21/1.41 (c0_1(a2408)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[381, 2272])).
% 1.21/1.41 tff(2275,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2276,plain,
% 1.21/1.41 (((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2277,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435))))),
% 1.21/1.41 inference(monotonicity,[status(thm)],[2276])).
% 1.21/1.41 tff(2278,plain,
% 1.21/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))),
% 1.21/1.41 inference(transitivity,[status(thm)],[2277, 2275])).
% 1.21/1.41 tff(2279,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.21/1.41 inference(quant_inst,[status(thm)],[])).
% 1.21/1.41 tff(2280,plain,
% 1.21/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2279, 2278])).
% 1.21/1.41 tff(2281,plain,
% 1.21/1.41 (~c1_1(a2408)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2280, 192, 2254, 2274, 2146, 2145, 2246, 2273, 1879, 2255, 2253])).
% 1.21/1.41 tff(2282,plain,
% 1.21/1.41 (c3_1(a2408)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[396, 2272])).
% 1.21/1.41 tff(2283,plain,
% 1.21/1.41 (~c2_1(a2417)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[1016, 192, 22, 2271, 2282, 2269, 2273, 1007, 2281])).
% 1.21/1.41 tff(2284,plain,
% 1.21/1.41 ($false),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2014, 192, 2144, 2254, 2145, 2246, 2245, 2270, 2269, 1336, 2255, 2283])).
% 1.21/1.41 tff(2285,plain,(hskp1 | c0_1(a2500) | c1_1(a2500) | hskp25 | c3_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.41 tff(2286,plain,
% 1.21/1.41 (hskp1),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2285, 935, 929, 889, 941])).
% 1.21/1.41 tff(2287,plain,
% 1.21/1.41 (((~hskp1) | (~c3_1(a2403))) <=> ((~hskp1) | (~c3_1(a2403)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2288,plain,
% 1.21/1.41 (((~c3_1(a2403)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a2403)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2289,axiom,((~c3_1(a2403)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause133')).
% 1.21/1.41 tff(2290,plain,
% 1.21/1.41 ((~hskp1) | (~c3_1(a2403))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2289, 2288])).
% 1.21/1.41 tff(2291,plain,
% 1.21/1.41 ((~hskp1) | (~c3_1(a2403))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2290, 2287])).
% 1.21/1.41 tff(2292,plain,
% 1.21/1.41 (~c3_1(a2403)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2291, 2286])).
% 1.21/1.41 tff(2293,plain,
% 1.21/1.41 (((~hskp1) | (~c2_1(a2403))) <=> ((~hskp1) | (~c2_1(a2403)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2294,plain,
% 1.21/1.41 (((~c2_1(a2403)) | (~hskp1)) <=> ((~hskp1) | (~c2_1(a2403)))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.41 tff(2295,axiom,((~c2_1(a2403)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause132')).
% 1.21/1.41 tff(2296,plain,
% 1.21/1.41 ((~hskp1) | (~c2_1(a2403))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2295, 2294])).
% 1.21/1.41 tff(2297,plain,
% 1.21/1.41 ((~hskp1) | (~c2_1(a2403))),
% 1.21/1.41 inference(modus_ponens,[status(thm)],[2296, 2293])).
% 1.21/1.41 tff(2298,plain,
% 1.21/1.41 (~c2_1(a2403)),
% 1.21/1.41 inference(unit_resolution,[status(thm)],[2297, 2286])).
% 1.21/1.41 tff(2299,plain,
% 1.21/1.41 (((~hskp1) | c1_1(a2403)) <=> ((~hskp1) | c1_1(a2403))),
% 1.21/1.41 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2300,axiom,((~hskp1) | c1_1(a2403)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause84')).
% 1.21/1.42 tff(2301,plain,
% 1.21/1.42 ((~hskp1) | c1_1(a2403)),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2300, 2299])).
% 1.21/1.42 tff(2302,plain,
% 1.21/1.42 ((~hskp1) | c1_1(a2403)),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2301, 2299])).
% 1.21/1.42 tff(2303,plain,
% 1.21/1.42 ((~hskp1) | c1_1(a2403)),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2302, 2299])).
% 1.21/1.42 tff(2304,plain,
% 1.21/1.42 ((~hskp1) | c1_1(a2403)),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2303, 2299])).
% 1.21/1.42 tff(2305,plain,
% 1.21/1.42 ((~hskp1) | c1_1(a2403)),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2304, 2299])).
% 1.21/1.42 tff(2306,plain,
% 1.21/1.42 (c1_1(a2403)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2305, 2286])).
% 1.21/1.42 tff(2307,plain,
% 1.21/1.42 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))))),
% 1.21/1.42 inference(bind,[status(th)],[])).
% 1.21/1.42 tff(2308,plain,
% 1.21/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.21/1.42 inference(quant_intro,[status(thm)],[2307])).
% 1.21/1.42 tff(2309,plain,
% 1.21/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2310,plain,
% 1.21/1.42 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | (~c0_1(W)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))))),
% 1.21/1.42 inference(bind,[status(th)],[])).
% 1.21/1.42 tff(2311,plain,
% 1.21/1.42 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.21/1.42 inference(quant_intro,[status(thm)],[2310])).
% 1.21/1.42 tff(2312,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c2_1(V)) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause203')).
% 1.21/1.42 tff(2313,plain,
% 1.21/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2312, 2311])).
% 1.21/1.42 tff(2314,plain,
% 1.21/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2313, 2309])).
% 1.21/1.42 tff(2315,plain,(
% 1.21/1.42 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.21/1.42 inference(skolemize,[status(sab)],[2314])).
% 1.21/1.42 tff(2316,plain,
% 1.21/1.42 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2315, 2308])).
% 1.21/1.42 tff(2317,assumption,(~c3_1(a2403)), introduced(assumption)).
% 1.21/1.42 tff(2318,assumption,(~c2_1(a2403)), introduced(assumption)).
% 1.21/1.42 tff(2319,plain,
% 1.21/1.42 (^[U: $i] : refl((hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.21/1.42 inference(bind,[status(th)],[])).
% 1.21/1.42 tff(2320,plain,
% 1.21/1.42 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.21/1.42 inference(quant_intro,[status(thm)],[2319])).
% 1.21/1.42 tff(2321,plain,
% 1.21/1.42 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2322,plain,
% 1.21/1.42 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | 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)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp6) | hskp21) <=> ((hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp21))), rewrite(((hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp21) <=> (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp6) | hskp21) <=> (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.21/1.42 inference(bind,[status(th)],[])).
% 1.21/1.42 tff(2323,plain,
% 1.21/1.42 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp6) | hskp21) <=> ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.21/1.42 inference(quant_intro,[status(thm)],[2322])).
% 1.21/1.42 tff(2324,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp6) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 1.21/1.42 tff(2325,plain,
% 1.21/1.42 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2324, 2323])).
% 1.21/1.42 tff(2326,plain,
% 1.21/1.42 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2325, 2321])).
% 1.21/1.42 tff(2327,plain,(
% 1.21/1.42 ![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.21/1.42 inference(skolemize,[status(sab)],[2326])).
% 1.21/1.42 tff(2328,plain,
% 1.21/1.42 (![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2327, 2320])).
% 1.21/1.42 tff(2329,assumption,(c1_1(a2403)), introduced(assumption)).
% 1.21/1.42 tff(2330,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2331,plain,
% 1.21/1.42 ((hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp23 | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2332,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2408) | (~c3_1(a2408))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[2331])).
% 1.21/1.42 tff(2333,plain,
% 1.21/1.42 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[2332, 2330])).
% 1.21/1.42 tff(2334,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(2335,plain,
% 1.21/1.42 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2408) | (~c3_1(a2408))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2334, 2333])).
% 1.21/1.42 tff(2336,plain,
% 1.21/1.42 ($false),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2335, 192, 629, 1009, 2329, 995, 2318, 2317, 628, 997])).
% 1.21/1.42 tff(2337,plain,(hskp19 | hskp23 | (~c1_1(a2403)) | c2_1(a2403) | c3_1(a2403) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(2338,plain,
% 1.21/1.42 (hskp23),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2337, 43, 2329, 2318, 2317, 889])).
% 1.21/1.42 tff(2339,plain,
% 1.21/1.42 (~c0_1(a2455)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[480, 2338])).
% 1.21/1.42 tff(2340,plain,
% 1.21/1.42 (c3_1(a2455)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[488, 2338])).
% 1.21/1.42 tff(2341,plain,
% 1.21/1.42 (c2_1(a2455)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[496, 2338])).
% 1.21/1.42 tff(2342,plain,
% 1.21/1.42 (((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp21 | hskp6 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp21 | hskp6 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2343,plain,
% 1.21/1.42 ((hskp21 | hskp6 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455))) <=> (hskp21 | hskp6 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2344,plain,
% 1.21/1.42 (((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp21 | hskp6 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp21 | hskp6 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[2343])).
% 1.21/1.42 tff(2345,plain,
% 1.21/1.42 (((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp21 | hskp6 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp21 | hskp6 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[2344, 2342])).
% 1.21/1.42 tff(2346,plain,
% 1.21/1.42 ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp21 | hskp6 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(2347,plain,
% 1.21/1.42 ((~![U: $i] : (hskp21 | hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp21 | hskp6 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2346, 2345])).
% 1.21/1.42 tff(2348,plain,
% 1.21/1.42 (hskp21),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2347, 192, 1142, 2341, 2340, 2339, 2328])).
% 1.21/1.42 tff(2349,plain,
% 1.21/1.42 (~c1_1(a2437)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1705, 2348])).
% 1.21/1.42 tff(2350,plain,
% 1.21/1.42 (c2_1(a2437)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1713, 2348])).
% 1.21/1.42 tff(2351,plain,
% 1.21/1.42 (c0_1(a2437)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1728, 2348])).
% 1.21/1.42 tff(2352,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2353,plain,
% 1.21/1.42 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500)) <=> (c0_1(a2500) | c1_1(a2500) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2354,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500)))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[2353])).
% 1.21/1.42 tff(2355,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500))),
% 1.21/1.42 inference(transitivity,[status(thm)],[2354, 2352])).
% 1.21/1.42 tff(2356,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(2357,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c2_1(a2500)),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 1.21/1.42 tff(2358,plain,
% 1.21/1.42 ($false),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2357, 192, 2059, 2058, 2329, 954, 953, 2057, 2318, 2317, 11, 2055])).
% 1.21/1.42 tff(2359,plain,((~hskp15) | (~c1_1(a2403)) | c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | c2_1(a2500)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(2360,plain,
% 1.21/1.42 (~hskp15),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2359, 2055, 954, 953, 2318, 2317, 2329])).
% 1.21/1.42 tff(2361,plain,
% 1.21/1.42 (~hskp23),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[506, 2360])).
% 1.21/1.42 tff(2362,plain,
% 1.21/1.42 (hskp19),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2337, 2361, 2329, 2318, 2317, 889])).
% 1.21/1.42 tff(2363,plain,
% 1.21/1.42 (c3_1(a2432)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[822, 2362])).
% 1.21/1.42 tff(2364,plain,
% 1.21/1.42 (c1_1(a2432)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[305, 2362])).
% 1.21/1.42 tff(2365,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2366,plain,
% 1.21/1.42 (((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500)) <=> (c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2367,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500)))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[2366])).
% 1.21/1.42 tff(2368,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500))),
% 1.21/1.42 inference(transitivity,[status(thm)],[2367, 2365])).
% 1.21/1.42 tff(2369,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2500) | c1_1(a2500) | c0_1(a2500))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(2370,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2500)),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2369, 2368])).
% 1.21/1.42 tff(2371,plain,
% 1.21/1.42 (c2_1(a2432)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2370, 192, 2364, 2363, 2329, 954, 953, 2318, 2317, 11, 2055])).
% 1.21/1.42 tff(2372,plain,
% 1.21/1.42 (~c0_1(a2432)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[297, 2362])).
% 1.21/1.42 tff(2373,plain,
% 1.21/1.42 ($false),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1261, 192, 2360, 2363, 2372, 475, 2371])).
% 1.21/1.42 tff(2374,plain,(c2_1(a2500) | (~c1_1(a2403)) | c0_1(a2500) | c1_1(a2500) | c2_1(a2403) | c3_1(a2403) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(2375,plain,
% 1.21/1.42 (c2_1(a2500)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2374, 2329, 954, 953, 2318, 2317, 889])).
% 1.21/1.42 tff(2376,plain,
% 1.21/1.42 (hskp29),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1048, 43, 954, 953, 2375, 889])).
% 1.21/1.42 tff(2377,plain,
% 1.21/1.42 (c3_1(a2409)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1064, 2376])).
% 1.21/1.42 tff(2378,plain,
% 1.21/1.42 (c2_1(a2409)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1056, 2376])).
% 1.21/1.42 tff(2379,plain,
% 1.21/1.42 (c0_1(a2409)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1675, 2376])).
% 1.21/1.42 tff(2380,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a2437) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c2_1(a2437)) | (~c0_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a2437) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2381,plain,
% 1.21/1.42 (((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2437) | (~c0_1(a2437)) | (~c2_1(a2437))) <=> (c1_1(a2437) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2382,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2437) | (~c0_1(a2437)) | (~c2_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a2437) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c2_1(a2437)) | (~c0_1(a2437))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[2381])).
% 1.21/1.42 tff(2383,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2437) | (~c0_1(a2437)) | (~c2_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a2437) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[2382, 2380])).
% 1.21/1.42 tff(2384,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2437) | (~c0_1(a2437)) | (~c2_1(a2437)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(2385,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a2437) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c2_1(a2437)) | (~c0_1(a2437))),
% 1.21/1.42 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 1.21/1.42 tff(2386,plain,
% 1.21/1.42 ($false),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2385, 192, 2379, 2378, 2377, 2351, 2350, 2329, 2349, 2318, 2317, 2316])).
% 1.21/1.42 tff(2387,plain,(hskp19 | (~c1_1(a2403)) | c2_1(a2403) | c3_1(a2403) | c0_1(a2500) | c1_1(a2500) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.21/1.42 tff(2388,plain,
% 1.21/1.42 (hskp19),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2387, 2306, 2298, 2292, 935, 929, 889])).
% 1.21/1.42 tff(2389,plain,
% 1.21/1.42 (~c0_1(a2432)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[297, 2388])).
% 1.21/1.42 tff(2390,plain,
% 1.21/1.42 (c3_1(a2432)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[822, 2388])).
% 1.21/1.42 tff(2391,plain,
% 1.21/1.42 (c1_1(a2432)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[305, 2388])).
% 1.21/1.42 tff(2392,plain,
% 1.21/1.42 (c2_1(a2500)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[2374, 2306, 935, 929, 2298, 2292, 889])).
% 1.21/1.42 tff(2393,plain,
% 1.21/1.42 (hskp4),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1404, 192, 1252, 1255, 954, 953, 1251, 982, 1018])).
% 1.21/1.42 tff(2394,plain,
% 1.21/1.42 (~c2_1(a2407)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1416, 2393])).
% 1.21/1.42 tff(2395,plain,
% 1.21/1.42 (~c1_1(a2407)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1410, 2393])).
% 1.21/1.42 tff(2396,plain,
% 1.21/1.42 (c0_1(a2407)),
% 1.21/1.42 inference(unit_resolution,[status(thm)],[1949, 2393])).
% 1.21/1.42 tff(2397,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2398,plain,
% 1.21/1.42 (((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432))) <=> (c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.42 inference(rewrite,[status(thm)],[])).
% 1.21/1.42 tff(2399,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.21/1.42 inference(monotonicity,[status(thm)],[2398])).
% 1.21/1.42 tff(2400,plain,
% 1.21/1.42 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.42 inference(transitivity,[status(thm)],[2399, 2397])).
% 1.21/1.42 tff(2401,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))),
% 1.21/1.42 inference(quant_inst,[status(thm)],[])).
% 1.21/1.42 tff(2402,plain,
% 1.21/1.42 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[2401, 2400])).
% 1.21/1.43 tff(2403,plain,
% 1.21/1.43 (~c0_1(a2403)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2402, 192, 1252, 2396, 2329, 1251, 2395, 2394, 2318, 1879, 2124])).
% 1.21/1.43 tff(2404,plain,
% 1.21/1.43 (hskp20),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1997, 2124])).
% 1.21/1.43 tff(2405,plain,
% 1.21/1.43 (~c2_1(a2435)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[802, 2404])).
% 1.21/1.43 tff(2406,plain,
% 1.21/1.43 (~c0_1(a2435)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[754, 2404])).
% 1.21/1.43 tff(2407,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2408,plain,
% 1.21/1.43 (((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2409,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435)))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[2408])).
% 1.21/1.43 tff(2410,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435))),
% 1.21/1.43 inference(transitivity,[status(thm)],[2409, 2407])).
% 1.21/1.43 tff(2411,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(2412,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c1_1(a2435)),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[2411, 2410])).
% 1.21/1.43 tff(2413,plain,
% 1.21/1.43 (c1_1(a2435)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2412, 192, 1252, 1255, 2329, 2406, 2405, 2318, 2317, 11, 2124])).
% 1.21/1.43 tff(2414,assumption,(c1_1(a2435)), introduced(assumption)).
% 1.21/1.43 tff(2415,plain,
% 1.21/1.43 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.21/1.43 inference(bind,[status(th)],[])).
% 1.21/1.43 tff(2416,plain,
% 1.21/1.43 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.43 inference(quant_intro,[status(thm)],[2415])).
% 1.21/1.43 tff(2417,plain,
% 1.21/1.43 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2418,plain,
% 1.21/1.43 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp15) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp15))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.21/1.43 inference(bind,[status(th)],[])).
% 1.21/1.43 tff(2419,plain,
% 1.21/1.43 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.43 inference(quant_intro,[status(thm)],[2418])).
% 1.21/1.43 tff(2420,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(V)) | c2_1(V)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause188')).
% 1.21/1.43 tff(2421,plain,
% 1.21/1.43 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[2420, 2419])).
% 1.21/1.43 tff(2422,plain,
% 1.21/1.43 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[2421, 2417])).
% 1.21/1.43 tff(2423,plain,(
% 1.21/1.43 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.43 inference(skolemize,[status(sab)],[2422])).
% 1.21/1.43 tff(2424,plain,
% 1.21/1.43 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[2423, 2416])).
% 1.21/1.43 tff(2425,assumption,(hskp29), introduced(assumption)).
% 1.21/1.43 tff(2426,plain,
% 1.21/1.43 (c2_1(a2409)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1056, 2425])).
% 1.21/1.43 tff(2427,plain,
% 1.21/1.43 (c0_1(a2409)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1675, 2425])).
% 1.21/1.43 tff(2428,plain,
% 1.21/1.43 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp15 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2435)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2429,plain,
% 1.21/1.43 ((hskp15 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (hskp15 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2435)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2430,plain,
% 1.21/1.43 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2435))))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[2429])).
% 1.21/1.43 tff(2431,plain,
% 1.21/1.43 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp15 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2435)))),
% 1.21/1.43 inference(transitivity,[status(thm)],[2430, 2428])).
% 1.21/1.43 tff(2432,plain,
% 1.21/1.43 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp15 | (~ndr1_0) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(2433,plain,
% 1.21/1.43 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp15 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2435))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[2432, 2431])).
% 1.21/1.43 tff(2434,plain,
% 1.21/1.43 (~c1_1(a2409)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2433, 192, 498, 2427, 2426, 2147, 722, 2424, 2414])).
% 1.21/1.43 tff(2435,plain,
% 1.21/1.43 (c3_1(a2409)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1064, 2425])).
% 1.21/1.43 tff(2436,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2437,plain,
% 1.21/1.43 (((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2409) | (~c0_1(a2409)) | (~c2_1(a2409))) <=> (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2438,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2409) | (~c0_1(a2409)) | (~c2_1(a2409)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409)))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[2437])).
% 1.21/1.43 tff(2439,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2409) | (~c0_1(a2409)) | (~c2_1(a2409)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))),
% 1.21/1.43 inference(transitivity,[status(thm)],[2438, 2436])).
% 1.21/1.43 tff(2440,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2409) | (~c0_1(a2409)) | (~c2_1(a2409)))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(2441,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409)),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[2440, 2439])).
% 1.21/1.43 tff(2442,plain,
% 1.21/1.43 ($false),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2441, 192, 2427, 2426, 2435, 2329, 2318, 2317, 2316, 2434])).
% 1.21/1.43 tff(2443,plain,((~hskp29) | (~c1_1(a2403)) | c2_1(a2403) | c3_1(a2403) | hskp15 | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.43 tff(2444,plain,
% 1.21/1.43 (~hskp29),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2443, 498, 2318, 2317, 2329, 2406, 2405, 2413])).
% 1.21/1.43 tff(2445,plain,
% 1.21/1.43 (~hskp0),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1537, 2444, 954, 953, 1018])).
% 1.21/1.43 tff(2446,plain,
% 1.21/1.43 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2447,plain,
% 1.21/1.43 ((hskp29 | hskp0 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403))) <=> (hskp29 | hskp0 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2448,plain,
% 1.21/1.43 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403)))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[2447])).
% 1.21/1.43 tff(2449,plain,
% 1.21/1.43 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))),
% 1.21/1.43 inference(transitivity,[status(thm)],[2448, 2446])).
% 1.21/1.43 tff(2450,plain,
% 1.21/1.43 ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403)))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(2451,plain,
% 1.21/1.43 ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403)),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 1.21/1.43 tff(2452,plain,
% 1.21/1.43 (hskp29 | hskp0 | c0_1(a2403)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2451, 192, 2329, 2318, 1548])).
% 1.21/1.43 tff(2453,plain,
% 1.21/1.43 ($false),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2452, 2445, 2444, 2403])).
% 1.21/1.43 tff(2454,plain,(hskp15 | (~c1_1(a2403)) | c2_1(a2403) | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500)) | c3_1(a2403) | (~c1_1(a2432)) | (~c3_1(a2432)) | c0_1(a2432)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.43 tff(2455,plain,
% 1.21/1.43 (hskp15),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2454, 2306, 2298, 935, 929, 2392, 2292, 2391, 2390, 2389])).
% 1.21/1.43 tff(2456,plain,
% 1.21/1.43 (~c2_1(a2422)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[528, 2455])).
% 1.21/1.43 tff(2457,plain,
% 1.21/1.43 (c3_1(a2422)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[514, 2455])).
% 1.21/1.43 tff(2458,plain,
% 1.21/1.43 (c1_1(a2422)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[522, 2455])).
% 1.21/1.43 tff(2459,plain,
% 1.21/1.43 (hskp20),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1316, 192, 2391, 2390, 2458, 2457, 2389, 2456, 851])).
% 1.21/1.43 tff(2460,plain,
% 1.21/1.43 (~c2_1(a2435)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[802, 2459])).
% 1.21/1.43 tff(2461,plain,
% 1.21/1.43 (~c0_1(a2435)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[754, 2459])).
% 1.21/1.43 tff(2462,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2463,plain,
% 1.21/1.43 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2464,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[2463])).
% 1.21/1.43 tff(2465,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435))),
% 1.21/1.43 inference(transitivity,[status(thm)],[2464, 2462])).
% 1.21/1.43 tff(2466,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(2467,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2422)) | (~c3_1(a2422)) | c1_1(a2435)),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[2466, 2465])).
% 1.21/1.43 tff(2468,plain,
% 1.21/1.43 (c1_1(a2435)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2467, 192, 2458, 2457, 2306, 2461, 2460, 2456, 2298, 2292, 11])).
% 1.21/1.43 tff(2469,plain,
% 1.21/1.43 (hskp4),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1404, 192, 2391, 2390, 935, 929, 2389, 982, 2392])).
% 1.21/1.43 tff(2470,plain,
% 1.21/1.43 (~c2_1(a2407)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1416, 2469])).
% 1.21/1.43 tff(2471,plain,
% 1.21/1.43 (~c1_1(a2407)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1410, 2469])).
% 1.21/1.43 tff(2472,plain,
% 1.21/1.43 (c0_1(a2407)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[1949, 2469])).
% 1.21/1.43 tff(2473,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | (~c1_1(a2435)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2474,plain,
% 1.21/1.43 (((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | (~c1_1(a2435)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2475,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | (~c1_1(a2435))))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[2474])).
% 1.21/1.43 tff(2476,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | (~c1_1(a2435)))),
% 1.21/1.43 inference(transitivity,[status(thm)],[2475, 2473])).
% 1.21/1.43 tff(2477,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(2478,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c1_1(a2407) | c2_1(a2407) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2407)) | (~c1_1(a2435))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[2477, 2476])).
% 1.21/1.43 tff(2479,plain,
% 1.21/1.43 ((~c0_1(a2403)) | (~c1_1(a2435))),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2478, 192, 2472, 2306, 2461, 2460, 2471, 2470, 2298, 1879])).
% 1.21/1.43 tff(2480,plain,
% 1.21/1.43 (~c0_1(a2403)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2479, 2468])).
% 1.21/1.43 tff(2481,plain,
% 1.21/1.43 (c3_1(a2435)),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[748, 2459])).
% 1.21/1.43 tff(2482,assumption,(~c0_1(a2403)), introduced(assumption)).
% 1.21/1.43 tff(2483,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a2435) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2435) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2484,plain,
% 1.21/1.43 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c2_1(a2435) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2485,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a2435) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 1.21/1.43 inference(monotonicity,[status(thm)],[2484])).
% 1.21/1.43 tff(2486,plain,
% 1.21/1.43 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2435) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.21/1.43 inference(transitivity,[status(thm)],[2485, 2483])).
% 1.21/1.43 tff(2487,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 1.21/1.43 inference(quant_inst,[status(thm)],[])).
% 1.21/1.43 tff(2488,plain,
% 1.21/1.43 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2435) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 1.21/1.43 inference(modus_ponens,[status(thm)],[2487, 2486])).
% 1.21/1.43 tff(2489,plain,
% 1.21/1.43 ($false),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2488, 192, 2201, 338, 330, 722, 322, 2318, 2317, 63, 2414, 2482])).
% 1.21/1.43 tff(2490,plain,((~hskp13) | (~c3_1(a2435)) | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2435)) | c0_1(a2403)), inference(lemma,lemma(discharge,[]))).
% 1.21/1.43 tff(2491,plain,
% 1.21/1.43 (~hskp13),
% 1.21/1.43 inference(unit_resolution,[status(thm)],[2490, 2481, 2460, 2298, 2292, 2468, 2480])).
% 1.21/1.43 tff(2492,plain,
% 1.21/1.43 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2493,plain,
% 1.21/1.43 ((hskp16 | hskp13 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403))) <=> (hskp16 | hskp13 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))),
% 1.21/1.43 inference(rewrite,[status(thm)],[])).
% 1.21/1.43 tff(2494,plain,
% 1.21/1.43 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403)))),
% 1.21/1.44 inference(monotonicity,[status(thm)],[2493])).
% 1.21/1.44 tff(2495,plain,
% 1.21/1.44 (((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403)))) <=> ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403))),
% 1.21/1.44 inference(transitivity,[status(thm)],[2494, 2492])).
% 1.21/1.44 tff(2496,plain,
% 1.21/1.44 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp16 | hskp13 | (~ndr1_0) | c0_1(a2403) | c2_1(a2403) | (~c1_1(a2403)))),
% 1.21/1.44 inference(quant_inst,[status(thm)],[])).
% 1.21/1.44 tff(2497,plain,
% 1.21/1.44 ((~![U: $i] : (hskp16 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp16 | hskp13 | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403)),
% 1.21/1.44 inference(modus_ponens,[status(thm)],[2496, 2495])).
% 1.21/1.44 tff(2498,plain,
% 1.21/1.44 (hskp16 | hskp13 | c0_1(a2403)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[2497, 192, 2306, 2298, 75])).
% 1.21/1.44 tff(2499,plain,
% 1.21/1.44 (hskp16),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[2498, 2491, 2480])).
% 1.21/1.44 tff(2500,plain,
% 1.21/1.44 (c0_1(a2425)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[425, 2499])).
% 1.21/1.44 tff(2501,plain,
% 1.21/1.44 (~c2_1(a2425)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[417, 2499])).
% 1.21/1.44 tff(2502,plain,
% 1.21/1.44 (~c3_1(a2425)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[411, 2499])).
% 1.21/1.44 tff(2503,plain,
% 1.21/1.44 (hskp19),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[2387, 2329, 2318, 2317, 954, 953, 889])).
% 1.21/1.44 tff(2504,plain,
% 1.21/1.44 (~c0_1(a2432)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[297, 2503])).
% 1.21/1.44 tff(2505,plain,
% 1.21/1.44 (c3_1(a2432)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[822, 2503])).
% 1.21/1.44 tff(2506,plain,
% 1.21/1.44 (c1_1(a2432)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[305, 2503])).
% 1.21/1.44 tff(2507,plain,
% 1.21/1.44 (hskp15),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[2454, 2329, 2318, 954, 953, 2375, 2317, 2506, 2505, 2504])).
% 1.21/1.44 tff(2508,plain,
% 1.21/1.44 (~c2_1(a2422)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[528, 2507])).
% 1.21/1.44 tff(2509,plain,
% 1.21/1.44 (c3_1(a2422)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[514, 2507])).
% 1.21/1.44 tff(2510,plain,
% 1.21/1.44 (c1_1(a2422)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[522, 2507])).
% 1.21/1.44 tff(2511,plain,
% 1.21/1.44 (hskp20),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[1316, 192, 2506, 2505, 2510, 2509, 2504, 2508, 851])).
% 1.21/1.44 tff(2512,plain,
% 1.21/1.44 (~c2_1(a2435)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[802, 2511])).
% 1.21/1.44 tff(2513,plain,
% 1.21/1.44 (~c0_1(a2435)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[754, 2511])).
% 1.21/1.44 tff(2514,plain,
% 1.21/1.44 (c1_1(a2435)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[2467, 192, 2510, 2509, 2329, 2513, 2512, 2508, 2318, 2317, 11])).
% 1.21/1.44 tff(2515,plain,
% 1.21/1.44 (hskp4),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[1404, 192, 2506, 2505, 954, 953, 2504, 982, 2375])).
% 1.21/1.44 tff(2516,plain,
% 1.21/1.44 (~c2_1(a2407)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[1416, 2515])).
% 1.21/1.44 tff(2517,plain,
% 1.21/1.44 (~c1_1(a2407)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[1410, 2515])).
% 1.21/1.44 tff(2518,plain,
% 1.21/1.44 (c0_1(a2407)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[1949, 2515])).
% 1.21/1.44 tff(2519,plain,
% 1.21/1.44 ((~c0_1(a2403)) | (~c1_1(a2435))),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[2478, 192, 2518, 2329, 2513, 2512, 2517, 2516, 2318, 1879])).
% 1.21/1.44 tff(2520,plain,
% 1.21/1.44 (~c0_1(a2403)),
% 1.21/1.44 inference(unit_resolution,[status(thm)],[2519, 2514])).
% 1.21/1.44 tff(2521,plain,
% 1.21/1.44 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 1.21/1.44 inference(bind,[status(th)],[])).
% 1.21/1.44 tff(2522,plain,
% 1.21/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.21/1.44 inference(quant_intro,[status(thm)],[2521])).
% 1.21/1.44 tff(2523,plain,
% 1.21/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.21/1.44 inference(rewrite,[status(thm)],[])).
% 1.21/1.44 tff(2524,plain,
% 1.21/1.44 (^[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))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c0_1(W))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 1.28/1.44 inference(bind,[status(th)],[])).
% 1.28/1.44 tff(2525,plain,
% 1.28/1.44 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.44 inference(quant_intro,[status(thm)],[2524])).
% 1.28/1.44 tff(2526,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause199')).
% 1.28/1.44 tff(2527,plain,
% 1.28/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2526, 2525])).
% 1.28/1.44 tff(2528,plain,
% 1.28/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2527, 2523])).
% 1.28/1.44 tff(2529,plain,(
% 1.28/1.44 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.44 inference(skolemize,[status(sab)],[2528])).
% 1.28/1.44 tff(2530,plain,
% 1.28/1.44 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2529, 2522])).
% 1.28/1.44 tff(2531,plain,
% 1.28/1.44 (c3_1(a2435)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[748, 2511])).
% 1.28/1.44 tff(2532,plain,
% 1.28/1.44 (hskp29),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[1585, 308, 953, 2375, 954, 707, 706, 1351, 889])).
% 1.28/1.44 tff(2533,plain,
% 1.28/1.44 (c3_1(a2409)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[1064, 2532])).
% 1.28/1.44 tff(2534,plain,
% 1.28/1.44 (c0_1(a2409)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[1675, 2532])).
% 1.28/1.44 tff(2535,plain,
% 1.28/1.44 (~c1_1(a2409)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[1919, 192, 308, 2534, 2533, 2531, 2513, 2512, 766])).
% 1.28/1.44 tff(2536,plain,
% 1.28/1.44 (c2_1(a2409)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[1056, 2532])).
% 1.28/1.44 tff(2537,plain,
% 1.28/1.44 ($false),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2441, 192, 2534, 2536, 2533, 2329, 2318, 2317, 2316, 2535])).
% 1.28/1.44 tff(2538,plain,(hskp12 | (~c1_1(a2403)) | c2_1(a2403) | c3_1(a2403) | c1_1(a2500) | c0_1(a2500) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.28/1.44 tff(2539,plain,
% 1.28/1.44 (hskp12),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2538, 706, 2318, 2317, 953, 954, 707, 2329, 1351, 889])).
% 1.28/1.44 tff(2540,plain,
% 1.28/1.44 (~c1_1(a2417)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[217, 2539])).
% 1.28/1.44 tff(2541,plain,
% 1.28/1.44 (~c0_1(a2417)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[223, 2539])).
% 1.28/1.44 tff(2542,plain,
% 1.28/1.44 (c3_1(a2417)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[231, 2539])).
% 1.28/1.44 tff(2543,plain,
% 1.28/1.44 (hskp29 | hskp0 | c2_1(a2432)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[1557, 192, 1252, 1251, 1548])).
% 1.28/1.44 tff(2544,plain,
% 1.28/1.44 (c2_1(a2432)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2543, 1538, 1040])).
% 1.28/1.44 tff(2545,plain,
% 1.28/1.44 (hskp15),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[1262, 2544])).
% 1.28/1.44 tff(2546,plain,
% 1.28/1.44 (~c2_1(a2422)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[528, 2545])).
% 1.28/1.44 tff(2547,plain,
% 1.28/1.44 (c1_1(a2422)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[522, 2545])).
% 1.28/1.44 tff(2548,plain,
% 1.28/1.44 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2549,plain,
% 1.28/1.44 ((hskp29 | hskp0 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422))) <=> (hskp29 | hskp0 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2550,plain,
% 1.28/1.44 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422)))),
% 1.28/1.44 inference(monotonicity,[status(thm)],[2549])).
% 1.28/1.44 tff(2551,plain,
% 1.28/1.44 (((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422)))) <=> ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422))),
% 1.28/1.44 inference(transitivity,[status(thm)],[2550, 2548])).
% 1.28/1.44 tff(2552,plain,
% 1.28/1.44 ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp29 | hskp0 | (~ndr1_0) | c0_1(a2422) | c2_1(a2422) | (~c1_1(a2422)))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(2553,plain,
% 1.28/1.44 ((~![U: $i] : (hskp29 | hskp0 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp29 | hskp0 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | c0_1(a2422)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2552, 2551])).
% 1.28/1.44 tff(2554,plain,
% 1.28/1.44 (c0_1(a2422)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2553, 192, 1040, 1538, 2547, 2546, 1548])).
% 1.28/1.44 tff(2555,plain,
% 1.28/1.44 (c3_1(a2422)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[514, 2545])).
% 1.28/1.44 tff(2556,plain,
% 1.28/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2557,plain,
% 1.28/1.44 (((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417))) <=> (c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2558,plain,
% 1.28/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425))))),
% 1.28/1.44 inference(monotonicity,[status(thm)],[2557])).
% 1.28/1.44 tff(2559,plain,
% 1.28/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.28/1.44 inference(transitivity,[status(thm)],[2558, 2556])).
% 1.28/1.44 tff(2560,plain,
% 1.28/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(2561,plain,
% 1.28/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | c1_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 1.28/1.44 tff(2562,plain,
% 1.28/1.44 (~c2_1(a2417)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2561, 192, 1351, 2547, 2555, 1010, 707, 706, 1008, 554, 2554])).
% 1.28/1.44 tff(2563,plain,
% 1.28/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2564,plain,
% 1.28/1.44 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2565,plain,
% 1.28/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425))))),
% 1.28/1.44 inference(monotonicity,[status(thm)],[2564])).
% 1.28/1.44 tff(2566,plain,
% 1.28/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425)))),
% 1.28/1.44 inference(transitivity,[status(thm)],[2565, 2563])).
% 1.28/1.44 tff(2567,plain,
% 1.28/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(2568,plain,
% 1.28/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2425) | c3_1(a2425) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c0_1(a2425))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2567, 2566])).
% 1.28/1.44 tff(2569,plain,
% 1.28/1.44 ($false),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2568, 192, 1351, 2547, 2555, 707, 706, 2546, 1019, 1008, 1336, 2562])).
% 1.28/1.44 tff(2570,plain,(hskp29 | (~c0_1(a2425)) | c2_1(a2425) | c3_1(a2425) | c0_1(a2417) | c1_1(a2417) | (~c3_1(a2417)) | (~c3_1(a2432)) | c0_1(a2432) | (~c1_1(a2432)) | c0_1(a2500) | c1_1(a2500) | (~c2_1(a2500))), inference(lemma,lemma(discharge,[]))).
% 1.28/1.44 tff(2571,plain,
% 1.28/1.44 (hskp29),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2570, 2541, 707, 1351, 706, 2542, 2540, 2505, 2504, 2506, 954, 953, 2375])).
% 1.28/1.44 tff(2572,plain,
% 1.28/1.44 (c3_1(a2409)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[1064, 2571])).
% 1.28/1.44 tff(2573,plain,
% 1.28/1.44 (c2_1(a2409)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[1056, 2571])).
% 1.28/1.44 tff(2574,plain,
% 1.28/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2417)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2575,plain,
% 1.28/1.44 (((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2417)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2576,plain,
% 1.28/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2417))))),
% 1.28/1.44 inference(monotonicity,[status(thm)],[2575])).
% 1.28/1.44 tff(2577,plain,
% 1.28/1.44 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2417)))),
% 1.28/1.44 inference(transitivity,[status(thm)],[2576, 2574])).
% 1.28/1.44 tff(2578,plain,
% 1.28/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(2579,plain,
% 1.28/1.44 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c3_1(a2417))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2578, 2577])).
% 1.28/1.44 tff(2580,plain,
% 1.28/1.44 (~c1_1(a2409)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2579, 192, 2573, 2572, 2542, 2541, 2540, 2318, 2317, 2530, 2520])).
% 1.28/1.44 tff(2581,plain,
% 1.28/1.44 (c0_1(a2409)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[1675, 2571])).
% 1.28/1.44 tff(2582,plain,
% 1.28/1.44 ($false),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2441, 192, 2581, 2573, 2572, 2329, 2318, 2317, 2316, 2580])).
% 1.28/1.44 tff(2583,plain,(c3_1(a2425) | (~c1_1(a2403)) | c2_1(a2403) | c3_1(a2403) | c2_1(a2425) | (~c0_1(a2425)) | c0_1(a2500) | c1_1(a2500) | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.28/1.44 tff(2584,plain,
% 1.28/1.44 ($false),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2583, 2502, 2501, 2298, 2292, 2306, 2500, 935, 929, 889])).
% 1.28/1.44 tff(2585,plain,(hskp25 | hskp31), inference(lemma,lemma(discharge,[]))).
% 1.28/1.44 tff(2586,plain,
% 1.28/1.44 (hskp31),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2585, 889])).
% 1.28/1.44 tff(2587,plain,
% 1.28/1.44 (((~hskp31) | c0_1(a2498)) <=> ((~hskp31) | c0_1(a2498))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2588,axiom,((~hskp31) | c0_1(a2498)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 1.28/1.44 tff(2589,plain,
% 1.28/1.44 ((~hskp31) | c0_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2588, 2587])).
% 1.28/1.44 tff(2590,plain,
% 1.28/1.44 ((~hskp31) | c0_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2589, 2587])).
% 1.28/1.44 tff(2591,plain,
% 1.28/1.44 ((~hskp31) | c0_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2590, 2587])).
% 1.28/1.44 tff(2592,plain,
% 1.28/1.44 ((~hskp31) | c0_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2591, 2587])).
% 1.28/1.44 tff(2593,plain,
% 1.28/1.44 ((~hskp31) | c0_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2592, 2587])).
% 1.28/1.44 tff(2594,plain,
% 1.28/1.44 (c0_1(a2498)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2593, 2586])).
% 1.28/1.44 tff(2595,plain,
% 1.28/1.44 (((~hskp31) | c2_1(a2498)) <=> ((~hskp31) | c2_1(a2498))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2596,axiom,((~hskp31) | c2_1(a2498)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 1.28/1.44 tff(2597,plain,
% 1.28/1.44 ((~hskp31) | c2_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2596, 2595])).
% 1.28/1.44 tff(2598,plain,
% 1.28/1.44 ((~hskp31) | c2_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2597, 2595])).
% 1.28/1.44 tff(2599,plain,
% 1.28/1.44 ((~hskp31) | c2_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2598, 2595])).
% 1.28/1.44 tff(2600,plain,
% 1.28/1.44 ((~hskp31) | c2_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2599, 2595])).
% 1.28/1.44 tff(2601,plain,
% 1.28/1.44 ((~hskp31) | c2_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2600, 2595])).
% 1.28/1.44 tff(2602,plain,
% 1.28/1.44 (c2_1(a2498)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2601, 2586])).
% 1.28/1.44 tff(2603,plain,
% 1.28/1.44 (((~hskp31) | c1_1(a2498)) <=> ((~hskp31) | c1_1(a2498))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2604,axiom,((~hskp31) | c1_1(a2498)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 1.28/1.44 tff(2605,plain,
% 1.28/1.44 ((~hskp31) | c1_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2604, 2603])).
% 1.28/1.44 tff(2606,plain,
% 1.28/1.44 ((~hskp31) | c1_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2605, 2603])).
% 1.28/1.44 tff(2607,plain,
% 1.28/1.44 ((~hskp31) | c1_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2606, 2603])).
% 1.28/1.44 tff(2608,plain,
% 1.28/1.44 ((~hskp31) | c1_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2607, 2603])).
% 1.28/1.44 tff(2609,plain,
% 1.28/1.44 ((~hskp31) | c1_1(a2498)),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2608, 2603])).
% 1.28/1.44 tff(2610,plain,
% 1.28/1.44 (c1_1(a2498)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2609, 2586])).
% 1.28/1.44 tff(2611,assumption,(c2_1(a2498)), introduced(assumption)).
% 1.28/1.44 tff(2612,assumption,(c1_1(a2498)), introduced(assumption)).
% 1.28/1.44 tff(2613,plain,
% 1.28/1.44 (((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2498) | (~c2_1(a2498)) | (~c1_1(a2498)))) <=> ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | (~ndr1_0) | c3_1(a2498) | (~c2_1(a2498)) | (~c1_1(a2498)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2614,plain,
% 1.28/1.44 ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2498) | (~c2_1(a2498)) | (~c1_1(a2498)))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(2615,plain,
% 1.28/1.44 ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | (~ndr1_0) | c3_1(a2498) | (~c2_1(a2498)) | (~c1_1(a2498))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2614, 2613])).
% 1.28/1.44 tff(2616,plain,
% 1.28/1.44 (hskp23 | c3_1(a2498)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2615, 192, 1158, 2612, 2611, 2087])).
% 1.28/1.44 tff(2617,plain,
% 1.28/1.44 (c3_1(a2498)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2616, 629])).
% 1.28/1.44 tff(2618,assumption,(c0_1(a2498)), introduced(assumption)).
% 1.28/1.44 tff(2619,plain,
% 1.28/1.44 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2620,plain,
% 1.28/1.44 ((hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2498))) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)))),
% 1.28/1.44 inference(rewrite,[status(thm)],[])).
% 1.28/1.44 tff(2621,plain,
% 1.28/1.44 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2498)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498))))),
% 1.28/1.44 inference(monotonicity,[status(thm)],[2620])).
% 1.28/1.44 tff(2622,plain,
% 1.28/1.44 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2498)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)))),
% 1.28/1.44 inference(transitivity,[status(thm)],[2621, 2619])).
% 1.28/1.44 tff(2623,plain,
% 1.28/1.44 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2498)))),
% 1.28/1.44 inference(quant_inst,[status(thm)],[])).
% 1.28/1.44 tff(2624,plain,
% 1.28/1.44 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498))),
% 1.28/1.44 inference(modus_ponens,[status(thm)],[2623, 2622])).
% 1.28/1.44 tff(2625,plain,
% 1.28/1.44 (hskp23 | hskp14 | (~c3_1(a2498))),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2624, 192, 2618, 2612, 42])).
% 1.28/1.44 tff(2626,plain,
% 1.28/1.44 (hskp14),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[2625, 2617, 629])).
% 1.28/1.44 tff(2627,plain,
% 1.28/1.44 (c1_1(a2420)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[695, 2626])).
% 1.28/1.44 tff(2628,plain,
% 1.28/1.44 (c0_1(a2414)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[1027, 876])).
% 1.28/1.44 tff(2629,plain,
% 1.28/1.44 (c2_1(a2420)),
% 1.28/1.44 inference(unit_resolution,[status(thm)],[687, 2626])).
% 1.28/1.44 tff(2630,assumption,(~c0_1(a2420)), introduced(assumption)).
% 1.28/1.44 tff(2631,plain,
% 1.28/1.44 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2632,plain,
% 1.28/1.45 ((hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2420) | (~c1_1(a2420)) | (~c2_1(a2420))) <=> (hskp19 | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2633,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2420) | (~c1_1(a2420)) | (~c2_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[2632])).
% 1.28/1.45 tff(2634,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2420) | (~c1_1(a2420)) | (~c2_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420)))),
% 1.28/1.45 inference(transitivity,[status(thm)],[2633, 2631])).
% 1.28/1.45 tff(2635,plain,
% 1.28/1.45 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2420) | (~c1_1(a2420)) | (~c2_1(a2420)))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(2636,plain,
% 1.28/1.45 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2420)) | c0_1(a2420) | (~c2_1(a2420))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[2635, 2634])).
% 1.28/1.45 tff(2637,plain,
% 1.28/1.45 ($false),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2636, 192, 43, 724, 723, 1098, 1078, 1077, 85, 2630])).
% 1.28/1.45 tff(2638,plain,(c0_1(a2420) | hskp19 | (~c1_1(a2420)) | (~c2_1(a2420)) | (~c0_1(a2414)) | c1_1(a2414) | c3_1(a2414)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.45 tff(2639,plain,
% 1.28/1.45 (c0_1(a2420)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2638, 2629, 2628, 882, 2627, 888, 43])).
% 1.28/1.45 tff(2640,plain,
% 1.28/1.45 (~c3_1(a2420)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[679, 2626])).
% 1.28/1.45 tff(2641,plain,
% 1.28/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c2_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c2_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2642,plain,
% 1.28/1.45 (((~ndr1_0) | (~c3_1(a2498)) | (~c2_1(a2498)) | (~c1_1(a2498)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c2_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2643,plain,
% 1.28/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2498)) | (~c2_1(a2498)) | (~c1_1(a2498)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c2_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[2642])).
% 1.28/1.45 tff(2644,plain,
% 1.28/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2498)) | (~c2_1(a2498)) | (~c1_1(a2498)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c2_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.28/1.45 inference(transitivity,[status(thm)],[2643, 2641])).
% 1.28/1.45 tff(2645,plain,
% 1.28/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2498)) | (~c2_1(a2498)) | (~c1_1(a2498)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(2646,plain,
% 1.28/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c2_1(a2498)) | (~c3_1(a2498)) | (~c1_1(a2498)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[2645, 2644])).
% 1.28/1.45 tff(2647,plain,
% 1.28/1.45 ($false),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2646, 192, 2612, 2611, 2627, 2628, 2640, 888, 882, 1076, 2639, 2617])).
% 1.28/1.45 tff(2648,plain,(hskp23 | (~c1_1(a2498)) | (~c2_1(a2498)) | hskp19 | (~c0_1(a2498)) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.28/1.45 tff(2649,plain,
% 1.28/1.45 (hskp23),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2648, 2610, 2602, 43, 2594, 921])).
% 1.28/1.45 tff(2650,plain,
% 1.28/1.45 (hskp15),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[506, 2649])).
% 1.28/1.45 tff(2651,plain,
% 1.28/1.45 (~c2_1(a2422)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[528, 2650])).
% 1.28/1.45 tff(2652,plain,
% 1.28/1.45 (c1_1(a2422)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[522, 2650])).
% 1.28/1.45 tff(2653,plain,
% 1.28/1.45 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2654,plain,
% 1.28/1.45 ((hskp25 | hskp19 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422))) <=> (hskp25 | hskp19 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2655,plain,
% 1.28/1.45 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[2654])).
% 1.28/1.45 tff(2656,plain,
% 1.28/1.45 (((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)))) <=> ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)))),
% 1.28/1.45 inference(transitivity,[status(thm)],[2655, 2653])).
% 1.28/1.45 tff(2657,plain,
% 1.28/1.45 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp19 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(2658,plain,
% 1.28/1.45 ((~![U: $i] : (hskp25 | hskp19 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp19 | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[2657, 2656])).
% 1.28/1.45 tff(2659,plain,
% 1.28/1.45 (~c0_1(a2422)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2658, 192, 889, 43, 2652, 2651, 106])).
% 1.28/1.45 tff(2660,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2418) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2418) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2661,plain,
% 1.28/1.45 ((hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418))) <=> (hskp19 | c0_1(a2418) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2662,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2418) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2418)) | (~c1_1(a2418))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[2661])).
% 1.28/1.45 tff(2663,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2418) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.28/1.45 inference(transitivity,[status(thm)],[2662, 2660])).
% 1.28/1.45 tff(2664,plain,
% 1.28/1.45 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(2665,plain,
% 1.28/1.45 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2418) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2418)) | (~c1_1(a2418))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 1.28/1.45 tff(2666,plain,
% 1.28/1.45 ($false),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2665, 192, 43, 2052, 2054, 1028, 2053, 1066, 1029, 85])).
% 1.28/1.45 tff(2667,plain,((~hskp10) | hskp19 | (~c1_1(a2418)) | (~c2_1(a2418)) | c0_1(a2418)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.45 tff(2668,plain,
% 1.28/1.45 ($false),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2667, 330, 338, 43, 1020, 322])).
% 1.28/1.45 tff(2669,plain,((~hskp13) | hskp19 | (~hskp10)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.45 tff(2670,plain,
% 1.28/1.45 (~hskp13),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2669, 43, 876])).
% 1.28/1.45 tff(2671,plain,
% 1.28/1.45 ($false),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[1271, 192, 64, 2670, 2652, 2651, 75, 2659])).
% 1.28/1.45 tff(2672,plain,(hskp25 | hskp16 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.28/1.45 tff(2673,plain,
% 1.28/1.45 (hskp25),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2672, 43, 64])).
% 1.28/1.45 tff(2674,plain,
% 1.28/1.45 (~c0_1(a2478)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[120, 2673])).
% 1.28/1.45 tff(2675,plain,
% 1.28/1.45 (c2_1(a2478)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[114, 2673])).
% 1.28/1.45 tff(2676,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2478) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2478) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2677,plain,
% 1.28/1.45 ((hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478))) <=> (hskp19 | c0_1(a2478) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2678,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2478) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2478)) | (~c2_1(a2478))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[2677])).
% 1.28/1.45 tff(2679,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2478) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.28/1.45 inference(transitivity,[status(thm)],[2678, 2676])).
% 1.28/1.45 tff(2680,plain,
% 1.28/1.45 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(2681,plain,
% 1.28/1.45 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2478) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2478)) | (~c2_1(a2478))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[2680, 2679])).
% 1.28/1.45 tff(2682,plain,
% 1.28/1.45 (~c1_1(a2478)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2681, 192, 43, 2675, 2628, 2674, 888, 882, 85])).
% 1.28/1.45 tff(2683,plain,
% 1.28/1.45 (~c3_1(a2478)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[126, 2673])).
% 1.28/1.45 tff(2684,plain,
% 1.28/1.45 (hskp12 | c1_1(a2478)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[266, 192, 64, 2675, 2683, 258])).
% 1.28/1.45 tff(2685,plain,
% 1.28/1.45 (hskp12),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2684, 2682])).
% 1.28/1.45 tff(2686,plain,
% 1.28/1.45 (c3_1(a2417)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[231, 2685])).
% 1.28/1.45 tff(2687,plain,
% 1.28/1.45 (~c1_1(a2417)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[217, 2685])).
% 1.28/1.45 tff(2688,plain,
% 1.28/1.45 (~c0_1(a2417)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[223, 2685])).
% 1.28/1.45 tff(2689,plain,
% 1.28/1.45 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2690,plain,
% 1.28/1.45 ((hskp19 | hskp5 | (~ndr1_0) | c3_1(a2414) | c2_1(a2414) | (~c0_1(a2414))) <=> (hskp19 | hskp5 | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2691,plain,
% 1.28/1.45 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2414) | c2_1(a2414) | (~c0_1(a2414)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414)))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[2690])).
% 1.28/1.45 tff(2692,plain,
% 1.28/1.45 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2414) | c2_1(a2414) | (~c0_1(a2414)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414))),
% 1.28/1.45 inference(transitivity,[status(thm)],[2691, 2689])).
% 1.28/1.45 tff(2693,plain,
% 1.28/1.45 ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2414) | c2_1(a2414) | (~c0_1(a2414)))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(2694,plain,
% 1.28/1.45 ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414)),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[2693, 2692])).
% 1.28/1.45 tff(2695,plain,
% 1.28/1.45 (hskp19 | hskp5 | c2_1(a2414)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2694, 192, 2628, 882, 53])).
% 1.28/1.45 tff(2696,plain,
% 1.28/1.45 (c2_1(a2414)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2695, 1955, 43])).
% 1.28/1.45 tff(2697,plain,
% 1.28/1.45 (~c1_1(a2478)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2681, 192, 43, 260, 2628, 279, 888, 882, 85])).
% 1.28/1.45 tff(2698,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2478) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2478) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2699,plain,
% 1.28/1.45 ((hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478))) <=> (hskp5 | c0_1(a2478) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2700,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2478) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[2699])).
% 1.28/1.45 tff(2701,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2478) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.45 inference(transitivity,[status(thm)],[2700, 2698])).
% 1.28/1.45 tff(2702,plain,
% 1.28/1.45 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(2703,plain,
% 1.28/1.45 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2478) | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[2702, 2701])).
% 1.28/1.45 tff(2704,plain,
% 1.28/1.45 (hskp5 | (~c2_1(a2417))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2703, 192, 260, 1010, 279, 1019, 1965, 2697])).
% 1.28/1.45 tff(2705,plain,
% 1.28/1.45 (~c2_1(a2417)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2704, 1955])).
% 1.28/1.45 tff(2706,plain,
% 1.28/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2707,plain,
% 1.28/1.45 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2708,plain,
% 1.28/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[2707])).
% 1.28/1.45 tff(2709,plain,
% 1.28/1.45 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.45 inference(transitivity,[status(thm)],[2708, 2706])).
% 1.28/1.45 tff(2710,plain,
% 1.28/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(2711,plain,
% 1.28/1.45 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[2710, 2709])).
% 1.28/1.45 tff(2712,plain,
% 1.28/1.45 ($false),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2711, 192, 260, 2628, 279, 1019, 1008, 888, 21, 2705, 2697, 2696])).
% 1.28/1.45 tff(2713,plain,(hskp5 | (~c2_1(a2478)) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~c3_1(a2417)) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.28/1.45 tff(2714,plain,
% 1.28/1.45 (hskp5),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2713, 2675, 2674, 2688, 2687, 2686, 43])).
% 1.28/1.45 tff(2715,plain,
% 1.28/1.45 (c0_1(a2408)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[381, 2714])).
% 1.28/1.45 tff(2716,plain,
% 1.28/1.45 (c3_1(a2408)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[396, 2714])).
% 1.28/1.45 tff(2717,plain,
% 1.28/1.45 (~c2_1(a2408)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[373, 2714])).
% 1.28/1.45 tff(2718,assumption,(~hskp14), introduced(assumption)).
% 1.28/1.45 tff(2719,assumption,(c1_1(a2410)), introduced(assumption)).
% 1.28/1.45 tff(2720,assumption,(c0_1(a2410)), introduced(assumption)).
% 1.28/1.45 tff(2721,plain,
% 1.28/1.45 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c3_1(a2410)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c3_1(a2410)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2722,plain,
% 1.28/1.45 ((hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2410)) | (~c1_1(a2410)) | (~c0_1(a2410))) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c3_1(a2410)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2723,plain,
% 1.28/1.45 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2410)) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c3_1(a2410))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[2722])).
% 1.28/1.45 tff(2724,plain,
% 1.28/1.45 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2410)) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c3_1(a2410)))),
% 1.28/1.45 inference(transitivity,[status(thm)],[2723, 2721])).
% 1.28/1.45 tff(2725,plain,
% 1.28/1.45 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2410)) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.28/1.45 inference(quant_inst,[status(thm)],[])).
% 1.28/1.45 tff(2726,plain,
% 1.28/1.45 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c3_1(a2410))),
% 1.28/1.45 inference(modus_ponens,[status(thm)],[2725, 2724])).
% 1.28/1.45 tff(2727,plain,
% 1.28/1.45 (hskp14 | (~c3_1(a2410))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2726, 192, 629, 2720, 2719, 42])).
% 1.28/1.45 tff(2728,plain,
% 1.28/1.45 (~c3_1(a2410)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2727, 2718])).
% 1.28/1.45 tff(2729,plain,
% 1.28/1.45 (hskp23 | hskp14 | (~c1_1(a2408))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[672, 192, 767, 612, 42])).
% 1.28/1.45 tff(2730,plain,
% 1.28/1.45 (~c1_1(a2408)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2729, 2718, 629])).
% 1.28/1.45 tff(2731,plain,
% 1.28/1.45 (hskp1 | c1_1(a2408) | (~c2_1(a2417))),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[1016, 192, 1010, 612, 1008, 611, 1007])).
% 1.28/1.45 tff(2732,plain,
% 1.28/1.45 (~c2_1(a2417)),
% 1.28/1.45 inference(unit_resolution,[status(thm)],[2731, 2730, 22])).
% 1.28/1.45 tff(2733,assumption,(~c2_1(a2410)), introduced(assumption)).
% 1.28/1.45 tff(2734,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a2417) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | c2_1(a2417) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a2417) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2735,plain,
% 1.28/1.45 ((hskp23 | (~ndr1_0) | c3_1(a2410) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2417) | c1_1(a2417) | (~c3_1(a2417))) <=> (hskp23 | c1_1(a2417) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.28/1.45 inference(rewrite,[status(thm)],[])).
% 1.28/1.45 tff(2736,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2410) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2417) | c1_1(a2417) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c1_1(a2417) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | c2_1(a2417) | (~c3_1(a2417))))),
% 1.28/1.45 inference(monotonicity,[status(thm)],[2735])).
% 1.28/1.45 tff(2737,plain,
% 1.28/1.45 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2410) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2417) | c1_1(a2417) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a2417) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[2736, 2734])).
% 1.28/1.46 tff(2738,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2410) | c2_1(a2410) | (~c1_1(a2410)) | c2_1(a2417) | c1_1(a2417) | (~c3_1(a2417)))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(2739,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c1_1(a2417) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | c3_1(a2410) | c2_1(a2417) | (~c3_1(a2417))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2738, 2737])).
% 1.28/1.46 tff(2740,plain,
% 1.28/1.46 ($false),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2739, 192, 629, 1010, 2719, 1008, 2733, 628, 2732, 2728])).
% 1.28/1.46 tff(2741,plain,(hskp14 | hskp23 | (~c3_1(a2417)) | (~c1_1(a2410)) | c1_1(a2417) | c2_1(a2410) | hskp1 | (~c3_1(a2408)) | c2_1(a2408) | (~c0_1(a2410)) | (~c0_1(a2408))), inference(lemma,lemma(discharge,[]))).
% 1.28/1.46 tff(2742,plain,
% 1.28/1.46 (hskp14),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2741, 904, 2686, 629, 2687, 896, 22, 2716, 2717, 912, 2715])).
% 1.28/1.46 tff(2743,plain,
% 1.28/1.46 (c1_1(a2420)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[695, 2742])).
% 1.28/1.46 tff(2744,plain,
% 1.28/1.46 (c2_1(a2420)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[687, 2742])).
% 1.28/1.46 tff(2745,plain,
% 1.28/1.46 (c0_1(a2420)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2638, 2744, 2628, 882, 2743, 888, 43])).
% 1.28/1.46 tff(2746,plain,
% 1.28/1.46 (~c3_1(a2420)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[679, 2742])).
% 1.28/1.46 tff(2747,plain,
% 1.28/1.46 (hskp20),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[739, 192, 2743, 2744, 2746, 665, 2745])).
% 1.28/1.46 tff(2748,plain,
% 1.28/1.46 (~c0_1(a2435)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[754, 2747])).
% 1.28/1.46 tff(2749,plain,
% 1.28/1.46 (c0_1(a2435) | (~c1_1(a2435))),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1325, 192, 64, 2670, 722, 75])).
% 1.28/1.46 tff(2750,plain,
% 1.28/1.46 (~c1_1(a2435)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2749, 2748])).
% 1.28/1.46 tff(2751,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2752,plain,
% 1.28/1.46 ((hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478))) <=> (hskp2 | c3_1(a2478) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2753,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[2752])).
% 1.28/1.46 tff(2754,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[2753, 2751])).
% 1.28/1.46 tff(2755,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(2756,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2755, 2754])).
% 1.28/1.46 tff(2757,plain,
% 1.28/1.46 (hskp2),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2756, 192, 2675, 912, 904, 2683, 896, 1282, 2682])).
% 1.28/1.46 tff(2758,plain,
% 1.28/1.46 (~c3_1(a2404)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1295, 2757])).
% 1.28/1.46 tff(2759,plain,
% 1.28/1.46 (~c2_1(a2404)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1301, 2757])).
% 1.28/1.46 tff(2760,plain,
% 1.28/1.46 (c0_1(a2404)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1308, 192, 2670, 22, 2759, 2758, 964])).
% 1.28/1.46 tff(2761,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2762,plain,
% 1.28/1.46 (((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2763,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435)))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[2762])).
% 1.28/1.46 tff(2764,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.28/1.46 inference(transitivity,[status(thm)],[2763, 2761])).
% 1.28/1.46 tff(2765,plain,
% 1.28/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(2766,plain,
% 1.28/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2765, 2764])).
% 1.28/1.46 tff(2767,plain,
% 1.28/1.46 (c0_1(a2435) | (~c0_1(a2404)) | (~c1_1(a2408)) | c1_1(a2435)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2766, 192, 2716, 722, 2717, 2759, 2758, 1336])).
% 1.28/1.46 tff(2768,plain,
% 1.28/1.46 (~c1_1(a2408)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2767, 2750, 2748, 2760])).
% 1.28/1.46 tff(2769,assumption,(~c1_1(a2478)), introduced(assumption)).
% 1.28/1.46 tff(2770,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2478) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2478) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2771,plain,
% 1.28/1.46 ((hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478))) <=> (hskp29 | c0_1(a2478) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2772,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2478) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[2771])).
% 1.28/1.46 tff(2773,plain,
% 1.28/1.46 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2478) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[2772, 2770])).
% 1.28/1.46 tff(2774,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(2775,plain,
% 1.28/1.46 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2478) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2774, 2773])).
% 1.28/1.46 tff(2776,plain,
% 1.28/1.46 ($false),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2775, 192, 1040, 260, 767, 612, 279, 1039, 2769, 1])).
% 1.28/1.46 tff(2777,plain,(c1_1(a2408) | hskp29 | (~c2_1(a2478)) | (~c0_1(a2408)) | (~c3_1(a2408)) | c0_1(a2478) | c1_1(a2478)), inference(lemma,lemma(discharge,[]))).
% 1.28/1.46 tff(2778,plain,
% 1.28/1.46 (hskp29),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2777, 2768, 2675, 2682, 2716, 2674, 2715])).
% 1.28/1.46 tff(2779,plain,
% 1.28/1.46 (c3_1(a2409)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1064, 2778])).
% 1.28/1.46 tff(2780,plain,
% 1.28/1.46 (c2_1(a2409)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1056, 2778])).
% 1.28/1.46 tff(2781,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2782,plain,
% 1.28/1.46 (((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2783,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420))))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[2782])).
% 1.28/1.46 tff(2784,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[2783, 2781])).
% 1.28/1.46 tff(2785,plain,
% 1.28/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(2786,plain,
% 1.28/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2420) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2414)) | (~c1_1(a2420)) | (~c0_1(a2420))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2785, 2784])).
% 1.28/1.46 tff(2787,plain,
% 1.28/1.46 (~c1_1(a2409)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2786, 192, 2780, 2779, 2743, 2628, 2746, 888, 882, 1076, 2745])).
% 1.28/1.46 tff(2788,plain,
% 1.28/1.46 (c0_1(a2409)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[1675, 2778])).
% 1.28/1.46 tff(2789,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2790,plain,
% 1.28/1.46 (((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2791,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[2790])).
% 1.28/1.46 tff(2792,plain,
% 1.28/1.46 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[2791, 2789])).
% 1.28/1.46 tff(2793,plain,
% 1.28/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(2794,plain,
% 1.28/1.46 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2793, 2792])).
% 1.28/1.46 tff(2795,plain,
% 1.28/1.46 ($false),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2794, 192, 2788, 2780, 2675, 2674, 2748, 722, 21, 2787, 2750, 2682])).
% 1.28/1.46 tff(2796,plain,((~hskp6) | c2_1(a2435) | hskp16 | hskp19 | hskp23 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.28/1.46 tff(2797,plain,
% 1.28/1.46 (~hskp6),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2796, 22, 64, 43, 629, 722])).
% 1.28/1.46 tff(2798,plain,
% 1.28/1.46 (hskp11 | hskp6),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2241, 192, 2686, 2688, 2687, 2196])).
% 1.28/1.46 tff(2799,plain,
% 1.28/1.46 (hskp11),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2798, 2797])).
% 1.28/1.46 tff(2800,plain,
% 1.28/1.46 (~c2_1(a2416)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[143, 2799])).
% 1.28/1.46 tff(2801,plain,
% 1.28/1.46 (~c1_1(a2416)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[149, 2799])).
% 1.28/1.46 tff(2802,plain,
% 1.28/1.46 (c3_1(a2416)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[157, 2799])).
% 1.28/1.46 tff(2803,plain,
% 1.28/1.46 (~c2_1(a2417)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2207, 192, 22, 2686, 2802, 2687, 2801, 2800, 1007])).
% 1.28/1.46 tff(2804,plain,
% 1.28/1.46 (~c2_1(a2414)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2711, 192, 2675, 2628, 2674, 2688, 2687, 888, 21, 2803, 2682])).
% 1.28/1.46 tff(2805,plain,
% 1.28/1.46 (^[U: $i] : refl((hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(2806,plain,
% 1.28/1.46 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[2805])).
% 1.28/1.46 tff(2807,plain,
% 1.28/1.46 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2808,plain,
% 1.28/1.46 (^[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) | hskp7) <=> ((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp7))), rewrite(((hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.28/1.46 inference(bind,[status(th)],[])).
% 1.28/1.46 tff(2809,plain,
% 1.28/1.46 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7) <=> ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.28/1.46 inference(quant_intro,[status(thm)],[2808])).
% 1.28/1.46 tff(2810,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp6) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 1.28/1.46 tff(2811,plain,
% 1.28/1.46 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2810, 2809])).
% 1.28/1.46 tff(2812,plain,
% 1.28/1.46 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2811, 2807])).
% 1.28/1.46 tff(2813,plain,(
% 1.28/1.46 ![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.28/1.46 inference(skolemize,[status(sab)],[2812])).
% 1.28/1.46 tff(2814,plain,
% 1.28/1.46 (![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2813, 2806])).
% 1.28/1.46 tff(2815,plain,
% 1.28/1.46 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp6 | c0_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp6 | c0_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2816,plain,
% 1.28/1.46 ((hskp7 | hskp6 | (~ndr1_0) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478))) <=> (hskp7 | hskp6 | c0_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2817,plain,
% 1.28/1.46 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp6 | c0_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.28/1.46 inference(monotonicity,[status(thm)],[2816])).
% 1.28/1.46 tff(2818,plain,
% 1.28/1.46 (((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp6 | c0_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(transitivity,[status(thm)],[2817, 2815])).
% 1.28/1.46 tff(2819,plain,
% 1.28/1.46 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp7 | hskp6 | (~ndr1_0) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.46 inference(quant_inst,[status(thm)],[])).
% 1.28/1.46 tff(2820,plain,
% 1.28/1.46 ((~![U: $i] : (hskp7 | hskp6 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp7 | hskp6 | c0_1(a2478) | (~ndr1_0) | c1_1(a2478) | (~c2_1(a2478))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2819, 2818])).
% 1.28/1.46 tff(2821,plain,
% 1.28/1.46 (hskp7 | hskp6 | c1_1(a2478)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2820, 192, 2675, 2674, 2814])).
% 1.28/1.46 tff(2822,plain,
% 1.28/1.46 (hskp7),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2821, 2797, 2682])).
% 1.28/1.46 tff(2823,plain,
% 1.28/1.46 (((~hskp7) | (~c1_1(a2411))) <=> ((~hskp7) | (~c1_1(a2411)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2824,plain,
% 1.28/1.46 (((~c1_1(a2411)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a2411)))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2825,axiom,((~c1_1(a2411)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 1.28/1.46 tff(2826,plain,
% 1.28/1.46 ((~hskp7) | (~c1_1(a2411))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2825, 2824])).
% 1.28/1.46 tff(2827,plain,
% 1.28/1.46 ((~hskp7) | (~c1_1(a2411))),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2826, 2823])).
% 1.28/1.46 tff(2828,plain,
% 1.28/1.46 (~c1_1(a2411)),
% 1.28/1.46 inference(unit_resolution,[status(thm)],[2827, 2822])).
% 1.28/1.46 tff(2829,plain,
% 1.28/1.46 (((~hskp7) | c2_1(a2411)) <=> ((~hskp7) | c2_1(a2411))),
% 1.28/1.46 inference(rewrite,[status(thm)],[])).
% 1.28/1.46 tff(2830,axiom,((~hskp7) | c2_1(a2411)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 1.28/1.46 tff(2831,plain,
% 1.28/1.46 ((~hskp7) | c2_1(a2411)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2830, 2829])).
% 1.28/1.46 tff(2832,plain,
% 1.28/1.46 ((~hskp7) | c2_1(a2411)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2831, 2829])).
% 1.28/1.46 tff(2833,plain,
% 1.28/1.46 ((~hskp7) | c2_1(a2411)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2832, 2829])).
% 1.28/1.46 tff(2834,plain,
% 1.28/1.46 ((~hskp7) | c2_1(a2411)),
% 1.28/1.46 inference(modus_ponens,[status(thm)],[2833, 2829])).
% 1.28/1.46 tff(2835,plain,
% 1.28/1.47 ((~hskp7) | c2_1(a2411)),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[2834, 2829])).
% 1.28/1.47 tff(2836,plain,
% 1.28/1.47 (c2_1(a2411)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[2835, 2822])).
% 1.28/1.47 tff(2837,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(2838,plain,
% 1.28/1.47 (((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(2839,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.28/1.47 inference(monotonicity,[status(thm)],[2838])).
% 1.28/1.47 tff(2840,plain,
% 1.28/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.28/1.47 inference(transitivity,[status(thm)],[2839, 2837])).
% 1.28/1.47 tff(2841,plain,
% 1.28/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.28/1.47 inference(quant_inst,[status(thm)],[])).
% 1.28/1.47 tff(2842,plain,
% 1.28/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478))),
% 1.28/1.47 inference(modus_ponens,[status(thm)],[2841, 2840])).
% 1.28/1.47 tff(2843,plain,
% 1.28/1.47 (~c0_1(a2411)),
% 1.28/1.47 inference(unit_resolution,[status(thm)],[2842, 192, 2675, 2836, 2674, 2688, 2687, 2828, 21, 2803, 2682])).
% 1.28/1.47 tff(2844,plain,
% 1.28/1.47 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.28/1.47 inference(bind,[status(th)],[])).
% 1.28/1.47 tff(2845,plain,
% 1.28/1.47 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.28/1.47 inference(quant_intro,[status(thm)],[2844])).
% 1.28/1.47 tff(2846,plain,
% 1.28/1.47 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.28/1.47 inference(rewrite,[status(thm)],[])).
% 1.28/1.47 tff(2847,plain,
% 1.28/1.47 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.28/1.47 inference(bind,[status(th)],[])).
% 1.28/1.47 tff(2848,plain,
% 1.28/1.47 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.28/1.47 inference(quant_intro,[status(thm)],[2847])).
% 1.31/1.47 tff(2849,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 1.31/1.47 tff(2850,plain,
% 1.31/1.47 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[2849, 2848])).
% 1.31/1.47 tff(2851,plain,
% 1.31/1.47 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[2850, 2846])).
% 1.31/1.47 tff(2852,plain,(
% 1.31/1.47 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.31/1.47 inference(skolemize,[status(sab)],[2851])).
% 1.31/1.47 tff(2853,plain,
% 1.31/1.47 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[2852, 2845])).
% 1.31/1.47 tff(2854,plain,
% 1.31/1.47 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2855,plain,
% 1.31/1.47 ((hskp0 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (hskp0 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2856,plain,
% 1.31/1.47 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417))))),
% 1.31/1.47 inference(monotonicity,[status(thm)],[2855])).
% 1.31/1.47 tff(2857,plain,
% 1.31/1.47 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417)))),
% 1.31/1.47 inference(transitivity,[status(thm)],[2856, 2854])).
% 1.31/1.47 tff(2858,plain,
% 1.31/1.47 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(2859,plain,
% 1.31/1.47 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | c2_1(a2417) | (~c3_1(a2417))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[2858, 2857])).
% 1.31/1.47 tff(2860,plain,
% 1.31/1.47 (hskp0),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2859, 192, 2686, 2688, 2687, 2853, 2803])).
% 1.31/1.47 tff(2861,plain,
% 1.31/1.47 (~c1_1(a2402)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[1512, 2860])).
% 1.31/1.47 tff(2862,plain,
% 1.31/1.47 (c3_1(a2402)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[1520, 2860])).
% 1.31/1.47 tff(2863,plain,
% 1.31/1.47 (c0_1(a2402)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[1528, 2860])).
% 1.31/1.47 tff(2864,plain,
% 1.31/1.47 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c1_1(a2411) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | c0_1(a2411) | (~c2_1(a2411)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2411) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | c0_1(a2411) | (~c2_1(a2411)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2865,plain,
% 1.31/1.47 ((hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411))) <=> (hskp29 | c1_1(a2411) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | c0_1(a2411) | (~c2_1(a2411)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2866,plain,
% 1.31/1.47 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c1_1(a2411) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | c0_1(a2411) | (~c2_1(a2411))))),
% 1.31/1.47 inference(monotonicity,[status(thm)],[2865])).
% 1.31/1.47 tff(2867,plain,
% 1.31/1.47 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2411) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | c0_1(a2411) | (~c2_1(a2411)))),
% 1.31/1.47 inference(transitivity,[status(thm)],[2866, 2864])).
% 1.31/1.47 tff(2868,plain,
% 1.31/1.47 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | (~c0_1(a2402)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(2869,plain,
% 1.31/1.47 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c1_1(a2411) | c1_1(a2402) | (~ndr1_0) | (~c0_1(a2402)) | (~c3_1(a2402)) | c0_1(a2411) | (~c2_1(a2411))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[2868, 2867])).
% 1.31/1.47 tff(2870,plain,
% 1.31/1.47 (hskp29),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2869, 192, 2836, 2863, 2862, 2828, 2861, 1039, 2843])).
% 1.31/1.47 tff(2871,plain,
% 1.31/1.47 (c2_1(a2409)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[1056, 2870])).
% 1.31/1.47 tff(2872,plain,
% 1.31/1.47 (c0_1(a2409)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[1675, 2870])).
% 1.31/1.47 tff(2873,plain,
% 1.31/1.47 (c3_1(a2409)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[1064, 2870])).
% 1.31/1.47 tff(2874,plain,
% 1.31/1.47 (~hskp24),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[1179, 1158, 43, 22, 1077, 1078, 1098])).
% 1.31/1.47 tff(2875,plain,
% 1.31/1.47 (^[U: $i] : refl((hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(2876,plain,
% 1.31/1.47 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[2875])).
% 1.31/1.47 tff(2877,plain,
% 1.31/1.47 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2878,plain,
% 1.31/1.47 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp15))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24) <=> ((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp24))), rewrite(((hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U))) | hskp24) <=> (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24) <=> (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(2879,plain,
% 1.31/1.47 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24) <=> ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[2878])).
% 1.31/1.47 tff(2880,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp15) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 1.31/1.47 tff(2881,plain,
% 1.31/1.47 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[2880, 2879])).
% 1.31/1.47 tff(2882,plain,
% 1.31/1.47 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[2881, 2877])).
% 1.31/1.47 tff(2883,plain,(
% 1.31/1.47 ![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.31/1.47 inference(skolemize,[status(sab)],[2882])).
% 1.31/1.47 tff(2884,plain,
% 1.31/1.47 (![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[2883, 2876])).
% 1.31/1.47 tff(2885,plain,
% 1.31/1.47 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp15 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2886,plain,
% 1.31/1.47 ((hskp24 | hskp15 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409))) <=> (hskp24 | hskp15 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2887,plain,
% 1.31/1.47 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409)))),
% 1.31/1.47 inference(monotonicity,[status(thm)],[2886])).
% 1.31/1.47 tff(2888,plain,
% 1.31/1.47 (((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)))) <=> ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp15 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409))),
% 1.31/1.47 inference(transitivity,[status(thm)],[2887, 2885])).
% 1.31/1.47 tff(2889,plain,
% 1.31/1.47 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp24 | hskp15 | (~ndr1_0) | c1_1(a2409) | (~c3_1(a2409)) | (~c2_1(a2409)))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(2890,plain,
% 1.31/1.47 ((~![U: $i] : (hskp24 | hskp15 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp24 | hskp15 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409)),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[2889, 2888])).
% 1.31/1.47 tff(2891,plain,
% 1.31/1.47 (hskp24 | c1_1(a2409)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2890, 192, 498, 1116, 1115, 2884])).
% 1.31/1.47 tff(2892,plain,
% 1.31/1.47 (c1_1(a2409)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2891, 2874])).
% 1.31/1.47 tff(2893,plain,
% 1.31/1.47 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2894,plain,
% 1.31/1.47 ((hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409))) <=> (hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2895,plain,
% 1.31/1.47 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409))))),
% 1.31/1.47 inference(monotonicity,[status(thm)],[2894])).
% 1.31/1.47 tff(2896,plain,
% 1.31/1.47 (((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)))) <=> ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)))),
% 1.31/1.47 inference(transitivity,[status(thm)],[2895, 2893])).
% 1.31/1.47 tff(2897,plain,
% 1.31/1.47 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(2898,plain,
% 1.31/1.47 ((~![U: $i] : (hskp23 | hskp14 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp23 | hskp14 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[2897, 2896])).
% 1.31/1.47 tff(2899,plain,
% 1.31/1.47 (hskp14 | (~c1_1(a2409))),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2898, 192, 2126, 1688, 1115, 42])).
% 1.31/1.47 tff(2900,plain,
% 1.31/1.47 (hskp14),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2899, 2892])).
% 1.31/1.47 tff(2901,plain,
% 1.31/1.47 (~c3_1(a2420)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[679, 2900])).
% 1.31/1.47 tff(2902,plain,
% 1.31/1.47 (c2_1(a2420)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[687, 2900])).
% 1.31/1.47 tff(2903,plain,
% 1.31/1.47 (c1_1(a2420)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[695, 2900])).
% 1.31/1.47 tff(2904,plain,
% 1.31/1.47 (((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c2_1(a2420)))) <=> ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c2_1(a2420)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2905,plain,
% 1.31/1.47 ((hskp23 | hskp6 | (~ndr1_0) | c3_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420))) <=> (hskp23 | hskp6 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c2_1(a2420)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2906,plain,
% 1.31/1.47 (((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420)))) <=> ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c2_1(a2420))))),
% 1.31/1.47 inference(monotonicity,[status(thm)],[2905])).
% 1.31/1.47 tff(2907,plain,
% 1.31/1.47 (((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420)))) <=> ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c2_1(a2420)))),
% 1.31/1.47 inference(transitivity,[status(thm)],[2906, 2904])).
% 1.31/1.47 tff(2908,plain,
% 1.31/1.47 ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp23 | hskp6 | (~ndr1_0) | c3_1(a2420) | (~c2_1(a2420)) | (~c1_1(a2420)))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(2909,plain,
% 1.31/1.47 ((~![U: $i] : (hskp23 | hskp6 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp23 | hskp6 | c3_1(a2420) | (~ndr1_0) | (~c1_1(a2420)) | (~c2_1(a2420))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[2908, 2907])).
% 1.31/1.47 tff(2910,plain,
% 1.31/1.47 ($false),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2909, 192, 2126, 1158, 2903, 2902, 2901, 2087])).
% 1.31/1.47 tff(2911,plain,(hskp6 | (~c0_1(a2409)) | (~c3_1(a2409)) | hskp15 | (~c2_1(a2409)) | hskp19 | hskp1 | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414))), inference(lemma,lemma(discharge,[]))).
% 1.31/1.47 tff(2912,plain,
% 1.31/1.47 (hskp15),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2911, 2873, 2797, 2872, 2871, 43, 22, 882, 888, 2628])).
% 1.31/1.47 tff(2913,plain,
% 1.31/1.47 (~c2_1(a2422)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[528, 2912])).
% 1.31/1.47 tff(2914,plain,
% 1.31/1.47 (c3_1(a2422)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[514, 2912])).
% 1.31/1.47 tff(2915,plain,
% 1.31/1.47 (c1_1(a2422)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[522, 2912])).
% 1.31/1.47 tff(2916,plain,
% 1.31/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2917,plain,
% 1.31/1.47 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2918,plain,
% 1.31/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422))))),
% 1.31/1.47 inference(monotonicity,[status(thm)],[2917])).
% 1.31/1.47 tff(2919,plain,
% 1.31/1.47 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.31/1.47 inference(transitivity,[status(thm)],[2918, 2916])).
% 1.31/1.47 tff(2920,plain,
% 1.31/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(2921,plain,
% 1.31/1.47 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[2920, 2919])).
% 1.31/1.47 tff(2922,plain,
% 1.31/1.47 ($false),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2921, 192, 2915, 2914, 2628, 2913, 2688, 2687, 882, 1336, 2803, 2804])).
% 1.31/1.47 tff(2923,plain,(hskp1 | hskp19 | hskp16 | hskp23 | c2_1(a2435)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.47 tff(2924,plain,
% 1.31/1.47 (hskp1),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2923, 722, 64, 629, 43])).
% 1.31/1.47 tff(2925,plain,
% 1.31/1.47 (c1_1(a2403)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2305, 2924])).
% 1.31/1.47 tff(2926,plain,
% 1.31/1.47 (~c2_1(a2403)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2297, 2924])).
% 1.31/1.47 tff(2927,plain,
% 1.31/1.47 (~c3_1(a2403)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2291, 2924])).
% 1.31/1.47 tff(2928,plain,
% 1.31/1.47 (hskp16 | hskp13 | (~c1_1(a2403)) | c0_1(a2403)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2497, 192, 2318, 75])).
% 1.31/1.47 tff(2929,plain,
% 1.31/1.47 (c0_1(a2403)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2928, 64, 2329, 65])).
% 1.31/1.47 tff(2930,plain,
% 1.31/1.47 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2931,plain,
% 1.31/1.47 ((hskp19 | hskp5 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c0_1(a2403))) <=> (hskp19 | hskp5 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2932,plain,
% 1.31/1.47 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c0_1(a2403)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403))))),
% 1.31/1.47 inference(monotonicity,[status(thm)],[2931])).
% 1.31/1.47 tff(2933,plain,
% 1.31/1.47 (((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c0_1(a2403)))) <=> ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))),
% 1.31/1.47 inference(transitivity,[status(thm)],[2932, 2930])).
% 1.31/1.47 tff(2934,plain,
% 1.31/1.47 ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp19 | hskp5 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c0_1(a2403)))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(2935,plain,
% 1.31/1.47 ((~![U: $i] : (hskp19 | hskp5 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp19 | hskp5 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[2934, 2933])).
% 1.31/1.47 tff(2936,plain,
% 1.31/1.47 (hskp5 | c3_1(a2403) | (~c0_1(a2403))),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2935, 192, 43, 2318, 53])).
% 1.31/1.47 tff(2937,plain,
% 1.31/1.47 (hskp5),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2936, 2929, 2317])).
% 1.31/1.47 tff(2938,plain,
% 1.31/1.47 (~c2_1(a2408)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[373, 2937])).
% 1.31/1.47 tff(2939,plain,
% 1.31/1.47 (c3_1(a2408)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[396, 2937])).
% 1.31/1.47 tff(2940,plain,
% 1.31/1.47 (c1_1(a2408)),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[2335, 192, 629, 2939, 2329, 2938, 2318, 2317, 628])).
% 1.31/1.47 tff(2941,plain,
% 1.31/1.47 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(2942,plain,
% 1.31/1.47 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[2941])).
% 1.31/1.47 tff(2943,plain,
% 1.31/1.47 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(2944,plain,
% 1.31/1.47 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(2945,plain,
% 1.31/1.48 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[2944])).
% 1.31/1.48 tff(2946,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause187')).
% 1.31/1.48 tff(2947,plain,
% 1.31/1.48 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[2946, 2945])).
% 1.31/1.48 tff(2948,plain,
% 1.31/1.48 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[2947, 2943])).
% 1.31/1.48 tff(2949,plain,(
% 1.31/1.48 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.48 inference(skolemize,[status(sab)],[2948])).
% 1.31/1.48 tff(2950,plain,
% 1.31/1.48 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[2949, 2942])).
% 1.31/1.48 tff(2951,plain,
% 1.31/1.48 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(2952,plain,
% 1.31/1.48 ((hskp14 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478))) <=> (hskp14 | c3_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(2953,plain,
% 1.31/1.48 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c3_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[2952])).
% 1.31/1.48 tff(2954,plain,
% 1.31/1.48 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.31/1.48 inference(transitivity,[status(thm)],[2953, 2951])).
% 1.31/1.48 tff(2955,plain,
% 1.31/1.48 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(2956,plain,
% 1.31/1.48 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c3_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[2955, 2954])).
% 1.31/1.48 tff(2957,plain,
% 1.31/1.48 (hskp14 | (~c0_1(a2403))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2956, 192, 260, 2329, 259, 2317, 2950, 2769])).
% 1.31/1.48 tff(2958,plain,
% 1.31/1.48 (hskp14),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2957, 2929])).
% 1.31/1.48 tff(2959,plain,
% 1.31/1.48 (c2_1(a2420)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[687, 2958])).
% 1.31/1.48 tff(2960,plain,
% 1.31/1.48 (c1_1(a2420)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[695, 2958])).
% 1.31/1.48 tff(2961,plain,
% 1.31/1.48 (c0_1(a2420)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2638, 2960, 1077, 2959, 1098, 1078, 43])).
% 1.31/1.48 tff(2962,plain,
% 1.31/1.48 (~c3_1(a2420)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[679, 2958])).
% 1.31/1.48 tff(2963,plain,
% 1.31/1.48 (hskp20),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[739, 192, 2960, 2959, 2962, 665, 2961])).
% 1.31/1.48 tff(2964,plain,
% 1.31/1.48 (~c0_1(a2435)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[754, 2963])).
% 1.31/1.48 tff(2965,plain,
% 1.31/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(2966,plain,
% 1.31/1.48 (((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(2967,plain,
% 1.31/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435)))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[2966])).
% 1.31/1.48 tff(2968,plain,
% 1.31/1.48 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.31/1.48 inference(transitivity,[status(thm)],[2967, 2965])).
% 1.31/1.48 tff(2969,plain,
% 1.31/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(2970,plain,
% 1.31/1.48 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[2969, 2968])).
% 1.31/1.48 tff(2971,plain,
% 1.31/1.48 (c0_1(a2435) | (~c1_1(a2408)) | c1_1(a2435)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2970, 192, 612, 2329, 722, 611, 2318, 2317, 11])).
% 1.31/1.48 tff(2972,plain,
% 1.31/1.48 (c1_1(a2435)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2971, 2147, 756])).
% 1.31/1.48 tff(2973,plain,
% 1.31/1.48 (hskp16 | hskp13 | c0_1(a2435) | (~c1_1(a2435))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[1325, 192, 722, 75])).
% 1.31/1.48 tff(2974,plain,
% 1.31/1.48 ($false),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2973, 2972, 2147, 64, 65])).
% 1.31/1.48 tff(2975,plain,(c0_1(a2435) | hskp16 | hskp13 | c2_1(a2435) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2403)) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.48 tff(2976,plain,
% 1.31/1.48 ($false),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2975, 2964, 2940, 65, 722, 64, 2939, 2329, 2938, 2318, 2317])).
% 1.31/1.48 tff(2977,plain,(hskp16 | hskp13 | c2_1(a2435) | (~c1_1(a2403)) | c2_1(a2403) | c3_1(a2403) | hskp23 | c3_1(a2414) | (~c0_1(a2414)) | c1_1(a2414) | hskp19 | (~c2_1(a2478)) | c3_1(a2478) | c1_1(a2478)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.48 tff(2978,plain,
% 1.31/1.48 ($false),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2977, 2927, 2926, 64, 2682, 629, 722, 2925, 882, 2628, 888, 43, 2675, 2683, 2670])).
% 1.31/1.48 tff(2979,plain,(c2_1(a2435) | hskp16 | hskp23 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.31/1.48 tff(2980,plain,
% 1.31/1.48 (c2_1(a2435)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2979, 629, 64, 43])).
% 1.31/1.48 tff(2981,plain,
% 1.31/1.48 (~hskp20),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[802, 2980])).
% 1.31/1.48 tff(2982,assumption,(hskp14), introduced(assumption)).
% 1.31/1.48 tff(2983,plain,
% 1.31/1.48 (c1_1(a2420)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[695, 2982])).
% 1.31/1.48 tff(2984,plain,
% 1.31/1.48 (c2_1(a2420)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[687, 2982])).
% 1.31/1.48 tff(2985,plain,
% 1.31/1.48 (c0_1(a2420)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2638, 2984, 2628, 882, 2983, 888, 43])).
% 1.31/1.48 tff(2986,plain,
% 1.31/1.48 (~c3_1(a2420)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[679, 2982])).
% 1.31/1.48 tff(2987,assumption,(~hskp20), introduced(assumption)).
% 1.31/1.48 tff(2988,plain,
% 1.31/1.48 ($false),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[739, 192, 2987, 2983, 2984, 2986, 665, 2985])).
% 1.31/1.48 tff(2989,plain,((~hskp14) | hskp20 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.31/1.48 tff(2990,plain,
% 1.31/1.48 (~hskp14),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2989, 2981, 43])).
% 1.31/1.48 tff(2991,plain,
% 1.31/1.48 (hskp23 | hskp14 | (~c1_1(a2408))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[672, 192, 2715, 2716, 42])).
% 1.31/1.48 tff(2992,plain,
% 1.31/1.48 (~c1_1(a2408)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2991, 2990, 629])).
% 1.31/1.48 tff(2993,plain,
% 1.31/1.48 (hskp29),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2777, 2992, 2675, 2682, 2716, 2674, 2715])).
% 1.31/1.48 tff(2994,plain,
% 1.31/1.48 (c3_1(a2409)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[1064, 2993])).
% 1.31/1.48 tff(2995,plain,
% 1.31/1.48 (c0_1(a2409)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[1675, 2993])).
% 1.31/1.48 tff(2996,plain,
% 1.31/1.48 (~c1_1(a2409)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2898, 192, 629, 2990, 2995, 2994, 42])).
% 1.31/1.48 tff(2997,plain,
% 1.31/1.48 (^[U: $i] : refl((hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(2998,plain,
% 1.31/1.48 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[2997])).
% 1.31/1.48 tff(2999,plain,
% 1.31/1.48 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3000,plain,
% 1.31/1.48 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp20) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp20))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp20) <=> (hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp20) | hskp18) <=> ((hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp18))), rewrite(((hskp20 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U))) | hskp18) <=> (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp20) | hskp18) <=> (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))))),
% 1.31/1.48 inference(bind,[status(th)],[])).
% 1.31/1.48 tff(3001,plain,
% 1.31/1.48 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp20) | hskp18) <=> ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.48 inference(quant_intro,[status(thm)],[3000])).
% 1.31/1.48 tff(3002,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp20) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 1.31/1.48 tff(3003,plain,
% 1.31/1.48 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[3002, 3001])).
% 1.31/1.48 tff(3004,plain,
% 1.31/1.48 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[3003, 2999])).
% 1.31/1.48 tff(3005,plain,(
% 1.31/1.48 ![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.48 inference(skolemize,[status(sab)],[3004])).
% 1.31/1.48 tff(3006,plain,
% 1.31/1.48 (![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[3005, 2998])).
% 1.31/1.48 tff(3007,plain,
% 1.31/1.48 (c2_1(a2409)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[1056, 2993])).
% 1.31/1.48 tff(3008,plain,
% 1.31/1.48 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp18 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3009,plain,
% 1.31/1.48 ((hskp20 | hskp18 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409))) <=> (hskp20 | hskp18 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3010,plain,
% 1.31/1.48 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409))))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[3009])).
% 1.31/1.48 tff(3011,plain,
% 1.31/1.48 (((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)))) <=> ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp18 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409)))),
% 1.31/1.48 inference(transitivity,[status(thm)],[3010, 3008])).
% 1.31/1.48 tff(3012,plain,
% 1.31/1.48 ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c0_1(a2409)))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(3013,plain,
% 1.31/1.48 ((~![U: $i] : (hskp20 | hskp18 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)))) | hskp20 | hskp18 | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c2_1(a2409))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[3012, 3011])).
% 1.31/1.48 tff(3014,plain,
% 1.31/1.48 (hskp18),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[3013, 192, 2981, 2995, 3007, 2994, 3006])).
% 1.31/1.48 tff(3015,assumption,(hskp18), introduced(assumption)).
% 1.31/1.48 tff(3016,plain,
% 1.31/1.48 (((~hskp18) | (~c3_1(a2428))) <=> ((~hskp18) | (~c3_1(a2428)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3017,plain,
% 1.31/1.48 (((~c3_1(a2428)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a2428)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3018,axiom,((~c3_1(a2428)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 1.31/1.48 tff(3019,plain,
% 1.31/1.48 ((~hskp18) | (~c3_1(a2428))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[3018, 3017])).
% 1.31/1.48 tff(3020,plain,
% 1.31/1.48 ((~hskp18) | (~c3_1(a2428))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[3019, 3016])).
% 1.31/1.48 tff(3021,plain,
% 1.31/1.48 (~c3_1(a2428)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[3020, 3015])).
% 1.31/1.48 tff(3022,plain,
% 1.31/1.48 (((~hskp18) | (~c2_1(a2428))) <=> ((~hskp18) | (~c2_1(a2428)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3023,plain,
% 1.31/1.48 (((~c2_1(a2428)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a2428)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3024,axiom,((~c2_1(a2428)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 1.31/1.48 tff(3025,plain,
% 1.31/1.48 ((~hskp18) | (~c2_1(a2428))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[3024, 3023])).
% 1.31/1.48 tff(3026,plain,
% 1.31/1.48 ((~hskp18) | (~c2_1(a2428))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[3025, 3022])).
% 1.31/1.48 tff(3027,plain,
% 1.31/1.48 (~c2_1(a2428)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[3026, 3015])).
% 1.31/1.48 tff(3028,plain,
% 1.31/1.48 (((~hskp18) | (~c0_1(a2428))) <=> ((~hskp18) | (~c0_1(a2428)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3029,plain,
% 1.31/1.48 (((~c0_1(a2428)) | (~hskp18)) <=> ((~hskp18) | (~c0_1(a2428)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3030,axiom,((~c0_1(a2428)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 1.31/1.48 tff(3031,plain,
% 1.31/1.48 ((~hskp18) | (~c0_1(a2428))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[3030, 3029])).
% 1.31/1.48 tff(3032,plain,
% 1.31/1.48 ((~hskp18) | (~c0_1(a2428))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[3031, 3028])).
% 1.31/1.48 tff(3033,plain,
% 1.31/1.48 (~c0_1(a2428)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[3032, 3015])).
% 1.31/1.48 tff(3034,plain,
% 1.31/1.48 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3035,plain,
% 1.31/1.48 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2428) | c0_1(a2428) | c2_1(a2428)) <=> (hskp13 | hskp1 | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3036,plain,
% 1.31/1.48 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2428) | c0_1(a2428) | c2_1(a2428))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0)))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[3035])).
% 1.31/1.48 tff(3037,plain,
% 1.31/1.48 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2428) | c0_1(a2428) | c2_1(a2428))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0))),
% 1.31/1.48 inference(transitivity,[status(thm)],[3036, 3034])).
% 1.31/1.48 tff(3038,plain,
% 1.31/1.48 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2428) | c0_1(a2428) | c2_1(a2428))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(3039,plain,
% 1.31/1.48 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0)),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[3038, 3037])).
% 1.31/1.48 tff(3040,plain,
% 1.31/1.48 ($false),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[3039, 192, 65, 22, 3033, 3027, 3021, 964])).
% 1.31/1.48 tff(3041,plain,((~hskp18) | hskp13 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.31/1.48 tff(3042,plain,
% 1.31/1.48 (hskp1),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[3041, 3014, 2670])).
% 1.31/1.48 tff(3043,plain,
% 1.31/1.48 (~c3_1(a2403)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2291, 3042])).
% 1.31/1.48 tff(3044,plain,
% 1.31/1.48 (~c2_1(a2403)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2297, 3042])).
% 1.31/1.48 tff(3045,plain,
% 1.31/1.48 (c1_1(a2403)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2305, 3042])).
% 1.31/1.48 tff(3046,plain,
% 1.31/1.48 ($false),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[2441, 192, 2995, 3007, 2994, 3045, 3044, 3043, 2316, 2996])).
% 1.31/1.48 tff(3047,plain,(hskp23 | hskp19 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.31/1.48 tff(3048,plain,
% 1.31/1.48 (hskp23),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[3047, 43, 64])).
% 1.31/1.48 tff(3049,plain,
% 1.31/1.48 (hskp15),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[506, 3048])).
% 1.31/1.48 tff(3050,plain,
% 1.31/1.48 (~c2_1(a2422)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[528, 3049])).
% 1.31/1.48 tff(3051,plain,
% 1.31/1.48 (c1_1(a2422)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[522, 3049])).
% 1.31/1.48 tff(3052,plain,
% 1.31/1.48 (c0_1(a2422)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[1271, 192, 64, 2670, 3051, 3050, 75])).
% 1.31/1.48 tff(3053,plain,
% 1.31/1.48 (~c0_1(a2455)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[480, 3048])).
% 1.31/1.48 tff(3054,plain,
% 1.31/1.48 (c2_1(a2455)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[496, 3048])).
% 1.31/1.48 tff(3055,plain,
% 1.31/1.48 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2455) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2455)) | (~c1_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2455) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3056,plain,
% 1.31/1.48 ((hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455))) <=> (hskp19 | c0_1(a2455) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3057,plain,
% 1.31/1.48 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2455) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2455)) | (~c1_1(a2455))))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[3056])).
% 1.31/1.48 tff(3058,plain,
% 1.31/1.48 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2455) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.31/1.48 inference(transitivity,[status(thm)],[3057, 3055])).
% 1.31/1.48 tff(3059,plain,
% 1.31/1.48 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2414) | c1_1(a2414) | (~c0_1(a2414)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(3060,plain,
% 1.31/1.48 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2455) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2455)) | (~c1_1(a2455))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[3059, 3058])).
% 1.31/1.48 tff(3061,plain,
% 1.31/1.48 (~c1_1(a2455)),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[3060, 192, 43, 3054, 2628, 3053, 888, 882, 85])).
% 1.31/1.48 tff(3062,plain,
% 1.31/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3063,plain,
% 1.31/1.48 ((hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478))) <=> (hskp2 | c3_1(a2478) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.31/1.48 inference(rewrite,[status(thm)],[])).
% 1.31/1.48 tff(3064,plain,
% 1.31/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.31/1.48 inference(monotonicity,[status(thm)],[3063])).
% 1.31/1.48 tff(3065,plain,
% 1.31/1.48 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.31/1.48 inference(transitivity,[status(thm)],[3064, 3062])).
% 1.31/1.48 tff(3066,plain,
% 1.31/1.48 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2422) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))),
% 1.31/1.48 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(3067,plain,
% 1.31/1.48 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2422) | (~ndr1_0) | (~c1_1(a2422)) | (~c0_1(a2422)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[3066, 3065])).
% 1.31/1.48 tff(3068,plain,
% 1.31/1.48 (hskp2 | (~c0_1(a2422))),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[3067, 192, 2675, 3051, 2683, 3050, 1282, 2682])).
% 1.31/1.48 tff(3069,plain,
% 1.31/1.48 (hskp2),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[3068, 3052])).
% 1.31/1.49 tff(3070,plain,
% 1.31/1.49 (~c3_1(a2404)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1295, 3069])).
% 1.31/1.49 tff(3071,plain,
% 1.31/1.49 (~c2_1(a2404)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1301, 3069])).
% 1.31/1.49 tff(3072,plain,
% 1.31/1.49 (c3_1(a2422)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[514, 3049])).
% 1.31/1.49 tff(3073,plain,
% 1.31/1.49 (c3_1(a2455)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[488, 3048])).
% 1.31/1.49 tff(3074,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3075,plain,
% 1.31/1.49 (((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3076,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[3075])).
% 1.31/1.49 tff(3077,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.49 inference(transitivity,[status(thm)],[3076, 3074])).
% 1.31/1.49 tff(3078,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(3079,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[3078, 3077])).
% 1.31/1.49 tff(3080,plain,
% 1.31/1.49 (~c0_1(a2404)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3079, 192, 3054, 3073, 3051, 3072, 3071, 3070, 554, 3061, 3052])).
% 1.31/1.49 tff(3081,plain,
% 1.31/1.49 (~c1_1(a2404)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1785, 3069])).
% 1.31/1.49 tff(3082,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2455) | c1_1(a2414) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2455) | c1_1(a2414) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3083,plain,
% 1.31/1.49 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404)) <=> (c0_1(a2455) | c1_1(a2414) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3084,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2455) | c1_1(a2414) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[3083])).
% 1.31/1.49 tff(3085,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2455) | c1_1(a2414) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.49 inference(transitivity,[status(thm)],[3084, 3082])).
% 1.31/1.49 tff(3086,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(3087,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2455) | c1_1(a2414) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[3086, 3085])).
% 1.31/1.49 tff(3088,plain,
% 1.31/1.49 (~c2_1(a2414)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3087, 192, 3054, 2628, 3053, 888, 3081, 3071, 21, 3061, 3080])).
% 1.31/1.49 tff(3089,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3090,plain,
% 1.31/1.49 (((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3091,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[3090])).
% 1.31/1.49 tff(3092,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.49 inference(transitivity,[status(thm)],[3091, 3089])).
% 1.31/1.49 tff(3093,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2422)) | (~c1_1(a2422)) | (~c0_1(a2422)) | c2_1(a2414) | c3_1(a2414) | (~c0_1(a2414)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(3094,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | c2_1(a2414) | (~c1_1(a2422)) | (~c0_1(a2422)) | (~c3_1(a2422)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[3093, 3092])).
% 1.31/1.49 tff(3095,plain,
% 1.31/1.49 ($false),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3094, 192, 3054, 3073, 3051, 3072, 2628, 882, 554, 3088, 3061, 3052])).
% 1.31/1.49 tff(3096,plain,(hskp19 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.31/1.49 tff(3097,plain,
% 1.31/1.49 (hskp19),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3096, 64])).
% 1.31/1.49 tff(3098,plain,
% 1.31/1.49 (~c0_1(a2432)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[297, 3097])).
% 1.31/1.49 tff(3099,plain,
% 1.31/1.49 (c3_1(a2432)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[822, 3097])).
% 1.31/1.49 tff(3100,plain,
% 1.31/1.49 (c1_1(a2432)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[305, 3097])).
% 1.31/1.49 tff(3101,plain,
% 1.31/1.49 (c2_1(a2432)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1997, 2987])).
% 1.31/1.49 tff(3102,plain,
% 1.31/1.49 (hskp15),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1262, 3101])).
% 1.31/1.49 tff(3103,plain,
% 1.31/1.49 (~c2_1(a2422)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[528, 3102])).
% 1.31/1.49 tff(3104,plain,
% 1.31/1.49 (c3_1(a2422)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[514, 3102])).
% 1.31/1.49 tff(3105,plain,
% 1.31/1.49 (c1_1(a2422)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[522, 3102])).
% 1.31/1.49 tff(3106,plain,
% 1.31/1.49 ($false),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1316, 192, 2987, 1252, 1255, 3105, 3104, 1251, 3103, 851])).
% 1.31/1.49 tff(3107,plain,(hskp20 | (~c1_1(a2432)) | (~c3_1(a2432)) | c0_1(a2432)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.49 tff(3108,plain,
% 1.31/1.49 (hskp20),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3107, 3100, 3099, 3098])).
% 1.31/1.49 tff(3109,plain,
% 1.31/1.49 (~c2_1(a2435)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[802, 3108])).
% 1.31/1.49 tff(3110,plain,
% 1.31/1.49 (~c0_1(a2435)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[754, 3108])).
% 1.31/1.49 tff(3111,plain,
% 1.31/1.49 (hskp13 | (~c1_1(a2435))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1325, 192, 64, 3110, 3109, 75])).
% 1.31/1.49 tff(3112,plain,
% 1.31/1.49 (~c1_1(a2435)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3111, 65])).
% 1.31/1.49 tff(3113,plain,
% 1.31/1.49 (hskp13 | c2_1(a2432)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[353, 192, 64, 3100, 3098, 75])).
% 1.31/1.49 tff(3114,plain,
% 1.31/1.49 (c2_1(a2432)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3113, 65])).
% 1.31/1.49 tff(3115,plain,
% 1.31/1.49 (hskp15 | (~c2_1(a2432))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1261, 192, 3099, 3098, 475])).
% 1.31/1.49 tff(3116,plain,
% 1.31/1.49 (hskp15),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3115, 3114])).
% 1.31/1.49 tff(3117,plain,
% 1.31/1.49 (~c2_1(a2422)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[528, 3116])).
% 1.31/1.49 tff(3118,plain,
% 1.31/1.49 (c3_1(a2422)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[514, 3116])).
% 1.31/1.49 tff(3119,plain,
% 1.31/1.49 (c1_1(a2422)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[522, 3116])).
% 1.31/1.49 tff(3120,assumption,(~c2_1(a2414)), introduced(assumption)).
% 1.31/1.49 tff(3121,assumption,(~c1_1(a2435)), introduced(assumption)).
% 1.31/1.49 tff(3122,plain,
% 1.31/1.49 ($false),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[2232, 192, 567, 566, 2628, 2147, 722, 565, 882, 1336, 3121, 3120])).
% 1.31/1.49 tff(3123,plain,(c2_1(a2414) | (~c1_1(a2422)) | (~c3_1(a2422)) | c0_1(a2435) | c2_1(a2435) | c2_1(a2422) | c1_1(a2435)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.49 tff(3124,plain,
% 1.31/1.49 (c2_1(a2414)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3123, 3119, 3118, 3110, 3109, 3117, 3112])).
% 1.31/1.49 tff(3125,plain,
% 1.31/1.49 (c3_1(a2435)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[748, 3108])).
% 1.31/1.49 tff(3126,plain,
% 1.31/1.49 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c0_1(a2435) | (~ndr1_0) | c1_1(a2435) | (~c3_1(a2435)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2435) | (~ndr1_0) | c1_1(a2435) | (~c3_1(a2435)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3127,plain,
% 1.31/1.49 ((hskp12 | (~ndr1_0) | c1_1(a2435) | c0_1(a2435) | (~c3_1(a2435))) <=> (hskp12 | c0_1(a2435) | (~ndr1_0) | c1_1(a2435) | (~c3_1(a2435)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3128,plain,
% 1.31/1.49 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | c0_1(a2435) | (~ndr1_0) | c1_1(a2435) | (~c3_1(a2435))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[3127])).
% 1.31/1.49 tff(3129,plain,
% 1.31/1.49 (((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2435) | (~ndr1_0) | c1_1(a2435) | (~c3_1(a2435)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[3128, 3126])).
% 1.31/1.49 tff(3130,plain,
% 1.31/1.49 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp12 | (~ndr1_0) | c1_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(3131,plain,
% 1.31/1.49 ((~![U: $i] : (hskp12 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp12 | c0_1(a2435) | (~ndr1_0) | c1_1(a2435) | (~c3_1(a2435))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[3130, 3129])).
% 1.31/1.49 tff(3132,plain,
% 1.31/1.49 (hskp12 | c1_1(a2435)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3131, 192, 3125, 3110, 1430])).
% 1.31/1.49 tff(3133,plain,
% 1.31/1.49 (hskp12),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3132, 3112])).
% 1.31/1.49 tff(3134,plain,
% 1.31/1.49 (~c1_1(a2417)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[217, 3133])).
% 1.31/1.49 tff(3135,plain,
% 1.31/1.49 (~c0_1(a2417)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[223, 3133])).
% 1.31/1.49 tff(3136,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2417)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2417)) | c1_1(a2435))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3137,plain,
% 1.31/1.49 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2417) | c0_1(a2417) | (~c2_1(a2417)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2417)) | c1_1(a2435))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3138,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2417) | c0_1(a2417) | (~c2_1(a2417)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2417)) | c1_1(a2435)))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[3137])).
% 1.31/1.49 tff(3139,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2417) | c0_1(a2417) | (~c2_1(a2417)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2417)) | c1_1(a2435))),
% 1.31/1.49 inference(transitivity,[status(thm)],[3138, 3136])).
% 1.31/1.49 tff(3140,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2417) | c0_1(a2417) | (~c2_1(a2417)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(3141,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c2_1(a2417)) | c1_1(a2435)),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[3140, 3139])).
% 1.31/1.49 tff(3142,plain,
% 1.31/1.49 ((~c2_1(a2414)) | (~c2_1(a2417))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3141, 192, 2628, 3110, 3109, 3135, 3134, 888, 21, 3112])).
% 1.31/1.49 tff(3143,plain,
% 1.31/1.49 (~c2_1(a2417)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3142, 3124])).
% 1.31/1.49 tff(3144,plain,
% 1.31/1.49 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(3145,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[3144])).
% 1.31/1.49 tff(3146,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3147,plain,
% 1.31/1.49 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.31/1.49 inference(bind,[status(th)],[])).
% 1.31/1.49 tff(3148,plain,
% 1.31/1.49 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.49 inference(quant_intro,[status(thm)],[3147])).
% 1.31/1.49 tff(3149,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 1.31/1.49 tff(3150,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[3149, 3148])).
% 1.31/1.49 tff(3151,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[3150, 3146])).
% 1.31/1.49 tff(3152,plain,(
% 1.31/1.49 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.49 inference(skolemize,[status(sab)],[3151])).
% 1.31/1.49 tff(3153,plain,
% 1.31/1.49 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[3152, 3145])).
% 1.31/1.49 tff(3154,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a2435) | c2_1(a2435) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a2435) | c2_1(a2435) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c3_1(a2435)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3155,plain,
% 1.31/1.49 ((hskp2 | (~ndr1_0) | c3_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435))) <=> (hskp2 | c0_1(a2435) | c2_1(a2435) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c3_1(a2435)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3156,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | c0_1(a2435) | c2_1(a2435) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c3_1(a2435))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[3155])).
% 1.31/1.49 tff(3157,plain,
% 1.31/1.49 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a2435) | c2_1(a2435) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c3_1(a2435)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[3156, 3154])).
% 1.31/1.49 tff(3158,plain,
% 1.31/1.49 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c2_1(a2435) | c0_1(a2435) | (~c3_1(a2435)))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(3159,plain,
% 1.31/1.49 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp2 | c0_1(a2435) | c2_1(a2435) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | (~c3_1(a2435))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[3158, 3157])).
% 1.31/1.49 tff(3160,plain,
% 1.31/1.49 (hskp2 | (~c2_1(a2414))),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3159, 192, 3125, 2628, 3110, 3109, 882, 3153])).
% 1.31/1.49 tff(3161,plain,
% 1.31/1.49 (hskp2),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3160, 3124])).
% 1.31/1.49 tff(3162,plain,
% 1.31/1.49 (~c3_1(a2404)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1295, 3161])).
% 1.31/1.49 tff(3163,plain,
% 1.31/1.49 (~c2_1(a2404)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[1301, 3161])).
% 1.31/1.49 tff(3164,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3165,plain,
% 1.31/1.49 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3166,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[3165])).
% 1.31/1.49 tff(3167,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[3166, 3164])).
% 1.31/1.49 tff(3168,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c2_1(a2404) | c3_1(a2404) | (~c0_1(a2404)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(3169,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2422) | c0_1(a2417) | c1_1(a2417) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | (~c0_1(a2404)) | c2_1(a2417) | (~c1_1(a2422)) | (~c3_1(a2422))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[3168, 3167])).
% 1.31/1.49 tff(3170,plain,
% 1.31/1.49 (~c0_1(a2404)),
% 1.31/1.49 inference(unit_resolution,[status(thm)],[3169, 192, 3119, 3118, 3117, 3135, 3134, 3163, 3162, 1336, 3143])).
% 1.31/1.49 tff(3171,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2432) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2432) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3172,plain,
% 1.31/1.49 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404)) <=> (c0_1(a2432) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.49 inference(rewrite,[status(thm)],[])).
% 1.31/1.49 tff(3173,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2432) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432))))),
% 1.31/1.49 inference(monotonicity,[status(thm)],[3172])).
% 1.31/1.49 tff(3174,plain,
% 1.31/1.49 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2432) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.49 inference(transitivity,[status(thm)],[3173, 3171])).
% 1.31/1.49 tff(3175,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2404) | c0_1(a2404) | c3_1(a2404))),
% 1.31/1.49 inference(quant_inst,[status(thm)],[])).
% 1.31/1.49 tff(3176,plain,
% 1.31/1.49 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2432) | c2_1(a2422) | c2_1(a2404) | c3_1(a2404) | (~ndr1_0) | c0_1(a2404) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432))),
% 1.31/1.49 inference(modus_ponens,[status(thm)],[3175, 3174])).
% 1.31/1.50 tff(3177,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3176, 192, 3100, 3119, 3118, 3098, 3117, 3163, 3162, 63, 3114, 3170])).
% 1.31/1.50 tff(3178,plain,(hskp13 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(3179,plain,
% 1.31/1.50 (hskp13),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3178, 64])).
% 1.31/1.50 tff(3180,plain,
% 1.31/1.50 (c2_1(a2418)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[329, 3179])).
% 1.31/1.50 tff(3181,plain,
% 1.31/1.50 (~c0_1(a2418)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[321, 3179])).
% 1.31/1.50 tff(3182,plain,
% 1.31/1.50 (c1_1(a2418)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[337, 3179])).
% 1.31/1.50 tff(3183,assumption,(hskp4), introduced(assumption)).
% 1.31/1.50 tff(3184,plain,
% 1.31/1.50 (~c1_1(a2407)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1410, 3183])).
% 1.31/1.50 tff(3185,plain,
% 1.31/1.50 (c0_1(a2407)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1949, 3183])).
% 1.31/1.50 tff(3186,plain,
% 1.31/1.50 (~c2_1(a2407)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1416, 3183])).
% 1.31/1.50 tff(3187,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[2138, 3186, 3185, 1252, 1251, 2054, 498, 3184, 2052, 1255, 2053])).
% 1.31/1.50 tff(3188,plain,((~hskp4) | (~c1_1(a2432)) | c0_1(a2432) | (~c2_1(a2418)) | hskp15 | (~c1_1(a2418)) | (~c3_1(a2432)) | c0_1(a2418)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(3189,plain,
% 1.31/1.50 (~hskp4),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3188, 498, 1251, 2054, 1252, 2052, 1255, 2053])).
% 1.31/1.50 tff(3190,assumption,(hskp9), introduced(assumption)).
% 1.31/1.50 tff(3191,plain,
% 1.31/1.50 (((~hskp9) | (~c1_1(a2413))) <=> ((~hskp9) | (~c1_1(a2413)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3192,plain,
% 1.31/1.50 (((~c1_1(a2413)) | (~hskp9)) <=> ((~hskp9) | (~c1_1(a2413)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3193,axiom,((~c1_1(a2413)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 1.31/1.50 tff(3194,plain,
% 1.31/1.50 ((~hskp9) | (~c1_1(a2413))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3193, 3192])).
% 1.31/1.50 tff(3195,plain,
% 1.31/1.50 ((~hskp9) | (~c1_1(a2413))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3194, 3191])).
% 1.31/1.50 tff(3196,plain,
% 1.31/1.50 (~c1_1(a2413)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3195, 3190])).
% 1.31/1.50 tff(3197,plain,
% 1.31/1.50 (((~hskp9) | (~c0_1(a2413))) <=> ((~hskp9) | (~c0_1(a2413)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3198,plain,
% 1.31/1.50 (((~c0_1(a2413)) | (~hskp9)) <=> ((~hskp9) | (~c0_1(a2413)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3199,axiom,((~c0_1(a2413)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 1.31/1.50 tff(3200,plain,
% 1.31/1.50 ((~hskp9) | (~c0_1(a2413))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3199, 3198])).
% 1.31/1.50 tff(3201,plain,
% 1.31/1.50 ((~hskp9) | (~c0_1(a2413))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3200, 3197])).
% 1.31/1.50 tff(3202,plain,
% 1.31/1.50 (~c0_1(a2413)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3201, 3190])).
% 1.31/1.50 tff(3203,plain,
% 1.31/1.50 (((~hskp9) | c2_1(a2413)) <=> ((~hskp9) | c2_1(a2413))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3204,axiom,((~hskp9) | c2_1(a2413)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause74')).
% 1.31/1.50 tff(3205,plain,
% 1.31/1.50 ((~hskp9) | c2_1(a2413)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3204, 3203])).
% 1.31/1.50 tff(3206,plain,
% 1.31/1.50 ((~hskp9) | c2_1(a2413)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3205, 3203])).
% 1.31/1.50 tff(3207,plain,
% 1.31/1.50 ((~hskp9) | c2_1(a2413)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3206, 3203])).
% 1.31/1.50 tff(3208,plain,
% 1.31/1.50 ((~hskp9) | c2_1(a2413)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3207, 3203])).
% 1.31/1.50 tff(3209,plain,
% 1.31/1.50 ((~hskp9) | c2_1(a2413)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3208, 3203])).
% 1.31/1.50 tff(3210,plain,
% 1.31/1.50 (c2_1(a2413)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3209, 3190])).
% 1.31/1.50 tff(3211,assumption,(~hskp4), introduced(assumption)).
% 1.31/1.50 tff(3212,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3213,plain,
% 1.31/1.50 ((hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413))) <=> (hskp4 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3214,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c1_1(a2432))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[3213])).
% 1.31/1.50 tff(3215,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[3214, 3212])).
% 1.31/1.50 tff(3216,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(3217,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c1_1(a2432))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3216, 3215])).
% 1.31/1.50 tff(3218,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3217, 192, 3211, 1252, 1255, 3210, 1251, 3202, 3196, 982])).
% 1.31/1.50 tff(3219,plain,((~hskp9) | hskp4 | (~c1_1(a2432)) | (~c3_1(a2432)) | c0_1(a2432)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(3220,plain,
% 1.31/1.50 (~hskp9),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3219, 3189, 1252, 1255, 1251])).
% 1.31/1.50 tff(3221,plain,
% 1.31/1.50 (((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp1 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp1 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3222,plain,
% 1.31/1.50 ((hskp9 | hskp1 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432))) <=> (hskp9 | hskp1 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3223,plain,
% 1.31/1.50 (((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp1 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp1 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[3222])).
% 1.31/1.50 tff(3224,plain,
% 1.31/1.50 (((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp1 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)))) <=> ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp1 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[3223, 3221])).
% 1.31/1.50 tff(3225,plain,
% 1.31/1.50 ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp9 | hskp1 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(3226,plain,
% 1.31/1.50 ((~![U: $i] : (hskp9 | hskp1 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp9 | hskp1 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2432)) | (~c1_1(a2432))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3225, 3224])).
% 1.31/1.50 tff(3227,plain,
% 1.31/1.50 (hskp9 | hskp1),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3226, 192, 1252, 1255, 1251, 32])).
% 1.31/1.50 tff(3228,plain,
% 1.31/1.50 (hskp1),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3227, 3220])).
% 1.31/1.50 tff(3229,plain,
% 1.31/1.50 (~c3_1(a2403)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[2291, 3228])).
% 1.31/1.50 tff(3230,plain,
% 1.31/1.50 (~c2_1(a2403)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[2297, 3228])).
% 1.31/1.50 tff(3231,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3232,plain,
% 1.31/1.50 (((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3233,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[3232])).
% 1.31/1.50 tff(3234,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[3233, 3231])).
% 1.31/1.50 tff(3235,plain,
% 1.31/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(3236,plain,
% 1.31/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c3_1(a2432)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3235, 3234])).
% 1.31/1.50 tff(3237,plain,
% 1.31/1.50 (c0_1(a2403)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3236, 192, 1252, 1255, 2052, 2054, 2053, 3230, 3229, 63, 2124])).
% 1.31/1.50 tff(3238,plain,
% 1.31/1.50 (c1_1(a2403)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[2305, 3228])).
% 1.31/1.50 tff(3239,plain,
% 1.31/1.50 (hskp20),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3107, 1252, 1255, 1251])).
% 1.31/1.50 tff(3240,plain,
% 1.31/1.50 (~c2_1(a2435)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[802, 3239])).
% 1.31/1.50 tff(3241,plain,
% 1.31/1.50 (~c0_1(a2435)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[754, 3239])).
% 1.31/1.50 tff(3242,plain,
% 1.31/1.50 (c1_1(a2435)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[2412, 192, 1252, 1255, 3238, 3241, 3240, 3230, 3229, 11, 2124])).
% 1.31/1.50 tff(3243,plain,
% 1.31/1.50 (~hskp29),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[2443, 3242, 498, 3229, 3230, 3241, 3240, 3238])).
% 1.31/1.50 tff(3244,plain,
% 1.31/1.50 (hskp0),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[2543, 3243, 2124])).
% 1.31/1.50 tff(3245,plain,
% 1.31/1.50 (~c1_1(a2402)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1512, 3244])).
% 1.31/1.50 tff(3246,plain,
% 1.31/1.50 (c3_1(a2402)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1520, 3244])).
% 1.31/1.50 tff(3247,plain,
% 1.31/1.50 (c3_1(a2435)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[748, 3239])).
% 1.31/1.50 tff(3248,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c2_1(a2435) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c2_1(a2435) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3249,plain,
% 1.31/1.50 ((hskp30 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435))) <=> (hskp30 | c2_1(a2435) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3250,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c2_1(a2435) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[3249])).
% 1.31/1.50 tff(3251,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c2_1(a2435) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[3250, 3248])).
% 1.31/1.50 tff(3252,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(3253,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c2_1(a2435) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3252, 3251])).
% 1.31/1.50 tff(3254,plain,
% 1.31/1.50 (hskp30),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3253, 192, 3247, 3238, 3240, 3229, 564, 3242, 3237])).
% 1.31/1.50 tff(3255,plain,
% 1.31/1.50 (c3_1(a2450)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[582, 3254])).
% 1.31/1.50 tff(3256,plain,
% 1.31/1.50 (c1_1(a2450)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[590, 3254])).
% 1.31/1.50 tff(3257,plain,
% 1.31/1.50 (c0_1(a2450)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[598, 3254])).
% 1.31/1.50 tff(3258,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2403) | c3_1(a2403) | c1_1(a2402) | (~ndr1_0) | (~c2_1(a2402)) | (~c3_1(a2402)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | c1_1(a2402) | (~ndr1_0) | (~c2_1(a2402)) | (~c3_1(a2402)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3259,plain,
% 1.31/1.50 (((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2402) | (~c2_1(a2402)) | (~c3_1(a2402))) <=> (c2_1(a2403) | c3_1(a2403) | c1_1(a2402) | (~ndr1_0) | (~c2_1(a2402)) | (~c3_1(a2402)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3260,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2402) | (~c2_1(a2402)) | (~c3_1(a2402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2403) | c3_1(a2403) | c1_1(a2402) | (~ndr1_0) | (~c2_1(a2402)) | (~c3_1(a2402)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[3259])).
% 1.31/1.50 tff(3261,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2402) | (~c2_1(a2402)) | (~c3_1(a2402)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | c1_1(a2402) | (~ndr1_0) | (~c2_1(a2402)) | (~c3_1(a2402)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[3260, 3258])).
% 1.31/1.50 tff(3262,plain,
% 1.31/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2402) | (~c2_1(a2402)) | (~c3_1(a2402)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(3263,plain,
% 1.31/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | c1_1(a2402) | (~ndr1_0) | (~c2_1(a2402)) | (~c3_1(a2402)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3262, 3261])).
% 1.31/1.50 tff(3264,plain,
% 1.31/1.50 (~c2_1(a2402)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3263, 192, 3257, 3256, 3255, 3246, 3230, 3229, 3245, 554, 3237])).
% 1.31/1.50 tff(3265,plain,
% 1.31/1.50 (^[V: $i, U: $i] : refl((hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(3266,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[3265])).
% 1.31/1.50 tff(3267,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3268,plain,
% 1.31/1.50 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | 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) | c1_1(U) | (~c3_1(U)) | c2_1(U) | (~c1_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | (~c1_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | (~c1_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | (~c1_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.31/1.50 inference(bind,[status(th)],[])).
% 1.31/1.50 tff(3269,plain,
% 1.31/1.50 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp4) <=> ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.31/1.50 inference(quant_intro,[status(thm)],[3268])).
% 1.31/1.50 tff(3270,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 1.31/1.50 tff(3271,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3270, 3269])).
% 1.31/1.50 tff(3272,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3271, 3267])).
% 1.31/1.50 tff(3273,plain,(
% 1.31/1.50 ![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.31/1.50 inference(skolemize,[status(sab)],[3272])).
% 1.31/1.50 tff(3274,plain,
% 1.31/1.50 (![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3273, 3266])).
% 1.31/1.50 tff(3275,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a2418) | c1_1(a2402) | (~ndr1_0) | c2_1(a2402) | (~c3_1(a2402)) | c3_1(a2418) | (~c1_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a2418) | c1_1(a2402) | (~ndr1_0) | c2_1(a2402) | (~c3_1(a2402)) | c3_1(a2418) | (~c1_1(a2418)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3276,plain,
% 1.31/1.50 ((hskp4 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | c2_1(a2402) | c0_1(a2418) | c3_1(a2418) | (~c1_1(a2418))) <=> (hskp4 | c0_1(a2418) | c1_1(a2402) | (~ndr1_0) | c2_1(a2402) | (~c3_1(a2402)) | c3_1(a2418) | (~c1_1(a2418)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3277,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | c2_1(a2402) | c0_1(a2418) | c3_1(a2418) | (~c1_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp4 | c0_1(a2418) | c1_1(a2402) | (~ndr1_0) | c2_1(a2402) | (~c3_1(a2402)) | c3_1(a2418) | (~c1_1(a2418))))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[3276])).
% 1.31/1.50 tff(3278,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | c2_1(a2402) | c0_1(a2418) | c3_1(a2418) | (~c1_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a2418) | c1_1(a2402) | (~ndr1_0) | c2_1(a2402) | (~c3_1(a2402)) | c3_1(a2418) | (~c1_1(a2418)))),
% 1.31/1.50 inference(transitivity,[status(thm)],[3277, 3275])).
% 1.31/1.50 tff(3279,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp4 | (~ndr1_0) | c1_1(a2402) | (~c3_1(a2402)) | c2_1(a2402) | c0_1(a2418) | c3_1(a2418) | (~c1_1(a2418)))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(3280,plain,
% 1.31/1.50 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | c2_1(U) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp4 | c0_1(a2418) | c1_1(a2402) | (~ndr1_0) | c2_1(a2402) | (~c3_1(a2402)) | c3_1(a2418) | (~c1_1(a2418))),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3279, 3278])).
% 1.31/1.50 tff(3281,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3280, 192, 3189, 2052, 3246, 2053, 3245, 3274, 2125, 3264])).
% 1.31/1.50 tff(3282,plain,(hskp15 | (~c1_1(a2418)) | c0_1(a2418) | (~c1_1(a2432)) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2418))), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(3283,plain,
% 1.31/1.50 (hskp15),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3282, 3182, 3181, 3100, 3098, 3099, 3180])).
% 1.31/1.50 tff(3284,plain,
% 1.31/1.50 (c1_1(a2422)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[522, 3283])).
% 1.31/1.50 tff(3285,plain,
% 1.31/1.50 (~c2_1(a2422)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[528, 3283])).
% 1.31/1.50 tff(3286,plain,
% 1.31/1.50 (c3_1(a2422)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[514, 3283])).
% 1.31/1.50 tff(3287,plain,
% 1.31/1.50 (hskp9 | hskp1),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3226, 192, 3100, 3099, 3098, 32])).
% 1.31/1.50 tff(3288,plain,
% 1.31/1.50 (hskp9),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3287, 22])).
% 1.31/1.50 tff(3289,plain,
% 1.31/1.50 (~c1_1(a2413)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3195, 3288])).
% 1.31/1.50 tff(3290,plain,
% 1.31/1.50 (~c0_1(a2413)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3201, 3288])).
% 1.31/1.50 tff(3291,plain,
% 1.31/1.50 (c2_1(a2413)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3209, 3288])).
% 1.31/1.50 tff(3292,plain,
% 1.31/1.50 (c2_1(a2414)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3123, 3121, 566, 2147, 722, 565, 567])).
% 1.31/1.50 tff(3293,assumption,(~c1_1(a2413)), introduced(assumption)).
% 1.31/1.50 tff(3294,assumption,(~c0_1(a2413)), introduced(assumption)).
% 1.31/1.50 tff(3295,assumption,(c2_1(a2413)), introduced(assumption)).
% 1.31/1.50 tff(3296,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3297,plain,
% 1.31/1.50 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3298,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435)))),
% 1.31/1.50 inference(monotonicity,[status(thm)],[3297])).
% 1.31/1.50 tff(3299,plain,
% 1.31/1.50 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435))),
% 1.31/1.50 inference(transitivity,[status(thm)],[3298, 3296])).
% 1.31/1.50 tff(3300,plain,
% 1.31/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.31/1.50 inference(quant_inst,[status(thm)],[])).
% 1.31/1.50 tff(3301,plain,
% 1.31/1.50 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435)),
% 1.31/1.50 inference(modus_ponens,[status(thm)],[3300, 3299])).
% 1.31/1.50 tff(3302,plain,
% 1.31/1.50 ((~c2_1(a2414)) | c1_1(a2435)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3301, 192, 2628, 3295, 2147, 722, 888, 3294, 3293, 21])).
% 1.31/1.50 tff(3303,plain,
% 1.31/1.50 ($false),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3302, 3292, 3121])).
% 1.31/1.50 tff(3304,plain,(c1_1(a2435) | (~c2_1(a2413)) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422))), inference(lemma,lemma(discharge,[]))).
% 1.31/1.50 tff(3305,plain,
% 1.31/1.50 (c1_1(a2435)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3304, 3291, 3110, 3109, 3290, 3289, 3286, 3285, 3284])).
% 1.31/1.50 tff(3306,plain,
% 1.31/1.50 (hskp4),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[3219, 3288, 3100, 3099, 3098])).
% 1.31/1.50 tff(3307,plain,
% 1.31/1.50 (~c2_1(a2407)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1416, 3306])).
% 1.31/1.50 tff(3308,plain,
% 1.31/1.50 (~c1_1(a2407)),
% 1.31/1.50 inference(unit_resolution,[status(thm)],[1410, 3306])).
% 1.31/1.50 tff(3309,plain,
% 1.31/1.50 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c2_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.31/1.50 inference(rewrite,[status(thm)],[])).
% 1.31/1.50 tff(3310,plain,
% 1.31/1.50 ((hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413))) <=> (hskp5 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3311,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c2_1(a2432))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[3310])).
% 1.31/1.51 tff(3312,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c2_1(a2432)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[3311, 3309])).
% 1.31/1.51 tff(3313,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2432) | (~c3_1(a2432)) | (~c2_1(a2432)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(3314,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2432) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2432)) | (~c2_1(a2432))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[3313, 3312])).
% 1.31/1.51 tff(3315,plain,
% 1.31/1.51 (~c2_1(a2432)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3314, 192, 1955, 1255, 3210, 1251, 3202, 3196, 1965])).
% 1.31/1.51 tff(3316,plain,
% 1.31/1.51 (hskp4),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3217, 192, 1252, 1255, 3210, 1251, 3202, 3196, 982])).
% 1.31/1.51 tff(3317,plain,
% 1.31/1.51 (~c2_1(a2407)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1416, 3316])).
% 1.31/1.51 tff(3318,plain,
% 1.31/1.51 (~c1_1(a2407)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1410, 3316])).
% 1.31/1.51 tff(3319,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2418) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2418)) | (~c2_1(a2418)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2418) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3320,plain,
% 1.31/1.51 ((hskp5 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413))) <=> (hskp5 | c0_1(a2418) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3321,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2418) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2418)) | (~c2_1(a2418))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[3320])).
% 1.31/1.51 tff(3322,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2418) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2418)) | (~c2_1(a2418)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[3321, 3319])).
% 1.31/1.51 tff(3323,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2418) | (~c3_1(a2418)) | (~c2_1(a2418)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(3324,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2418) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2418)) | (~c2_1(a2418))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[3323, 3322])).
% 1.31/1.51 tff(3325,plain,
% 1.31/1.51 (~c3_1(a2418)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3324, 192, 1955, 2054, 3210, 2053, 3202, 3196, 1965])).
% 1.31/1.51 tff(3326,plain,
% 1.31/1.51 (hskp6 | c3_1(a2418)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[2090, 192, 629, 2052, 2054, 2087])).
% 1.31/1.51 tff(3327,plain,
% 1.31/1.51 (hskp6),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3326, 3325])).
% 1.31/1.51 tff(3328,plain,
% 1.31/1.51 (~c2_1(a2410)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[895, 3327])).
% 1.31/1.51 tff(3329,plain,
% 1.31/1.51 (c0_1(a2407)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1949, 3316])).
% 1.31/1.51 tff(3330,plain,
% 1.31/1.51 (c1_1(a2410)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[903, 3327])).
% 1.31/1.51 tff(3331,plain,
% 1.31/1.51 (c0_1(a2410)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[911, 3327])).
% 1.31/1.51 tff(3332,plain,
% 1.31/1.51 ($false),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[2136, 192, 1252, 3331, 3330, 3329, 1251, 3328, 3318, 3317, 1879, 3315])).
% 1.31/1.51 tff(3333,plain,((~hskp9) | (~c1_1(a2432)) | c0_1(a2432) | hskp23 | (~c1_1(a2418)) | (~c2_1(a2418)) | (~c3_1(a2432)) | hskp5 | c0_1(a2418)), inference(lemma,lemma(discharge,[]))).
% 1.31/1.51 tff(3334,plain,
% 1.31/1.51 (hskp5),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3333, 3288, 3098, 629, 3182, 3180, 3099, 3100, 3181])).
% 1.31/1.51 tff(3335,plain,
% 1.31/1.51 (~c2_1(a2408)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[373, 3334])).
% 1.31/1.51 tff(3336,plain,
% 1.31/1.51 (c0_1(a2407)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1949, 3306])).
% 1.31/1.51 tff(3337,plain,
% 1.31/1.51 (c0_1(a2408)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[381, 3334])).
% 1.31/1.51 tff(3338,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3339,plain,
% 1.31/1.51 (((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432))) <=> (c0_1(a2432) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3340,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2432) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2432) | (~c1_1(a2432))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[3339])).
% 1.31/1.51 tff(3341,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2432) | (~c1_1(a2432)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[3340, 3338])).
% 1.31/1.51 tff(3342,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2407) | c1_1(a2407) | (~c0_1(a2407)) | c2_1(a2432) | c0_1(a2432) | (~c1_1(a2432)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(3343,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2432) | c2_1(a2408) | c1_1(a2407) | c2_1(a2407) | (~ndr1_0) | (~c0_1(a2407)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2432) | (~c1_1(a2432))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[3342, 3341])).
% 1.31/1.51 tff(3344,plain,
% 1.31/1.51 (~c1_1(a2408)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3343, 192, 3100, 3337, 3336, 3098, 3335, 3308, 3307, 1879, 1869])).
% 1.31/1.51 tff(3345,plain,
% 1.31/1.51 (c3_1(a2408)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[396, 3334])).
% 1.31/1.51 tff(3346,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2413) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2413)) | (~c3_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2413) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2413)) | (~c3_1(a2413)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3347,plain,
% 1.31/1.51 ((hskp1 | (~ndr1_0) | c1_1(a2413) | (~c3_1(a2413)) | (~c2_1(a2413)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp1 | c1_1(a2413) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2413)) | (~c3_1(a2413)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3348,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2413) | (~c3_1(a2413)) | (~c2_1(a2413)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2413) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2413)) | (~c3_1(a2413))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[3347])).
% 1.31/1.51 tff(3349,plain,
% 1.31/1.51 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2413) | (~c3_1(a2413)) | (~c2_1(a2413)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2413) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2413)) | (~c3_1(a2413)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[3348, 3346])).
% 1.31/1.51 tff(3350,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2413) | (~c3_1(a2413)) | (~c2_1(a2413)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(3351,plain,
% 1.31/1.51 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2413) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2413)) | (~c3_1(a2413))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[3350, 3349])).
% 1.31/1.51 tff(3352,plain,
% 1.31/1.51 (~c3_1(a2413)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3351, 192, 22, 3291, 3345, 3289, 3335, 1007, 3344])).
% 1.31/1.51 tff(3353,plain,
% 1.31/1.51 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c3_1(a2413))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c3_1(a2413))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3354,plain,
% 1.31/1.51 ((hskp16 | hskp12 | (~ndr1_0) | c3_1(a2413) | c1_1(a2413) | (~c2_1(a2413))) <=> (hskp16 | hskp12 | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c3_1(a2413))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3355,plain,
% 1.31/1.51 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2413) | c1_1(a2413) | (~c2_1(a2413)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c3_1(a2413)))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[3354])).
% 1.31/1.51 tff(3356,plain,
% 1.31/1.51 (((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2413) | c1_1(a2413) | (~c2_1(a2413)))) <=> ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c3_1(a2413))),
% 1.31/1.51 inference(transitivity,[status(thm)],[3355, 3353])).
% 1.31/1.51 tff(3357,plain,
% 1.31/1.51 ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | (hskp16 | hskp12 | (~ndr1_0) | c3_1(a2413) | c1_1(a2413) | (~c2_1(a2413)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(3358,plain,
% 1.31/1.51 ((~![U: $i] : (hskp16 | hskp12 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)))) | hskp16 | hskp12 | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c3_1(a2413)),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[3357, 3356])).
% 1.31/1.51 tff(3359,plain,
% 1.31/1.51 (hskp12 | c3_1(a2413)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3358, 192, 64, 3291, 3289, 258])).
% 1.31/1.51 tff(3360,plain,
% 1.31/1.51 (hskp12),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3359, 3352])).
% 1.31/1.51 tff(3361,plain,
% 1.31/1.51 (~c1_1(a2417)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[217, 3360])).
% 1.31/1.51 tff(3362,plain,
% 1.31/1.51 (c3_1(a2417)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[231, 3360])).
% 1.31/1.51 tff(3363,plain,
% 1.31/1.51 (~c2_1(a2417)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[1016, 192, 22, 3362, 3345, 3361, 3335, 1007, 3344])).
% 1.31/1.51 tff(3364,plain,
% 1.31/1.51 (~c0_1(a2417)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[223, 3360])).
% 1.31/1.51 tff(3365,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3366,plain,
% 1.31/1.51 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3367,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417)))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[3366])).
% 1.31/1.51 tff(3368,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417))),
% 1.31/1.51 inference(transitivity,[status(thm)],[3367, 3365])).
% 1.31/1.51 tff(3369,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(3370,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2417) | c1_1(a2417) | c1_1(a2414) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c0_1(a2414)) | (~c2_1(a2414)) | c2_1(a2417)),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[3369, 3368])).
% 1.31/1.51 tff(3371,plain,
% 1.31/1.51 (~c2_1(a2414)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3370, 192, 2628, 3291, 3364, 3361, 888, 3290, 3289, 21, 3363])).
% 1.31/1.51 tff(3372,plain,
% 1.31/1.51 (c1_1(a2435)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3123, 3371, 3286, 3110, 3109, 3285, 3284])).
% 1.31/1.51 tff(3373,plain,
% 1.31/1.51 ($false),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[2225, 192, 3125, 2628, 3109, 3364, 3361, 882, 1336, 3372, 3363, 3371])).
% 1.31/1.51 tff(3374,plain,(hskp1 | hskp16 | c2_1(a2432) | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.31/1.51 tff(3375,plain,
% 1.31/1.51 (hskp1),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3374, 1869, 64, 629])).
% 1.31/1.51 tff(3376,plain,
% 1.31/1.51 (~c3_1(a2403)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[2291, 3375])).
% 1.31/1.51 tff(3377,plain,
% 1.31/1.51 (~c2_1(a2403)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[2297, 3375])).
% 1.31/1.51 tff(3378,plain,
% 1.31/1.51 (c0_1(a2403)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3236, 192, 3100, 3099, 3182, 3180, 3181, 3377, 3376, 63, 1869])).
% 1.31/1.51 tff(3379,plain,
% 1.31/1.51 (c1_1(a2403)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[2305, 3375])).
% 1.31/1.51 tff(3380,plain,
% 1.31/1.51 (c1_1(a2435)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[2412, 192, 3100, 3099, 3379, 3110, 3109, 3377, 3376, 11, 1869])).
% 1.31/1.51 tff(3381,plain,
% 1.31/1.51 (hskp30),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3253, 192, 3125, 3379, 3109, 3376, 564, 3380, 3378])).
% 1.31/1.51 tff(3382,plain,
% 1.31/1.51 (c3_1(a2450)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[582, 3381])).
% 1.31/1.51 tff(3383,plain,
% 1.31/1.51 (c1_1(a2450)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[590, 3381])).
% 1.31/1.51 tff(3384,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3385,plain,
% 1.31/1.51 (((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3386,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[3385])).
% 1.31/1.51 tff(3387,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[3386, 3384])).
% 1.31/1.51 tff(3388,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(3389,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[3388, 3387])).
% 1.31/1.51 tff(3390,plain,
% 1.31/1.51 (~c2_1(a2450)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3389, 192, 3383, 3382, 2628, 3379, 888, 882, 3376, 1076, 3378])).
% 1.31/1.51 tff(3391,plain,
% 1.31/1.51 (c0_1(a2450)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[598, 3381])).
% 1.31/1.51 tff(3392,plain,
% 1.31/1.51 (hskp12),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[869, 192, 3391, 3383, 3382, 3125, 3110, 3109, 766])).
% 1.31/1.51 tff(3393,plain,
% 1.31/1.51 (~c1_1(a2417)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[217, 3392])).
% 1.31/1.51 tff(3394,plain,
% 1.31/1.51 (c3_1(a2417)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[231, 3392])).
% 1.31/1.51 tff(3395,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3396,plain,
% 1.31/1.51 (((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417))) <=> (c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3397,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417))))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[3396])).
% 1.31/1.51 tff(3398,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.31/1.51 inference(transitivity,[status(thm)],[3397, 3395])).
% 1.31/1.51 tff(3399,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2417) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(3400,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c2_1(a2417)) | (~c3_1(a2417))),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[3399, 3398])).
% 1.31/1.51 tff(3401,plain,
% 1.31/1.51 (~c2_1(a2417)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3400, 192, 3391, 3383, 3382, 3394, 3393, 3377, 3376, 554, 3378])).
% 1.31/1.51 tff(3402,plain,
% 1.31/1.51 (~c0_1(a2417)),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[223, 3392])).
% 1.31/1.51 tff(3403,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3404,plain,
% 1.31/1.51 (((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417))),
% 1.31/1.51 inference(rewrite,[status(thm)],[])).
% 1.31/1.51 tff(3405,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417)))),
% 1.31/1.51 inference(monotonicity,[status(thm)],[3404])).
% 1.31/1.51 tff(3406,plain,
% 1.31/1.51 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417))),
% 1.31/1.51 inference(transitivity,[status(thm)],[3405, 3403])).
% 1.31/1.51 tff(3407,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.31/1.51 inference(quant_inst,[status(thm)],[])).
% 1.31/1.51 tff(3408,plain,
% 1.31/1.51 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2417) | c1_1(a2417) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417)),
% 1.31/1.51 inference(modus_ponens,[status(thm)],[3407, 3406])).
% 1.31/1.51 tff(3409,plain,
% 1.31/1.51 ($false),
% 1.31/1.51 inference(unit_resolution,[status(thm)],[3408, 192, 3383, 3382, 3379, 3402, 3393, 3377, 3376, 11, 3401, 3390])).
% 1.31/1.51 tff(3410,plain,(c2_1(a2432) | hskp16 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.31/1.52 tff(3411,plain,
% 1.31/1.52 (c2_1(a2432)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3410, 629, 64])).
% 1.31/1.52 tff(3412,plain,
% 1.31/1.52 ((~c1_1(a2408)) | (~c1_1(a2435))),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[2038, 192, 3337, 3336, 3110, 3109, 3335, 3308, 3307, 1879])).
% 1.31/1.52 tff(3413,plain,
% 1.31/1.52 (~c1_1(a2408)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3412, 3305])).
% 1.31/1.52 tff(3414,plain,
% 1.31/1.52 (c1_1(a2408) | (~c3_1(a2413))),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3351, 192, 22, 3291, 3345, 3289, 3335, 1007])).
% 1.31/1.52 tff(3415,plain,
% 1.31/1.52 (~c3_1(a2413)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3414, 3413])).
% 1.31/1.52 tff(3416,plain,
% 1.31/1.52 (hskp12),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3359, 3415])).
% 1.31/1.52 tff(3417,plain,
% 1.31/1.52 (~c1_1(a2417)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[217, 3416])).
% 1.31/1.52 tff(3418,plain,
% 1.31/1.52 (c3_1(a2417)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[231, 3416])).
% 1.31/1.52 tff(3419,plain,
% 1.31/1.52 (~c2_1(a2417)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1016, 192, 22, 3418, 3345, 3417, 3335, 1007, 3413])).
% 1.31/1.52 tff(3420,plain,
% 1.31/1.52 (~c0_1(a2417)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[223, 3416])).
% 1.31/1.52 tff(3421,plain,
% 1.31/1.52 (~c2_1(a2414)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3370, 192, 2628, 3291, 3420, 3417, 888, 3290, 3289, 21, 3419])).
% 1.31/1.52 tff(3422,plain,
% 1.31/1.52 ($false),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[2225, 192, 3125, 2628, 3109, 3420, 3417, 882, 1336, 3305, 3419, 3421])).
% 1.31/1.52 tff(3423,plain,(hskp1 | hskp16 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.31/1.52 tff(3424,plain,
% 1.31/1.52 (hskp1),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3423, 629, 64])).
% 1.31/1.52 tff(3425,plain,
% 1.31/1.52 (~c3_1(a2403)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[2291, 3424])).
% 1.31/1.52 tff(3426,plain,
% 1.31/1.52 (~c2_1(a2403)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[2297, 3424])).
% 1.31/1.52 tff(3427,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2432) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2432) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3428,plain,
% 1.31/1.52 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c0_1(a2432) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3429,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2432) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432))))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[3428])).
% 1.31/1.52 tff(3430,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2432) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.52 inference(transitivity,[status(thm)],[3429, 3427])).
% 1.31/1.52 tff(3431,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2432) | (~c1_1(a2432)) | (~c2_1(a2432)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(3432,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2432) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2432)) | (~c1_1(a2432))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[3431, 3430])).
% 1.31/1.52 tff(3433,plain,
% 1.31/1.52 (c0_1(a2403)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3432, 192, 3100, 3284, 3286, 3098, 3285, 3426, 3425, 63, 3411])).
% 1.31/1.52 tff(3434,plain,
% 1.31/1.52 (c1_1(a2403)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[2305, 3424])).
% 1.31/1.52 tff(3435,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3436,plain,
% 1.31/1.52 (((~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3437,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432))))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[3436])).
% 1.31/1.52 tff(3438,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)))),
% 1.31/1.52 inference(transitivity,[status(thm)],[3437, 3435])).
% 1.31/1.52 tff(3439,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(3440,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2432)) | (~c2_1(a2432)) | (~c1_1(a2432))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[3439, 3438])).
% 1.31/1.52 tff(3441,plain,
% 1.31/1.52 ($false),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3440, 192, 3100, 3099, 2628, 3434, 888, 882, 3425, 1076, 3411, 3433])).
% 1.31/1.52 tff(3442,plain,(hskp23 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.31/1.52 tff(3443,plain,
% 1.31/1.52 (hskp23),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3442, 64])).
% 1.31/1.52 tff(3444,plain,
% 1.31/1.52 (~c0_1(a2455)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[480, 3443])).
% 1.31/1.52 tff(3445,plain,
% 1.31/1.52 (c3_1(a2455)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[488, 3443])).
% 1.31/1.52 tff(3446,plain,
% 1.31/1.52 (c2_1(a2455)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[496, 3443])).
% 1.31/1.52 tff(3447,plain,
% 1.31/1.52 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2455) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2455)) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2455) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3448,plain,
% 1.31/1.52 ((hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413))) <=> (hskp5 | c0_1(a2455) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3449,plain,
% 1.31/1.52 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2455) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2455)) | (~c2_1(a2455))))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[3448])).
% 1.31/1.52 tff(3450,plain,
% 1.31/1.52 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2455) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2455)) | (~c2_1(a2455)))),
% 1.31/1.52 inference(transitivity,[status(thm)],[3449, 3447])).
% 1.31/1.52 tff(3451,plain,
% 1.31/1.52 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(3452,plain,
% 1.31/1.52 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2455) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | (~c3_1(a2455)) | (~c2_1(a2455))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[3451, 3450])).
% 1.31/1.52 tff(3453,plain,
% 1.31/1.52 (hskp5),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3452, 192, 3446, 3445, 3291, 3444, 3290, 3289, 1965])).
% 1.31/1.52 tff(3454,plain,
% 1.31/1.52 (~c2_1(a2408)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[373, 3453])).
% 1.31/1.52 tff(3455,plain,
% 1.31/1.52 (c0_1(a2408)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[381, 3453])).
% 1.31/1.52 tff(3456,plain,
% 1.31/1.52 (~c1_1(a2408)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[2038, 192, 3455, 3336, 3110, 3109, 3454, 3308, 3307, 1879, 3305])).
% 1.31/1.52 tff(3457,plain,
% 1.31/1.52 (c3_1(a2408)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[396, 3453])).
% 1.31/1.52 tff(3458,plain,
% 1.31/1.52 (~c3_1(a2413)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3351, 192, 22, 3291, 3457, 3289, 3454, 1007, 3456])).
% 1.31/1.52 tff(3459,plain,
% 1.31/1.52 (hskp12),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3359, 3458])).
% 1.31/1.52 tff(3460,plain,
% 1.31/1.52 (~c1_1(a2417)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[217, 3459])).
% 1.31/1.52 tff(3461,plain,
% 1.31/1.52 (c3_1(a2417)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[231, 3459])).
% 1.31/1.52 tff(3462,plain,
% 1.31/1.52 (~c2_1(a2417)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1016, 192, 22, 3461, 3457, 3460, 3454, 1007, 3456])).
% 1.31/1.52 tff(3463,plain,
% 1.31/1.52 (~c0_1(a2417)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[223, 3459])).
% 1.31/1.52 tff(3464,plain,
% 1.31/1.52 (~c2_1(a2414)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3370, 192, 2628, 3291, 3463, 3460, 888, 3290, 3289, 21, 3462])).
% 1.31/1.52 tff(3465,plain,
% 1.31/1.52 ($false),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[2225, 192, 3125, 2628, 3109, 3463, 3460, 882, 1336, 3305, 3462, 3464])).
% 1.31/1.52 tff(3466,plain,(hskp1 | hskp16), inference(lemma,lemma(discharge,[]))).
% 1.31/1.52 tff(3467,plain,
% 1.31/1.52 (hskp1),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3466, 64])).
% 1.31/1.52 tff(3468,plain,
% 1.31/1.52 (~c3_1(a2403)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[2291, 3467])).
% 1.31/1.52 tff(3469,plain,
% 1.31/1.52 (~c2_1(a2403)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[2297, 3467])).
% 1.31/1.52 tff(3470,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a2422) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2422) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3471,plain,
% 1.31/1.52 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c2_1(a2422) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3472,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a2422) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422))))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[3471])).
% 1.31/1.52 tff(3473,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2422) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422)))),
% 1.31/1.52 inference(transitivity,[status(thm)],[3472, 3470])).
% 1.31/1.52 tff(3474,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(3475,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2422) | c0_1(a2418) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2422)) | (~c3_1(a2422))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[3474, 3473])).
% 1.31/1.52 tff(3476,plain,
% 1.31/1.52 (c0_1(a2403)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3475, 192, 3284, 3286, 3182, 3180, 3285, 3181, 3469, 3468, 63])).
% 1.31/1.52 tff(3477,plain,
% 1.31/1.52 (c1_1(a2403)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[2305, 3467])).
% 1.31/1.52 tff(3478,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3479,plain,
% 1.31/1.52 (((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3480,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455))))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[3479])).
% 1.31/1.52 tff(3481,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.31/1.52 inference(transitivity,[status(thm)],[3480, 3478])).
% 1.31/1.52 tff(3482,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(3483,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2414) | c3_1(a2414) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | (~c0_1(a2414)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455))),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[3482, 3481])).
% 1.31/1.52 tff(3484,plain,
% 1.31/1.52 (~c1_1(a2455)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3483, 192, 3446, 3445, 2628, 3477, 888, 882, 3468, 1076, 3476])).
% 1.31/1.52 tff(3485,plain,
% 1.31/1.52 (c1_1(a2435)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[2467, 192, 3284, 3286, 3477, 3110, 3109, 3285, 3469, 3468, 11])).
% 1.31/1.52 tff(3486,plain,
% 1.31/1.52 (hskp30),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3253, 192, 3125, 3477, 3109, 3468, 564, 3485, 3476])).
% 1.31/1.52 tff(3487,plain,
% 1.31/1.52 (c3_1(a2450)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[582, 3486])).
% 1.31/1.52 tff(3488,plain,
% 1.31/1.52 (c1_1(a2450)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[590, 3486])).
% 1.31/1.52 tff(3489,plain,
% 1.31/1.52 (c0_1(a2450)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[598, 3486])).
% 1.31/1.52 tff(3490,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3491,plain,
% 1.31/1.52 (((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3492,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[3491])).
% 1.31/1.52 tff(3493,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.52 inference(transitivity,[status(thm)],[3492, 3490])).
% 1.31/1.52 tff(3494,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(3495,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[3494, 3493])).
% 1.31/1.52 tff(3496,plain,
% 1.31/1.52 ($false),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3495, 192, 3489, 3488, 3487, 3446, 3445, 3469, 3468, 554, 3476, 3484])).
% 1.31/1.52 tff(3497,plain,(hskp16), inference(lemma,lemma(discharge,[]))).
% 1.31/1.52 tff(3498,plain,
% 1.31/1.52 (~c3_1(a2425)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[411, 3497])).
% 1.31/1.52 tff(3499,plain,
% 1.31/1.52 (~c2_1(a2425)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[417, 3497])).
% 1.31/1.52 tff(3500,plain,
% 1.31/1.52 (c0_1(a2425)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[425, 3497])).
% 1.31/1.52 tff(3501,plain,
% 1.31/1.52 (hskp19 | hskp5),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[449, 192, 3500, 3499, 3498, 53])).
% 1.31/1.52 tff(3502,plain,
% 1.31/1.52 (hskp5),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3501, 43])).
% 1.31/1.52 tff(3503,plain,
% 1.31/1.52 (c0_1(a2408)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[381, 3502])).
% 1.31/1.52 tff(3504,plain,
% 1.31/1.52 (~c1_1(a2455)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3060, 192, 43, 497, 2628, 481, 888, 882, 85])).
% 1.31/1.52 tff(3505,plain,
% 1.31/1.52 (c3_1(a2408)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[396, 3502])).
% 1.31/1.52 tff(3506,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3507,plain,
% 1.31/1.52 (((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3508,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[3507])).
% 1.31/1.52 tff(3509,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.52 inference(transitivity,[status(thm)],[3508, 3506])).
% 1.31/1.52 tff(3510,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(3511,plain,
% 1.31/1.52 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[3510, 3509])).
% 1.31/1.52 tff(3512,plain,
% 1.31/1.52 (~c1_1(a2408)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3511, 192, 497, 489, 3500, 3503, 3505, 3499, 3498, 554, 3504])).
% 1.31/1.52 tff(3513,plain,
% 1.31/1.52 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2455) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2455) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3514,plain,
% 1.31/1.52 ((hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455))) <=> (hskp29 | c0_1(a2455) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3515,plain,
% 1.31/1.52 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | c0_1(a2455) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.31/1.52 inference(monotonicity,[status(thm)],[3514])).
% 1.31/1.52 tff(3516,plain,
% 1.31/1.52 (((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2455) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.52 inference(transitivity,[status(thm)],[3515, 3513])).
% 1.31/1.52 tff(3517,plain,
% 1.31/1.52 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp29 | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c0_1(a2408)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)))),
% 1.31/1.52 inference(quant_inst,[status(thm)],[])).
% 1.31/1.52 tff(3518,plain,
% 1.31/1.52 ((~![V: $i, U: $i] : (hskp29 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp29 | c0_1(a2455) | (~ndr1_0) | c1_1(a2408) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.31/1.52 inference(modus_ponens,[status(thm)],[3517, 3516])).
% 1.31/1.52 tff(3519,plain,
% 1.31/1.52 (hskp29),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[3518, 192, 497, 3503, 3505, 481, 1039, 3512, 3504])).
% 1.31/1.52 tff(3520,plain,
% 1.31/1.52 (c3_1(a2409)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1064, 3519])).
% 1.31/1.52 tff(3521,plain,
% 1.31/1.52 (c0_1(a2409)),
% 1.31/1.52 inference(unit_resolution,[status(thm)],[1675, 3519])).
% 1.31/1.52 tff(3522,plain,
% 1.31/1.52 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.31/1.52 inference(rewrite,[status(thm)],[])).
% 1.31/1.52 tff(3523,plain,
% 1.31/1.52 (((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3524,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[3523])).
% 1.37/1.53 tff(3525,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.37/1.53 inference(transitivity,[status(thm)],[3524, 3522])).
% 1.37/1.53 tff(3526,plain,
% 1.37/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2409)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(3527,plain,
% 1.37/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2409)) | (~c3_1(a2409)) | (~c1_1(a2409)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[3526, 3525])).
% 1.37/1.53 tff(3528,plain,
% 1.37/1.53 (~c1_1(a2409)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3527, 192, 3521, 3520, 497, 489, 3500, 3499, 3498, 554, 3504])).
% 1.37/1.53 tff(3529,plain,
% 1.37/1.53 (~c2_1(a2408)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[373, 3502])).
% 1.37/1.53 tff(3530,plain,
% 1.37/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3531,plain,
% 1.37/1.53 ((hskp1 | (~ndr1_0) | c1_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp1 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3532,plain,
% 1.37/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[3531])).
% 1.37/1.53 tff(3533,plain,
% 1.37/1.53 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.37/1.53 inference(transitivity,[status(thm)],[3532, 3530])).
% 1.37/1.53 tff(3534,plain,
% 1.37/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(3535,plain,
% 1.37/1.53 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 1.37/1.53 tff(3536,plain,
% 1.37/1.53 (hskp1),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3535, 192, 497, 489, 3505, 3529, 1007, 3512, 3504])).
% 1.37/1.53 tff(3537,plain,
% 1.37/1.53 (~c3_1(a2403)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2291, 3536])).
% 1.37/1.53 tff(3538,plain,
% 1.37/1.53 (~c2_1(a2403)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2297, 3536])).
% 1.37/1.53 tff(3539,plain,
% 1.37/1.53 (c1_1(a2403)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2305, 3536])).
% 1.37/1.53 tff(3540,plain,
% 1.37/1.53 (c2_1(a2409)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[1056, 3519])).
% 1.37/1.53 tff(3541,plain,
% 1.37/1.53 ($false),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2441, 192, 3521, 3540, 3520, 3539, 3538, 3537, 2316, 3528])).
% 1.37/1.53 tff(3542,plain,((~hskp23) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.37/1.53 tff(3543,plain,
% 1.37/1.53 (~hskp23),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3542, 43])).
% 1.37/1.53 tff(3544,plain,
% 1.37/1.53 ($false),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2648, 2602, 2610, 43, 629, 2594, 921])).
% 1.37/1.53 tff(3545,plain,(hskp25 | hskp19 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.37/1.53 tff(3546,plain,
% 1.37/1.53 (hskp25),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3545, 3543, 43])).
% 1.37/1.53 tff(3547,plain,
% 1.37/1.53 (~c0_1(a2478)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[120, 3546])).
% 1.37/1.53 tff(3548,plain,
% 1.37/1.53 (c2_1(a2478)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[114, 3546])).
% 1.37/1.53 tff(3549,plain,
% 1.37/1.53 (hskp25),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3545, 629, 43])).
% 1.37/1.53 tff(3550,plain,
% 1.37/1.53 (~c0_1(a2478)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[120, 3549])).
% 1.37/1.53 tff(3551,plain,
% 1.37/1.53 (c2_1(a2478)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[114, 3549])).
% 1.37/1.53 tff(3552,plain,
% 1.37/1.53 (~c1_1(a2478)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2681, 192, 43, 3551, 2628, 3550, 888, 882, 85])).
% 1.37/1.53 tff(3553,plain,
% 1.37/1.53 (~c3_1(a2478)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[126, 3549])).
% 1.37/1.53 tff(3554,assumption,(hskp1), introduced(assumption)).
% 1.37/1.53 tff(3555,plain,
% 1.37/1.53 (~c2_1(a2403)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2297, 3554])).
% 1.37/1.53 tff(3556,plain,
% 1.37/1.53 (~c3_1(a2403)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2291, 3554])).
% 1.37/1.53 tff(3557,plain,
% 1.37/1.53 (hskp10),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[796, 629, 722, 43, 279, 259, 260])).
% 1.37/1.53 tff(3558,plain,
% 1.37/1.53 (~c3_1(a2414)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[881, 3557])).
% 1.37/1.53 tff(3559,plain,
% 1.37/1.53 (~c1_1(a2414)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[887, 3557])).
% 1.37/1.53 tff(3560,plain,
% 1.37/1.53 (c0_1(a2414)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[1027, 3557])).
% 1.37/1.53 tff(3561,plain,
% 1.37/1.53 (~c1_1(a2478)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2681, 192, 43, 260, 3560, 279, 3559, 3558, 85])).
% 1.37/1.53 tff(3562,assumption,(~c1_1(a2403)), introduced(assumption)).
% 1.37/1.53 tff(3563,assumption,(c0_1(a2403)), introduced(assumption)).
% 1.37/1.53 tff(3564,plain,
% 1.37/1.53 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp10 | c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3565,plain,
% 1.37/1.53 ((hskp10 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403))) <=> (hskp10 | c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3566,plain,
% 1.37/1.53 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403))))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[3565])).
% 1.37/1.53 tff(3567,plain,
% 1.37/1.53 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp10 | c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)))),
% 1.37/1.53 inference(transitivity,[status(thm)],[3566, 3564])).
% 1.37/1.53 tff(3568,plain,
% 1.37/1.53 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(3569,plain,
% 1.37/1.53 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)))) | hskp10 | c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[3568, 3567])).
% 1.37/1.53 tff(3570,plain,
% 1.37/1.53 (hskp10 | c1_1(a2403) | (~c0_1(a2403))),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3569, 192, 2318, 2317, 95])).
% 1.37/1.53 tff(3571,plain,
% 1.37/1.53 (hskp10),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3570, 3563, 3562])).
% 1.37/1.53 tff(3572,plain,
% 1.37/1.53 (~c3_1(a2414)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[881, 3571])).
% 1.37/1.53 tff(3573,plain,
% 1.37/1.53 (~c1_1(a2414)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[887, 3571])).
% 1.37/1.53 tff(3574,plain,
% 1.37/1.53 (hskp5),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2936, 3563, 2317])).
% 1.37/1.53 tff(3575,plain,
% 1.37/1.53 (c0_1(a2408)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[381, 3574])).
% 1.37/1.53 tff(3576,plain,
% 1.37/1.53 (~c2_1(a2408)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[373, 3574])).
% 1.37/1.53 tff(3577,plain,
% 1.37/1.53 (c3_1(a2408)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[396, 3574])).
% 1.37/1.53 tff(3578,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a2403) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a2403) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3579,plain,
% 1.37/1.53 (((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c1_1(a2403) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3580,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c1_1(a2403) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435))))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[3579])).
% 1.37/1.53 tff(3581,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a2403) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 1.37/1.53 inference(transitivity,[status(thm)],[3580, 3578])).
% 1.37/1.53 tff(3582,plain,
% 1.37/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(3583,plain,
% 1.37/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c1_1(a2403) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c1_1(a2435))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[3582, 3581])).
% 1.37/1.53 tff(3584,plain,
% 1.37/1.53 (c0_1(a2435) | (~c1_1(a2408)) | (~c1_1(a2435))),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3583, 192, 767, 3562, 722, 611, 2318, 1879, 3563])).
% 1.37/1.53 tff(3585,plain,
% 1.37/1.53 (~c1_1(a2435)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3584, 2147, 756])).
% 1.37/1.53 tff(3586,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3587,plain,
% 1.37/1.53 (((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3588,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435)))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[3587])).
% 1.37/1.53 tff(3589,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435))),
% 1.37/1.53 inference(transitivity,[status(thm)],[3588, 3586])).
% 1.37/1.53 tff(3590,plain,
% 1.37/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(3591,plain,
% 1.37/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c3_1(a2408)) | c1_1(a2435)),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[3590, 3589])).
% 1.37/1.53 tff(3592,plain,
% 1.37/1.53 (c0_1(a2435) | (~c1_1(a2408)) | c1_1(a2435)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3591, 192, 612, 722, 611, 2318, 2317, 1336, 3563])).
% 1.37/1.53 tff(3593,plain,
% 1.37/1.53 ($false),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3592, 3585, 2147, 756])).
% 1.37/1.53 tff(3594,plain,(c0_1(a2435) | (~c1_1(a2408)) | (~c3_1(a2408)) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | (~c0_1(a2408)) | c1_1(a2403)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.53 tff(3595,plain,
% 1.37/1.53 (c0_1(a2435)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3594, 756, 3577, 722, 3576, 2318, 2317, 3563, 3575, 3562])).
% 1.37/1.53 tff(3596,plain,
% 1.37/1.53 (~hskp20),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[754, 3595])).
% 1.37/1.53 tff(3597,plain,
% 1.37/1.53 (hskp23 | hskp14 | (~c1_1(a2408))),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[672, 192, 3575, 3577, 42])).
% 1.37/1.53 tff(3598,plain,
% 1.37/1.53 (hskp14),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3597, 756, 629])).
% 1.37/1.53 tff(3599,plain,
% 1.37/1.53 (~c3_1(a2420)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[679, 3598])).
% 1.37/1.53 tff(3600,plain,
% 1.37/1.53 (c2_1(a2420)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[687, 3598])).
% 1.37/1.53 tff(3601,plain,
% 1.37/1.53 (c1_1(a2420)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[695, 3598])).
% 1.37/1.53 tff(3602,plain,
% 1.37/1.53 (hskp20 | (~c0_1(a2420))),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[739, 192, 3601, 3600, 3599, 665])).
% 1.37/1.53 tff(3603,plain,
% 1.37/1.53 (~c0_1(a2420)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3602, 3596])).
% 1.37/1.53 tff(3604,plain,
% 1.37/1.53 (c0_1(a2414)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[1027, 3571])).
% 1.37/1.53 tff(3605,plain,
% 1.37/1.53 ($false),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2636, 192, 43, 3601, 3600, 3604, 3573, 3572, 85, 3603])).
% 1.37/1.53 tff(3606,plain,((~c1_1(a2408)) | hskp19 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2403) | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.37/1.53 tff(3607,plain,
% 1.37/1.53 (~c1_1(a2408)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3606, 629, 722, 2318, 2317, 3563, 3562, 43])).
% 1.37/1.53 tff(3608,plain,
% 1.37/1.53 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a2403) | c0_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a2403) | c0_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3609,plain,
% 1.37/1.53 ((hskp19 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478))) <=> (hskp19 | c1_1(a2403) | c0_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3610,plain,
% 1.37/1.53 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c1_1(a2403) | c0_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2478)) | (~c2_1(a2478))))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[3609])).
% 1.37/1.53 tff(3611,plain,
% 1.37/1.53 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a2403) | c0_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.37/1.53 inference(transitivity,[status(thm)],[3610, 3608])).
% 1.37/1.53 tff(3612,plain,
% 1.37/1.53 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2403) | c1_1(a2403) | (~c0_1(a2403)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(3613,plain,
% 1.37/1.53 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c1_1(a2403) | c0_1(a2478) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2478)) | (~c2_1(a2478))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[3612, 3611])).
% 1.37/1.53 tff(3614,plain,
% 1.37/1.53 (c1_1(a2403) | (~c0_1(a2403)) | (~c1_1(a2478))),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3613, 192, 43, 260, 279, 2317, 85])).
% 1.37/1.53 tff(3615,plain,
% 1.37/1.53 (~c1_1(a2478)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3614, 3563, 3562])).
% 1.37/1.53 tff(3616,plain,
% 1.37/1.53 (hskp29),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2777, 3607, 260, 3575, 3577, 279, 3615])).
% 1.37/1.53 tff(3617,plain,
% 1.37/1.53 (c0_1(a2409)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[1675, 3616])).
% 1.37/1.53 tff(3618,plain,
% 1.37/1.53 (c3_1(a2409)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[1064, 3616])).
% 1.37/1.53 tff(3619,plain,
% 1.37/1.53 (c2_1(a2409)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[1056, 3616])).
% 1.37/1.53 tff(3620,plain,
% 1.37/1.53 (hskp14 | (~c1_1(a2409))),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2898, 192, 629, 1688, 1115, 42])).
% 1.37/1.53 tff(3621,plain,
% 1.37/1.53 (hskp14),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3620, 1699])).
% 1.37/1.53 tff(3622,plain,
% 1.37/1.53 (~c3_1(a2420)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[679, 3621])).
% 1.37/1.53 tff(3623,plain,
% 1.37/1.53 (c1_1(a2420)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[695, 3621])).
% 1.37/1.53 tff(3624,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2403) | c3_1(a2420) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2420)) | (~c0_1(a2420)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2403) | c3_1(a2420) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3625,plain,
% 1.37/1.53 (((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2403) | c3_1(a2403) | (~c0_1(a2403))) <=> (c1_1(a2403) | c3_1(a2420) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3626,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2403) | c3_1(a2403) | (~c0_1(a2403)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c1_1(a2403) | c3_1(a2420) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2420)) | (~c0_1(a2420))))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[3625])).
% 1.37/1.53 tff(3627,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2403) | c3_1(a2403) | (~c0_1(a2403)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2403) | c3_1(a2420) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.37/1.53 inference(transitivity,[status(thm)],[3626, 3624])).
% 1.37/1.53 tff(3628,plain,
% 1.37/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c1_1(a2403) | c3_1(a2403) | (~c0_1(a2403)))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(3629,plain,
% 1.37/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c1_1(a2403) | c3_1(a2420) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c3_1(a2409)) | (~c2_1(a2409)) | (~c1_1(a2409)) | (~c1_1(a2420)) | (~c0_1(a2420))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[3628, 3627])).
% 1.37/1.53 tff(3630,plain,
% 1.37/1.53 (~c0_1(a2420)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3629, 192, 1116, 1115, 3623, 3562, 3622, 2317, 1076, 1699, 3563])).
% 1.37/1.53 tff(3631,plain,
% 1.37/1.53 (c2_1(a2420)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[687, 3621])).
% 1.37/1.53 tff(3632,plain,
% 1.37/1.53 ($false),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2636, 192, 43, 3623, 3631, 1098, 1078, 1077, 85, 3630])).
% 1.37/1.53 tff(3633,plain,((~c1_1(a2409)) | hskp19 | (~c0_1(a2414)) | c1_1(a2414) | c3_1(a2414) | (~c2_1(a2409)) | (~c3_1(a2409)) | c1_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | hskp23 | (~c0_1(a2409))), inference(lemma,lemma(discharge,[]))).
% 1.37/1.53 tff(3634,plain,
% 1.37/1.53 (~c1_1(a2409)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3633, 3619, 43, 3573, 3572, 3604, 3618, 3562, 2317, 3563, 629, 3617])).
% 1.37/1.53 tff(3635,plain,
% 1.37/1.53 (~hskp1),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[2305, 3562])).
% 1.37/1.53 tff(3636,plain,
% 1.37/1.53 ($false),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[1129, 192, 3635, 3619, 3618, 3577, 3576, 1007, 3634, 3607])).
% 1.37/1.53 tff(3637,plain,(hskp23 | hskp19 | c1_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | (~c2_1(a2478)) | c0_1(a2478) | c2_1(a2435) | c2_1(a2403)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.53 tff(3638,plain,
% 1.37/1.53 (hskp23),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3637, 3563, 3562, 2317, 43, 260, 279, 722, 2318])).
% 1.37/1.53 tff(3639,plain,
% 1.37/1.53 (~c0_1(a2455)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[480, 3638])).
% 1.37/1.53 tff(3640,plain,
% 1.37/1.53 (c2_1(a2455)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[496, 3638])).
% 1.37/1.53 tff(3641,plain,
% 1.37/1.53 (~c1_1(a2455)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[3060, 192, 43, 3640, 3604, 3639, 3573, 3572, 85])).
% 1.37/1.53 tff(3642,plain,
% 1.37/1.53 (c3_1(a2455)),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[488, 3638])).
% 1.37/1.53 tff(3643,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3644,plain,
% 1.37/1.53 (((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455))) <=> (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(3645,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[3644])).
% 1.37/1.53 tff(3646,plain,
% 1.37/1.53 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.37/1.53 inference(transitivity,[status(thm)],[3645, 3643])).
% 1.37/1.53 tff(3647,plain,
% 1.37/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c0_1(a2403)) | c1_1(a2455) | (~c2_1(a2455)) | (~c3_1(a2455)))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(3648,plain,
% 1.37/1.53 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c0_1(a2403)) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3647, 3646])).
% 1.37/1.54 tff(3649,plain,
% 1.37/1.54 (~c1_1(a2408)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3648, 192, 3640, 3642, 3575, 3577, 2318, 2317, 554, 3563, 3641])).
% 1.37/1.54 tff(3650,plain,
% 1.37/1.54 ($false),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3535, 192, 3635, 3640, 3642, 3577, 3576, 1007, 3649, 3641])).
% 1.37/1.54 tff(3651,plain,((~c0_1(a2403)) | c2_1(a2403) | c3_1(a2403) | hskp19 | c1_1(a2403) | (~c2_1(a2478)) | c0_1(a2478) | c2_1(a2435)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.54 tff(3652,plain,
% 1.37/1.54 (~c0_1(a2403)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3651, 3562, 2317, 43, 2318, 260, 279, 722])).
% 1.37/1.54 tff(3653,plain,
% 1.37/1.54 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3654,plain,
% 1.37/1.54 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403)) <=> (hskp13 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3655,plain,
% 1.37/1.54 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403)))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[3654])).
% 1.37/1.54 tff(3656,plain,
% 1.37/1.54 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))),
% 1.37/1.54 inference(transitivity,[status(thm)],[3655, 3653])).
% 1.37/1.54 tff(3657,plain,
% 1.37/1.54 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(3658,plain,
% 1.37/1.54 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3657, 3656])).
% 1.37/1.54 tff(3659,plain,
% 1.37/1.54 (hskp13 | hskp1 | c3_1(a2403) | c0_1(a2403)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3658, 192, 2318, 964])).
% 1.37/1.54 tff(3660,plain,
% 1.37/1.54 (hskp13),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3659, 3652, 2317, 3635])).
% 1.37/1.54 tff(3661,plain,
% 1.37/1.54 (~c0_1(a2418)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[321, 3660])).
% 1.37/1.54 tff(3662,plain,
% 1.37/1.54 (c2_1(a2418)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[329, 3660])).
% 1.37/1.54 tff(3663,plain,
% 1.37/1.54 (c1_1(a2418)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[337, 3660])).
% 1.37/1.54 tff(3664,plain,
% 1.37/1.54 (~hskp10),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[2667, 3663, 43, 3662, 3661])).
% 1.37/1.54 tff(3665,plain,
% 1.37/1.54 (^[U: $i] : refl((hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(3666,plain,
% 1.37/1.54 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[3665])).
% 1.37/1.54 tff(3667,plain,
% 1.37/1.54 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3668,plain,
% 1.37/1.54 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp1))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp1) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1) <=> (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(3669,plain,
% 1.37/1.54 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1) <=> ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[3668])).
% 1.37/1.54 tff(3670,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 1.37/1.54 tff(3671,plain,
% 1.37/1.54 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3670, 3669])).
% 1.37/1.54 tff(3672,plain,
% 1.37/1.54 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3671, 3667])).
% 1.37/1.54 tff(3673,plain,(
% 1.37/1.54 ![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(skolemize,[status(sab)],[3672])).
% 1.37/1.54 tff(3674,plain,
% 1.37/1.54 (![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3673, 3666])).
% 1.37/1.54 tff(3675,plain,
% 1.37/1.54 (^[U: $i] : refl((hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(3676,plain,
% 1.37/1.54 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[3675])).
% 1.37/1.54 tff(3677,plain,
% 1.37/1.54 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3678,plain,
% 1.37/1.54 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U))), ((((~ndr1_0) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U)))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp1) <=> ((hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp1))), rewrite(((hskp14 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U)) | hskp1) <=> (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))), (((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp1) <=> (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(3679,plain,
% 1.37/1.54 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp1) <=> ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[3678])).
% 1.37/1.54 tff(3680,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c2_1(U)) | c3_1(U)) | hskp14) | hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 1.37/1.54 tff(3681,plain,
% 1.37/1.54 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3680, 3679])).
% 1.37/1.54 tff(3682,plain,
% 1.37/1.54 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3681, 3677])).
% 1.37/1.54 tff(3683,plain,(
% 1.37/1.54 ![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(skolemize,[status(sab)],[3682])).
% 1.37/1.54 tff(3684,plain,
% 1.37/1.54 (![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3683, 3676])).
% 1.37/1.54 tff(3685,plain,
% 1.37/1.54 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp14 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp14 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3686,plain,
% 1.37/1.54 ((hskp14 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403)) <=> (hskp14 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3687,plain,
% 1.37/1.54 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp14 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp14 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403)))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[3686])).
% 1.37/1.54 tff(3688,plain,
% 1.37/1.54 (((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp14 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403))) <=> ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp14 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403))),
% 1.37/1.54 inference(transitivity,[status(thm)],[3687, 3685])).
% 1.37/1.54 tff(3689,plain,
% 1.37/1.54 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp14 | hskp1 | (~ndr1_0) | c3_1(a2403) | c0_1(a2403) | c2_1(a2403))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(3690,plain,
% 1.37/1.54 ((~![U: $i] : (hskp14 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp14 | hskp1 | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403)),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3689, 3688])).
% 1.37/1.54 tff(3691,plain,
% 1.37/1.54 (hskp14 | hskp1 | c3_1(a2403) | c0_1(a2403)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3690, 192, 2318, 3684])).
% 1.37/1.54 tff(3692,plain,
% 1.37/1.54 (hskp14),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3691, 2482, 2317, 22])).
% 1.37/1.54 tff(3693,plain,
% 1.37/1.54 (~c3_1(a2420)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[679, 3692])).
% 1.37/1.54 tff(3694,plain,
% 1.37/1.54 (c2_1(a2420)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[687, 3692])).
% 1.37/1.54 tff(3695,plain,
% 1.37/1.54 (c1_1(a2420)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[695, 3692])).
% 1.37/1.54 tff(3696,plain,
% 1.37/1.54 (hskp23 | hskp6),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[2909, 192, 3695, 3694, 3693, 2087])).
% 1.37/1.54 tff(3697,plain,
% 1.37/1.54 (hskp6),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3696, 629])).
% 1.37/1.54 tff(3698,plain,
% 1.37/1.54 (~c2_1(a2410)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[895, 3697])).
% 1.37/1.54 tff(3699,plain,
% 1.37/1.54 (c1_1(a2410)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[903, 3697])).
% 1.37/1.54 tff(3700,plain,
% 1.37/1.54 (c0_1(a2410)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[911, 3697])).
% 1.37/1.54 tff(3701,plain,
% 1.37/1.54 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3702,plain,
% 1.37/1.54 ((hskp5 | hskp1 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410))) <=> (hskp5 | hskp1 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3703,plain,
% 1.37/1.54 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[3702])).
% 1.37/1.54 tff(3704,plain,
% 1.37/1.54 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[3703, 3701])).
% 1.37/1.54 tff(3705,plain,
% 1.37/1.54 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(3706,plain,
% 1.37/1.54 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3705, 3704])).
% 1.37/1.54 tff(3707,plain,
% 1.37/1.54 (hskp5),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3706, 192, 22, 3700, 3699, 3698, 3674])).
% 1.37/1.54 tff(3708,plain,
% 1.37/1.54 (c3_1(a2408)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[396, 3707])).
% 1.37/1.54 tff(3709,plain,
% 1.37/1.54 (~c2_1(a2408)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[373, 3707])).
% 1.37/1.54 tff(3710,plain,
% 1.37/1.54 (c1_1(a2408)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[637, 3709, 96, 629, 3708])).
% 1.37/1.54 tff(3711,plain,
% 1.37/1.54 (hskp13),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3659, 2482, 2317, 22])).
% 1.37/1.54 tff(3712,plain,
% 1.37/1.54 (~c0_1(a2418)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[321, 3711])).
% 1.37/1.54 tff(3713,plain,
% 1.37/1.54 (c2_1(a2418)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[329, 3711])).
% 1.37/1.54 tff(3714,plain,
% 1.37/1.54 (c1_1(a2418)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[337, 3711])).
% 1.37/1.54 tff(3715,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2418) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2418)) | (~c1_1(a2418)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3716,plain,
% 1.37/1.54 (((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c0_1(a2418) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3717,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2418) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2418)) | (~c1_1(a2418))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[3716])).
% 1.37/1.54 tff(3718,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2418)) | (~c1_1(a2418)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[3717, 3715])).
% 1.37/1.54 tff(3719,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(3720,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2418) | c2_1(a2408) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c2_1(a2418)) | (~c1_1(a2418))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3719, 3718])).
% 1.37/1.54 tff(3721,plain,
% 1.37/1.54 ($false),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3720, 192, 3714, 3713, 3708, 3712, 3709, 2318, 2317, 63, 2482, 3710])).
% 1.37/1.54 tff(3722,plain,(hskp23 | c2_1(a2403) | c3_1(a2403) | c0_1(a2403) | hskp10 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.37/1.54 tff(3723,plain,
% 1.37/1.54 (hskp23),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3722, 3652, 2317, 2318, 3664, 3635])).
% 1.37/1.54 tff(3724,plain,
% 1.37/1.54 (hskp15),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[506, 3723])).
% 1.37/1.54 tff(3725,plain,
% 1.37/1.54 (~c2_1(a2422)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[528, 3724])).
% 1.37/1.54 tff(3726,plain,
% 1.37/1.54 (c3_1(a2422)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[514, 3724])).
% 1.37/1.54 tff(3727,plain,
% 1.37/1.54 (c1_1(a2422)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[522, 3724])).
% 1.37/1.54 tff(3728,plain,
% 1.37/1.54 ($false),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3475, 192, 3727, 3726, 3663, 3662, 3725, 3661, 2318, 2317, 63, 3652])).
% 1.37/1.54 tff(3729,plain,(c1_1(a2403) | c2_1(a2403) | c3_1(a2403) | hskp19 | (~c2_1(a2478)) | c0_1(a2478) | c2_1(a2435)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.54 tff(3730,plain,
% 1.37/1.54 (c1_1(a2403)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3729, 722, 2317, 43, 260, 279, 2318])).
% 1.37/1.54 tff(3731,plain,
% 1.37/1.54 (~hskp13),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[2669, 3557, 43])).
% 1.37/1.54 tff(3732,plain,
% 1.37/1.54 (hskp16),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[2977, 3731, 722, 3730, 2318, 2317, 629, 3558, 3560, 3559, 43, 260, 259, 3561])).
% 1.37/1.54 tff(3733,plain,
% 1.37/1.54 (~c3_1(a2425)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[411, 3732])).
% 1.37/1.54 tff(3734,plain,
% 1.37/1.54 (~c2_1(a2425)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[417, 3732])).
% 1.37/1.54 tff(3735,plain,
% 1.37/1.54 (c0_1(a2425)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[425, 3732])).
% 1.37/1.54 tff(3736,plain,
% 1.37/1.54 (hskp5),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[449, 192, 43, 3735, 3734, 3733, 53])).
% 1.37/1.54 tff(3737,plain,
% 1.37/1.54 (~c2_1(a2408)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[373, 3736])).
% 1.37/1.54 tff(3738,plain,
% 1.37/1.54 (c3_1(a2408)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[396, 3736])).
% 1.37/1.54 tff(3739,plain,
% 1.37/1.54 (c1_1(a2408)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[2335, 192, 629, 3738, 3730, 3737, 2318, 2317, 628])).
% 1.37/1.54 tff(3740,plain,
% 1.37/1.54 (c0_1(a2408)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[381, 3736])).
% 1.37/1.54 tff(3741,plain,
% 1.37/1.54 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3742,plain,
% 1.37/1.54 ((hskp2 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478))) <=> (hskp2 | c3_1(a2478) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3743,plain,
% 1.37/1.54 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[3742])).
% 1.37/1.54 tff(3744,plain,
% 1.37/1.54 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[3743, 3741])).
% 1.37/1.54 tff(3745,plain,
% 1.37/1.54 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(3746,plain,
% 1.37/1.54 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3745, 3744])).
% 1.37/1.54 tff(3747,plain,
% 1.37/1.54 (hskp2 | (~c1_1(a2408))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3746, 192, 260, 3740, 259, 3737, 1282, 3561])).
% 1.37/1.54 tff(3748,plain,
% 1.37/1.54 (hskp2),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3747, 3739])).
% 1.37/1.54 tff(3749,plain,
% 1.37/1.54 (~c2_1(a2404)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[1301, 3748])).
% 1.37/1.54 tff(3750,plain,
% 1.37/1.54 (~c1_1(a2404)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[1785, 3748])).
% 1.37/1.54 tff(3751,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c1_1(a2408)) | (~c3_1(a2408)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c1_1(a2408)) | (~c3_1(a2408)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3752,plain,
% 1.37/1.54 (((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404)) <=> (c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c1_1(a2408)) | (~c3_1(a2408)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3753,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c1_1(a2408)) | (~c3_1(a2408))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[3752])).
% 1.37/1.54 tff(3754,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c1_1(a2408)) | (~c3_1(a2408)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[3753, 3751])).
% 1.37/1.54 tff(3755,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(3756,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c1_1(a2408)) | (~c3_1(a2408))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3755, 3754])).
% 1.37/1.54 tff(3757,plain,
% 1.37/1.54 (c0_1(a2404)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3756, 192, 3738, 3730, 3737, 3750, 3749, 2318, 2317, 11, 3739])).
% 1.37/1.54 tff(3758,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c0_1(a2408)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3759,plain,
% 1.37/1.54 (((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2403) | c0_1(a2403) | (~c1_1(a2403))) <=> (c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3760,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2403) | c0_1(a2403) | (~c1_1(a2403)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c0_1(a2408))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[3759])).
% 1.37/1.54 tff(3761,plain,
% 1.37/1.54 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2403) | c0_1(a2403) | (~c1_1(a2403)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c0_1(a2408)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[3760, 3758])).
% 1.37/1.54 tff(3762,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2408) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2403) | c0_1(a2403) | (~c1_1(a2403)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(3763,plain,
% 1.37/1.54 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c2_1(a2408) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2403) | (~c0_1(a2404)) | (~c1_1(a2408)) | (~c0_1(a2408))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3762, 3761])).
% 1.37/1.54 tff(3764,plain,
% 1.37/1.54 (c0_1(a2403) | (~c0_1(a2404))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3763, 192, 3740, 3730, 3737, 3750, 3749, 2318, 1879, 3739])).
% 1.37/1.54 tff(3765,plain,
% 1.37/1.54 (c0_1(a2403)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3764, 3757])).
% 1.37/1.54 tff(3766,plain,
% 1.37/1.54 (hskp14 | (~c1_1(a2408))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[672, 192, 629, 3740, 3738, 42])).
% 1.37/1.54 tff(3767,plain,
% 1.37/1.54 (hskp14),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[3766, 3739])).
% 1.37/1.54 tff(3768,plain,
% 1.37/1.54 (c2_1(a2420)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[687, 3767])).
% 1.37/1.54 tff(3769,plain,
% 1.37/1.54 (c1_1(a2420)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[695, 3767])).
% 1.37/1.54 tff(3770,plain,
% 1.37/1.54 (c0_1(a2420)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[2638, 3769, 3558, 3768, 3560, 3559, 43])).
% 1.37/1.54 tff(3771,plain,
% 1.37/1.54 (~c3_1(a2420)),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[679, 3767])).
% 1.37/1.54 tff(3772,plain,
% 1.37/1.54 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2420) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2420)) | (~c0_1(a2420)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2420) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3773,plain,
% 1.37/1.54 ((hskp30 | (~ndr1_0) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408))) <=> (hskp30 | c3_1(a2420) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(3774,plain,
% 1.37/1.54 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c3_1(a2420) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2420)) | (~c0_1(a2420))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[3773])).
% 1.37/1.54 tff(3775,plain,
% 1.37/1.54 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2420) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2420)) | (~c0_1(a2420)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[3774, 3772])).
% 1.37/1.54 tff(3776,plain,
% 1.37/1.54 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2420) | (~c1_1(a2420)) | (~c0_1(a2420)) | c2_1(a2408) | (~c1_1(a2408)) | (~c3_1(a2408)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(3777,plain,
% 1.37/1.54 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c3_1(a2420) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c1_1(a2420)) | (~c0_1(a2420))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[3776, 3775])).
% 1.37/1.55 tff(3778,plain,
% 1.37/1.55 (hskp30),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3777, 192, 3769, 3738, 3771, 3737, 564, 3739, 3770])).
% 1.37/1.55 tff(3779,plain,
% 1.37/1.55 (c0_1(a2450)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[598, 3778])).
% 1.37/1.55 tff(3780,plain,
% 1.37/1.55 (c3_1(a2450)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[582, 3778])).
% 1.37/1.55 tff(3781,plain,
% 1.37/1.55 (c1_1(a2450)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[590, 3778])).
% 1.37/1.55 tff(3782,plain,
% 1.37/1.55 (hskp6),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2909, 192, 629, 3769, 3768, 3771, 2087])).
% 1.37/1.55 tff(3783,plain,
% 1.37/1.55 (~c2_1(a2410)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[895, 3782])).
% 1.37/1.55 tff(3784,plain,
% 1.37/1.55 (c0_1(a2410)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[911, 3782])).
% 1.37/1.55 tff(3785,plain,
% 1.37/1.55 (c1_1(a2410)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[903, 3782])).
% 1.37/1.55 tff(3786,assumption,(c3_1(a2450)), introduced(assumption)).
% 1.37/1.55 tff(3787,assumption,(c1_1(a2450)), introduced(assumption)).
% 1.37/1.55 tff(3788,plain,
% 1.37/1.55 (~c2_1(a2450)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3389, 192, 3787, 3786, 1028, 3730, 1066, 1029, 2317, 1076, 3563])).
% 1.37/1.55 tff(3789,plain,
% 1.37/1.55 (~c1_1(a2478)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2681, 192, 43, 260, 1028, 279, 1066, 1029, 85])).
% 1.37/1.55 tff(3790,assumption,(c0_1(a2450)), introduced(assumption)).
% 1.37/1.55 tff(3791,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3792,plain,
% 1.37/1.55 ((hskp2 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478))) <=> (hskp2 | c3_1(a2478) | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3793,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | c3_1(a2478) | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[3792])).
% 1.37/1.55 tff(3794,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[3793, 3791])).
% 1.37/1.55 tff(3795,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp2 | (~ndr1_0) | c2_1(a2450) | (~c1_1(a2450)) | (~c0_1(a2450)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(3796,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp2 | c3_1(a2478) | (~ndr1_0) | (~c0_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[3795, 3794])).
% 1.37/1.55 tff(3797,plain,
% 1.37/1.55 (hskp2),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3796, 192, 3790, 3787, 260, 259, 1282, 3789, 3788])).
% 1.37/1.55 tff(3798,plain,
% 1.37/1.55 (~c2_1(a2404)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1301, 3797])).
% 1.37/1.55 tff(3799,plain,
% 1.37/1.55 (~c1_1(a2404)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1785, 3797])).
% 1.37/1.55 tff(3800,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3801,plain,
% 1.37/1.55 (((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404)) <=> (c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3802,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[3801])).
% 1.37/1.55 tff(3803,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[3802, 3800])).
% 1.37/1.55 tff(3804,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2404) | c1_1(a2404) | c0_1(a2404))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(3805,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2404) | c2_1(a2404) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c0_1(a2404) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[3804, 3803])).
% 1.37/1.55 tff(3806,plain,
% 1.37/1.55 (c0_1(a2404)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3805, 192, 3787, 3786, 3730, 3799, 3798, 2318, 2317, 11, 3788])).
% 1.37/1.55 tff(3807,plain,
% 1.37/1.55 (c0_1(a2420)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[2638, 1028, 724, 723, 43, 1066, 1029])).
% 1.37/1.55 tff(3808,plain,
% 1.37/1.55 (hskp20),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[740, 3807])).
% 1.37/1.55 tff(3809,plain,
% 1.37/1.55 (~c0_1(a2435)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[754, 3808])).
% 1.37/1.55 tff(3810,plain,
% 1.37/1.55 (c3_1(a2435)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[748, 3808])).
% 1.37/1.55 tff(3811,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3812,plain,
% 1.37/1.55 ((hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | (~c3_1(a2435))) <=> (hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3813,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[3812])).
% 1.37/1.55 tff(3814,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[3813, 3811])).
% 1.37/1.55 tff(3815,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp23 | (~ndr1_0) | c3_1(a2403) | c2_1(a2403) | (~c1_1(a2403)) | c2_1(a2435) | c1_1(a2435) | (~c3_1(a2435)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(3816,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[3815, 3814])).
% 1.37/1.55 tff(3817,plain,
% 1.37/1.55 (hskp23 | (~c1_1(a2403)) | c1_1(a2435) | (~c3_1(a2435))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3816, 192, 722, 2318, 2317, 628])).
% 1.37/1.55 tff(3818,plain,
% 1.37/1.55 (c1_1(a2435)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3817, 3810, 3730, 629])).
% 1.37/1.55 tff(3819,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2404)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2404)) | (~c1_1(a2435)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3820,plain,
% 1.37/1.55 (((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2404)) | (~c1_1(a2435)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3821,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2404)) | (~c1_1(a2435))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[3820])).
% 1.37/1.55 tff(3822,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2404)) | (~c1_1(a2435)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[3821, 3819])).
% 1.37/1.55 tff(3823,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2404) | c1_1(a2404) | (~c0_1(a2404)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(3824,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2410) | c1_1(a2404) | c2_1(a2404) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | (~c0_1(a2404)) | (~c1_1(a2435))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[3823, 3822])).
% 1.37/1.55 tff(3825,plain,
% 1.37/1.55 (c0_1(a2435) | (~c0_1(a2404)) | (~c1_1(a2435))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3824, 192, 2720, 2719, 722, 2733, 3799, 3798, 1879])).
% 1.37/1.55 tff(3826,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3825, 3818, 3809, 3806])).
% 1.37/1.55 tff(3827,plain,((~hskp10) | (~c0_1(a2410)) | (~c1_1(a2410)) | c2_1(a2435) | c2_1(a2410) | hskp23 | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2420)) | (~c2_1(a2420)) | c3_1(a2420) | hskp19 | (~c1_1(a2450)) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c2_1(a2478)) | c3_1(a2478) | c0_1(a2478) | (~c0_1(a2403))), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(3828,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3827, 3785, 3784, 3557, 722, 3783, 629, 2318, 2317, 3769, 3768, 3771, 43, 3781, 3780, 3779, 260, 259, 279, 3765])).
% 1.37/1.55 tff(3829,plain,(hskp23 | c2_1(a2435) | c2_1(a2403) | c3_1(a2403) | hskp19 | (~c2_1(a2478)) | c3_1(a2478) | c0_1(a2478)), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(3830,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3829, 3556, 3555, 43, 722, 629, 3551, 3553, 3550])).
% 1.37/1.55 tff(3831,plain,((~hskp1) | hskp19 | c2_1(a2435) | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(3832,plain,
% 1.37/1.55 (~hskp1),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3831, 629, 722, 43])).
% 1.37/1.55 tff(3833,plain,
% 1.37/1.55 (~hskp18),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3041, 3832, 2670])).
% 1.37/1.55 tff(3834,assumption,(hskp17), introduced(assumption)).
% 1.37/1.55 tff(3835,plain,
% 1.37/1.55 (~c1_1(a2427)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1811, 3834])).
% 1.37/1.55 tff(3836,plain,
% 1.37/1.55 (c3_1(a2427)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1819, 3834])).
% 1.37/1.55 tff(3837,plain,
% 1.37/1.55 (c2_1(a2427)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[1827, 3834])).
% 1.37/1.55 tff(3838,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3839,plain,
% 1.37/1.55 (((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427))) <=> (c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3840,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[3839])).
% 1.37/1.55 tff(3841,plain,
% 1.37/1.55 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[3840, 3838])).
% 1.37/1.55 tff(3842,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | (~c3_1(a2408)) | (~c1_1(a2408)) | (~c0_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c1_1(a2427) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(3843,plain,
% 1.37/1.55 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a2427) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2408)) | (~c0_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | (~c2_1(a2427)) | (~c3_1(a2427))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[3842, 3841])).
% 1.37/1.55 tff(3844,plain,
% 1.37/1.55 (~c1_1(a2408)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3843, 192, 3837, 3836, 3500, 767, 612, 3835, 3499, 3498, 554])).
% 1.37/1.55 tff(3845,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2427) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2427)) | (~c3_1(a2427)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2427) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3846,plain,
% 1.37/1.55 ((hskp1 | (~ndr1_0) | c1_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408))) <=> (hskp1 | c1_1(a2427) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3847,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | c1_1(a2427) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2427)) | (~c3_1(a2427))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[3846])).
% 1.37/1.55 tff(3848,plain,
% 1.37/1.55 (((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))) <=> ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2427) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2427)) | (~c3_1(a2427)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[3847, 3845])).
% 1.37/1.55 tff(3849,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp1 | (~ndr1_0) | c1_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c2_1(a2408) | c1_1(a2408) | (~c3_1(a2408)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(3850,plain,
% 1.37/1.55 ((~![V: $i, U: $i] : (hskp1 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp1 | c1_1(a2427) | c2_1(a2408) | (~ndr1_0) | c1_1(a2408) | (~c3_1(a2408)) | (~c2_1(a2427)) | (~c3_1(a2427))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[3849, 3848])).
% 1.37/1.55 tff(3851,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3850, 192, 22, 3837, 3836, 612, 3835, 611, 1007, 3844])).
% 1.37/1.55 tff(3852,plain,((~hskp17) | hskp1 | (~c3_1(a2408)) | c2_1(a2408) | (~c0_1(a2408))), inference(lemma,lemma(discharge,[]))).
% 1.37/1.55 tff(3853,plain,
% 1.37/1.55 (~hskp17),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3852, 3832, 3505, 3529, 3503])).
% 1.37/1.55 tff(3854,plain,
% 1.37/1.55 (^[U: $i] : refl((hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 1.37/1.55 inference(bind,[status(th)],[])).
% 1.37/1.55 tff(3855,plain,
% 1.37/1.55 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.37/1.55 inference(quant_intro,[status(thm)],[3854])).
% 1.37/1.55 tff(3856,plain,
% 1.37/1.55 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3857,plain,
% 1.37/1.55 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp17) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp17))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp17) <=> (hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp17) | hskp18) <=> ((hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp18))), rewrite(((hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp18) <=> (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp17) | hskp18) <=> (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 1.37/1.55 inference(bind,[status(th)],[])).
% 1.37/1.55 tff(3858,plain,
% 1.37/1.55 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp17) | hskp18) <=> ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.37/1.55 inference(quant_intro,[status(thm)],[3857])).
% 1.37/1.55 tff(3859,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp17) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause144')).
% 1.37/1.55 tff(3860,plain,
% 1.37/1.55 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[3859, 3858])).
% 1.37/1.55 tff(3861,plain,
% 1.37/1.55 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[3860, 3856])).
% 1.37/1.55 tff(3862,plain,(
% 1.37/1.55 ![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.37/1.55 inference(skolemize,[status(sab)],[3861])).
% 1.37/1.55 tff(3863,plain,
% 1.37/1.55 (![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[3862, 3855])).
% 1.37/1.55 tff(3864,plain,
% 1.37/1.55 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp18 | hskp17 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp18 | hskp17 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3865,plain,
% 1.37/1.55 ((hskp18 | hskp17 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435))) <=> (hskp18 | hskp17 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3866,plain,
% 1.37/1.55 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp18 | hskp17 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[3865])).
% 1.37/1.55 tff(3867,plain,
% 1.37/1.55 (((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435)))) <=> ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp18 | hskp17 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435)))),
% 1.37/1.55 inference(transitivity,[status(thm)],[3866, 3864])).
% 1.37/1.55 tff(3868,plain,
% 1.37/1.55 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp18 | hskp17 | (~ndr1_0) | c0_1(a2435) | c2_1(a2435) | (~c1_1(a2435)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(3869,plain,
% 1.37/1.55 ((~![U: $i] : (hskp18 | hskp17 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp18 | hskp17 | c0_1(a2435) | c2_1(a2435) | (~ndr1_0) | (~c1_1(a2435))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[3868, 3867])).
% 1.37/1.55 tff(3870,plain,
% 1.37/1.55 (hskp18 | hskp17 | c0_1(a2435) | (~c1_1(a2435))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3869, 192, 722, 3863])).
% 1.37/1.55 tff(3871,plain,
% 1.37/1.55 (~c1_1(a2435)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3870, 2147, 3853, 3833])).
% 1.37/1.55 tff(3872,plain,
% 1.37/1.55 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c3_1(a2435) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c3_1(a2435) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3873,plain,
% 1.37/1.55 ((hskp13 | hskp1 | (~ndr1_0) | c3_1(a2435) | c0_1(a2435) | c2_1(a2435)) <=> (hskp13 | hskp1 | c3_1(a2435) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(3874,plain,
% 1.37/1.55 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2435) | c0_1(a2435) | c2_1(a2435))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | c3_1(a2435) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0)))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[3873])).
% 1.37/1.55 tff(3875,plain,
% 1.37/1.55 (((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2435) | c0_1(a2435) | c2_1(a2435))) <=> ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c3_1(a2435) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0))),
% 1.37/1.55 inference(transitivity,[status(thm)],[3874, 3872])).
% 1.37/1.55 tff(3876,plain,
% 1.37/1.55 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | (hskp13 | hskp1 | (~ndr1_0) | c3_1(a2435) | c0_1(a2435) | c2_1(a2435))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(3877,plain,
% 1.37/1.55 ((~![U: $i] : (hskp13 | hskp1 | (~ndr1_0) | c3_1(U) | c0_1(U) | c2_1(U))) | hskp13 | hskp1 | c3_1(a2435) | c0_1(a2435) | c2_1(a2435) | (~ndr1_0)),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[3876, 3875])).
% 1.37/1.55 tff(3878,plain,
% 1.37/1.55 (hskp1 | c3_1(a2435) | c0_1(a2435)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3877, 192, 2670, 722, 964])).
% 1.37/1.55 tff(3879,plain,
% 1.37/1.55 (c3_1(a2435)),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[3878, 2147, 3832])).
% 1.40/1.55 tff(3880,plain,
% 1.40/1.55 (hskp12 | c1_1(a2435)),
% 1.40/1.55 inference(unit_resolution,[status(thm)],[3131, 192, 3879, 2147, 1430])).
% 1.40/1.55 tff(3881,plain,
% 1.40/1.55 (hskp12),
% 1.40/1.55 inference(unit_resolution,[status(thm)],[3880, 3121])).
% 1.40/1.55 tff(3882,plain,
% 1.40/1.55 (~c0_1(a2417)),
% 1.40/1.55 inference(unit_resolution,[status(thm)],[223, 3881])).
% 1.40/1.55 tff(3883,plain,
% 1.40/1.55 (c3_1(a2417)),
% 1.40/1.55 inference(unit_resolution,[status(thm)],[231, 3881])).
% 1.40/1.55 tff(3884,plain,
% 1.40/1.55 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.40/1.55 inference(rewrite,[status(thm)],[])).
% 1.40/1.55 tff(3885,plain,
% 1.40/1.55 ((hskp15 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417))) <=> (hskp15 | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.40/1.55 inference(rewrite,[status(thm)],[])).
% 1.40/1.55 tff(3886,plain,
% 1.40/1.55 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417))))),
% 1.40/1.55 inference(monotonicity,[status(thm)],[3885])).
% 1.40/1.55 tff(3887,plain,
% 1.40/1.55 (((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417)))),
% 1.40/1.55 inference(transitivity,[status(thm)],[3886, 3884])).
% 1.40/1.55 tff(3888,plain,
% 1.40/1.55 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | (hskp15 | (~ndr1_0) | c0_1(a2417) | (~c3_1(a2417)) | (~c2_1(a2417)))),
% 1.40/1.55 inference(quant_inst,[status(thm)],[])).
% 1.40/1.55 tff(3889,plain,
% 1.40/1.55 ((~![U: $i] : (hskp15 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)))) | hskp15 | c0_1(a2417) | (~ndr1_0) | (~c2_1(a2417)) | (~c3_1(a2417))),
% 1.40/1.56 inference(modus_ponens,[status(thm)],[3888, 3887])).
% 1.40/1.56 tff(3890,plain,
% 1.40/1.56 (~c2_1(a2417)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3889, 192, 498, 3883, 3882, 475])).
% 1.40/1.56 tff(3891,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | c1_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | c1_1(a2435))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(3892,plain,
% 1.40/1.56 (((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | c1_1(a2435))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(3893,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | c1_1(a2435)))),
% 1.40/1.56 inference(monotonicity,[status(thm)],[3892])).
% 1.40/1.56 tff(3894,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | c1_1(a2435))),
% 1.40/1.56 inference(transitivity,[status(thm)],[3893, 3891])).
% 1.40/1.56 tff(3895,plain,
% 1.40/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2408)) | c2_1(a2408) | (~c1_1(a2408)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.40/1.56 inference(quant_inst,[status(thm)],[])).
% 1.40/1.56 tff(3896,plain,
% 1.40/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | c2_1(a2408) | (~ndr1_0) | (~c1_1(a2408)) | (~c3_1(a2408)) | (~c0_1(a2425)) | c1_1(a2435)),
% 1.40/1.56 inference(modus_ponens,[status(thm)],[3895, 3894])).
% 1.40/1.56 tff(3897,plain,
% 1.40/1.56 (c0_1(a2435) | (~c1_1(a2408)) | c1_1(a2435)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3896, 192, 3500, 3505, 722, 3499, 3498, 3529, 1336])).
% 1.40/1.56 tff(3898,plain,
% 1.40/1.56 (~c1_1(a2408)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3897, 3121, 2147])).
% 1.40/1.56 tff(3899,plain,
% 1.40/1.56 (hskp29),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2777, 3898, 3552, 3551, 3505, 3550, 3503])).
% 1.40/1.56 tff(3900,plain,
% 1.40/1.56 (c2_1(a2409)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1056, 3899])).
% 1.40/1.56 tff(3901,plain,
% 1.40/1.56 (c0_1(a2409)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1675, 3899])).
% 1.40/1.56 tff(3902,plain,
% 1.40/1.56 (c3_1(a2409)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1064, 3899])).
% 1.40/1.56 tff(3903,plain,
% 1.40/1.56 (hskp6),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2911, 3902, 498, 3901, 3900, 43, 3832, 882, 888, 2628])).
% 1.40/1.56 tff(3904,plain,
% 1.40/1.56 (c0_1(a2410)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[911, 3903])).
% 1.40/1.56 tff(3905,plain,
% 1.40/1.56 (c1_1(a2410)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[903, 3903])).
% 1.40/1.56 tff(3906,plain,
% 1.40/1.56 (~c1_1(a2417)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[217, 3881])).
% 1.40/1.56 tff(3907,plain,
% 1.40/1.56 (~c2_1(a2410)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[895, 3903])).
% 1.40/1.56 tff(3908,plain,
% 1.40/1.56 (hskp14),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2741, 3907, 3505, 629, 3906, 3883, 3832, 3905, 3529, 3904, 3503])).
% 1.40/1.56 tff(3909,plain,
% 1.40/1.56 (c2_1(a2420)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[687, 3908])).
% 1.40/1.56 tff(3910,plain,
% 1.40/1.56 (c1_1(a2420)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[695, 3908])).
% 1.40/1.56 tff(3911,plain,
% 1.40/1.56 (c0_1(a2420)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2638, 3910, 2628, 882, 43, 888, 3909])).
% 1.40/1.56 tff(3912,plain,
% 1.40/1.56 (~c3_1(a2420)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[679, 3908])).
% 1.40/1.56 tff(3913,plain,
% 1.40/1.56 (~c1_1(a2409)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2786, 192, 3900, 3902, 3910, 2628, 3912, 888, 882, 1076, 3911])).
% 1.40/1.56 tff(3914,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(3915,plain,
% 1.40/1.56 (((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(3916,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.40/1.56 inference(monotonicity,[status(thm)],[3915])).
% 1.40/1.56 tff(3917,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.56 inference(transitivity,[status(thm)],[3916, 3914])).
% 1.40/1.56 tff(3918,plain,
% 1.40/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2409) | (~c2_1(a2409)) | (~c0_1(a2409)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.40/1.56 inference(quant_inst,[status(thm)],[])).
% 1.40/1.56 tff(3919,plain,
% 1.40/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c0_1(a2409)) | (~c2_1(a2409)) | c1_1(a2409) | c2_1(a2417) | c1_1(a2478) | (~c2_1(a2478))),
% 1.40/1.56 inference(modus_ponens,[status(thm)],[3918, 3917])).
% 1.40/1.56 tff(3920,plain,
% 1.40/1.56 ($false),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3919, 192, 3901, 3900, 3551, 3550, 3882, 3906, 21, 3913, 3890, 3552])).
% 1.40/1.56 tff(3921,plain,(c1_1(a2435) | hskp15 | hskp19 | hskp23 | c0_1(a2435) | c2_1(a2435)), inference(lemma,lemma(discharge,[]))).
% 1.40/1.56 tff(3922,plain,
% 1.40/1.56 (hskp15),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3921, 3871, 43, 629, 2147, 722])).
% 1.40/1.56 tff(3923,plain,
% 1.40/1.56 (c1_1(a2422)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[522, 3922])).
% 1.40/1.56 tff(3924,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(3925,plain,
% 1.40/1.56 (((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(3926,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.40/1.56 inference(monotonicity,[status(thm)],[3925])).
% 1.40/1.56 tff(3927,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.56 inference(transitivity,[status(thm)],[3926, 3924])).
% 1.40/1.56 tff(3928,plain,
% 1.40/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2414) | (~c2_1(a2414)) | (~c0_1(a2414)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.40/1.56 inference(quant_inst,[status(thm)],[])).
% 1.40/1.56 tff(3929,plain,
% 1.40/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2435) | c2_1(a2435) | c1_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c2_1(a2414)) | c1_1(a2435) | c1_1(a2478) | (~c2_1(a2478))),
% 1.40/1.56 inference(modus_ponens,[status(thm)],[3928, 3927])).
% 1.40/1.56 tff(3930,plain,
% 1.40/1.56 (c0_1(a2435) | (~c2_1(a2414)) | c1_1(a2435)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3929, 192, 3551, 2628, 3550, 722, 888, 21, 3552])).
% 1.40/1.56 tff(3931,plain,
% 1.40/1.56 (~c2_1(a2414)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3930, 3871, 2147])).
% 1.40/1.56 tff(3932,plain,
% 1.40/1.56 (c3_1(a2422)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[514, 3922])).
% 1.40/1.56 tff(3933,plain,
% 1.40/1.56 (~c2_1(a2422)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[528, 3922])).
% 1.40/1.56 tff(3934,plain,
% 1.40/1.56 ($false),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3123, 3933, 3932, 3871, 2147, 722, 3931, 3923])).
% 1.40/1.56 tff(3935,plain,(c0_1(a2435) | c2_1(a2435) | hskp19 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.40/1.56 tff(3936,plain,
% 1.40/1.56 (c0_1(a2435)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3935, 629, 43, 722])).
% 1.40/1.56 tff(3937,plain,
% 1.40/1.56 (~hskp20),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[754, 3936])).
% 1.40/1.56 tff(3938,plain,
% 1.40/1.56 (~hskp14),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2989, 3937, 43])).
% 1.40/1.56 tff(3939,plain,
% 1.40/1.56 (hskp23 | hskp14 | (~c1_1(a2408))),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[672, 192, 3503, 3505, 42])).
% 1.40/1.56 tff(3940,plain,
% 1.40/1.56 (~c1_1(a2408)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3939, 3938, 629])).
% 1.40/1.56 tff(3941,plain,
% 1.40/1.56 (hskp29),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2777, 3940, 3552, 3551, 3505, 3550, 3503])).
% 1.40/1.56 tff(3942,plain,
% 1.40/1.56 (c3_1(a2409)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1064, 3941])).
% 1.40/1.56 tff(3943,plain,
% 1.40/1.56 (c2_1(a2409)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1056, 3941])).
% 1.40/1.56 tff(3944,plain,
% 1.40/1.56 (c0_1(a2409)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1675, 3941])).
% 1.40/1.56 tff(3945,plain,
% 1.40/1.56 ($false),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3013, 192, 3937, 3833, 3944, 3943, 3942, 3006])).
% 1.40/1.56 tff(3946,plain,(hskp23 | hskp19 | c2_1(a2435)), inference(lemma,lemma(discharge,[]))).
% 1.40/1.56 tff(3947,plain,
% 1.40/1.56 (c2_1(a2435)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3946, 3543, 43])).
% 1.40/1.56 tff(3948,plain,
% 1.40/1.56 (~hskp20),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[802, 3947])).
% 1.40/1.56 tff(3949,plain,
% 1.40/1.56 (~hskp14),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2989, 3948, 43])).
% 1.40/1.56 tff(3950,plain,
% 1.40/1.56 (~c1_1(a2408)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3939, 3949, 3543])).
% 1.40/1.56 tff(3951,plain,
% 1.40/1.56 (hskp23 | c1_1(a2408) | (~c1_1(a2425))),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[635, 192, 3505, 3499, 3498, 3529, 628])).
% 1.40/1.56 tff(3952,plain,
% 1.40/1.56 (~c1_1(a2425)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3951, 3950, 3543])).
% 1.40/1.56 tff(3953,plain,
% 1.40/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2478) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2478) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(3954,plain,
% 1.40/1.56 ((hskp19 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478))) <=> (hskp19 | c0_1(a2478) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(3955,plain,
% 1.40/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | c0_1(a2478) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2478)) | (~c2_1(a2478))))),
% 1.40/1.56 inference(monotonicity,[status(thm)],[3954])).
% 1.40/1.56 tff(3956,plain,
% 1.40/1.56 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2478) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.40/1.56 inference(transitivity,[status(thm)],[3955, 3953])).
% 1.40/1.56 tff(3957,plain,
% 1.40/1.56 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | (hskp19 | (~ndr1_0) | c3_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.40/1.56 inference(quant_inst,[status(thm)],[])).
% 1.40/1.56 tff(3958,plain,
% 1.40/1.56 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)))) | hskp19 | c0_1(a2478) | c3_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2478)) | (~c2_1(a2478))),
% 1.40/1.56 inference(modus_ponens,[status(thm)],[3957, 3956])).
% 1.40/1.56 tff(3959,plain,
% 1.40/1.56 (~c1_1(a2478)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3958, 192, 43, 3548, 3500, 3547, 3498, 85, 3952])).
% 1.40/1.56 tff(3960,plain,
% 1.40/1.56 (hskp29),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2777, 3959, 3950, 3548, 3505, 3547, 3503])).
% 1.40/1.56 tff(3961,plain,
% 1.40/1.56 (c3_1(a2409)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1064, 3960])).
% 1.40/1.56 tff(3962,plain,
% 1.40/1.56 (c0_1(a2409)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1675, 3960])).
% 1.40/1.56 tff(3963,plain,
% 1.40/1.56 (~c1_1(a2409)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2898, 192, 3543, 3949, 3962, 3961, 42])).
% 1.40/1.56 tff(3964,plain,
% 1.40/1.56 (c2_1(a2409)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1056, 3960])).
% 1.40/1.56 tff(3965,plain,
% 1.40/1.56 (hskp18),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3013, 192, 3948, 3962, 3964, 3961, 3006])).
% 1.40/1.56 tff(3966,plain,
% 1.40/1.56 (hskp1),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3041, 3965, 2670])).
% 1.40/1.56 tff(3967,plain,
% 1.40/1.56 (~c3_1(a2403)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2291, 3966])).
% 1.40/1.56 tff(3968,plain,
% 1.40/1.56 (~c2_1(a2403)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2297, 3966])).
% 1.40/1.56 tff(3969,plain,
% 1.40/1.56 (c1_1(a2403)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2305, 3966])).
% 1.40/1.56 tff(3970,plain,
% 1.40/1.56 ($false),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2441, 192, 3962, 3964, 3961, 3969, 3968, 3967, 2316, 3963])).
% 1.40/1.56 tff(3971,plain,(hskp19), inference(lemma,lemma(discharge,[]))).
% 1.40/1.56 tff(3972,plain,
% 1.40/1.56 (~c0_1(a2432)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[297, 3971])).
% 1.40/1.56 tff(3973,plain,
% 1.40/1.56 (c3_1(a2432)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[822, 3971])).
% 1.40/1.56 tff(3974,plain,
% 1.40/1.56 (c1_1(a2432)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[305, 3971])).
% 1.40/1.56 tff(3975,plain,
% 1.40/1.56 (hskp9 | hskp1),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3226, 192, 3974, 3973, 3972, 32])).
% 1.40/1.56 tff(3976,plain,
% 1.40/1.56 (hskp9),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3975, 22])).
% 1.40/1.56 tff(3977,plain,
% 1.40/1.56 (~c1_1(a2413)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3195, 3976])).
% 1.40/1.56 tff(3978,plain,
% 1.40/1.56 (~c0_1(a2413)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3201, 3976])).
% 1.40/1.56 tff(3979,plain,
% 1.40/1.56 (hskp20),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3107, 3974, 3973, 3972])).
% 1.40/1.56 tff(3980,plain,
% 1.40/1.56 (~c2_1(a2435)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[802, 3979])).
% 1.40/1.56 tff(3981,plain,
% 1.40/1.56 (~c0_1(a2435)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[754, 3979])).
% 1.40/1.56 tff(3982,plain,
% 1.40/1.56 (c2_1(a2413)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3209, 3976])).
% 1.40/1.56 tff(3983,plain,
% 1.40/1.56 (hskp5 | (~c2_1(a2432))),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3314, 192, 3973, 3982, 3972, 3978, 3977, 1965])).
% 1.40/1.56 tff(3984,plain,
% 1.40/1.56 (~c2_1(a2432)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3983, 1955])).
% 1.40/1.56 tff(3985,plain,
% 1.40/1.56 (c2_1(a2432) | c1_1(a2435)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[2006, 192, 3974, 3973, 3500, 3981, 3980, 3499, 3498, 1336])).
% 1.40/1.56 tff(3986,plain,
% 1.40/1.56 (c1_1(a2435)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3985, 3984])).
% 1.40/1.56 tff(3987,plain,
% 1.40/1.56 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(3988,plain,
% 1.40/1.56 ((hskp5 | hskp1 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425))) <=> (hskp5 | hskp1 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(3989,plain,
% 1.40/1.56 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425))))),
% 1.40/1.56 inference(monotonicity,[status(thm)],[3988])).
% 1.40/1.56 tff(3990,plain,
% 1.40/1.56 (((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.40/1.56 inference(transitivity,[status(thm)],[3989, 3987])).
% 1.40/1.56 tff(3991,plain,
% 1.40/1.56 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp5 | hskp1 | (~ndr1_0) | c2_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.40/1.56 inference(quant_inst,[status(thm)],[])).
% 1.40/1.56 tff(3992,plain,
% 1.40/1.56 ((~![U: $i] : (hskp5 | hskp1 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp5 | hskp1 | c2_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425))),
% 1.40/1.56 inference(modus_ponens,[status(thm)],[3991, 3990])).
% 1.40/1.56 tff(3993,plain,
% 1.40/1.56 (hskp5 | hskp1 | (~c1_1(a2425))),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3992, 192, 3500, 3499, 3674])).
% 1.40/1.56 tff(3994,plain,
% 1.40/1.56 (~c1_1(a2425)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3993, 1955, 22])).
% 1.40/1.56 tff(3995,plain,
% 1.40/1.56 (((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | c2_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp5 | c2_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(3996,plain,
% 1.40/1.56 ((hskp22 | hskp5 | (~ndr1_0) | c1_1(a2425) | c2_1(a2425) | (~c0_1(a2425))) <=> (hskp22 | hskp5 | c2_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(3997,plain,
% 1.40/1.56 (((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | (~ndr1_0) | c1_1(a2425) | c2_1(a2425) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | c2_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425))))),
% 1.40/1.56 inference(monotonicity,[status(thm)],[3996])).
% 1.40/1.56 tff(3998,plain,
% 1.40/1.56 (((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | (~ndr1_0) | c1_1(a2425) | c2_1(a2425) | (~c0_1(a2425)))) <=> ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp5 | c2_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425)))),
% 1.40/1.56 inference(transitivity,[status(thm)],[3997, 3995])).
% 1.40/1.56 tff(3999,plain,
% 1.40/1.56 ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp22 | hskp5 | (~ndr1_0) | c1_1(a2425) | c2_1(a2425) | (~c0_1(a2425)))),
% 1.40/1.56 inference(quant_inst,[status(thm)],[])).
% 1.40/1.56 tff(4000,plain,
% 1.40/1.56 ((~![U: $i] : (hskp22 | hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))) | hskp22 | hskp5 | c2_1(a2425) | (~ndr1_0) | c1_1(a2425) | (~c0_1(a2425))),
% 1.40/1.56 inference(modus_ponens,[status(thm)],[3999, 3998])).
% 1.40/1.56 tff(4001,plain,
% 1.40/1.56 (hskp22 | hskp5 | c1_1(a2425)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[4000, 192, 3500, 3499, 1495])).
% 1.40/1.56 tff(4002,plain,
% 1.40/1.56 (hskp22),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[4001, 1955, 3994])).
% 1.40/1.56 tff(4003,plain,
% 1.40/1.56 (~c2_1(a2453)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1456, 4002])).
% 1.40/1.56 tff(4004,plain,
% 1.40/1.56 (~c1_1(a2453)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1475, 4002])).
% 1.40/1.56 tff(4005,plain,
% 1.40/1.56 (~c0_1(a2453)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1462, 4002])).
% 1.40/1.56 tff(4006,plain,
% 1.40/1.56 (c3_1(a2435)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[748, 3979])).
% 1.40/1.56 tff(4007,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(4008,plain,
% 1.40/1.56 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453)) <=> (c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(4009,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 1.40/1.56 inference(monotonicity,[status(thm)],[4008])).
% 1.40/1.56 tff(4010,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.56 inference(transitivity,[status(thm)],[4009, 4007])).
% 1.40/1.56 tff(4011,plain,
% 1.40/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2425) | c3_1(a2425) | (~c0_1(a2425)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))),
% 1.40/1.56 inference(quant_inst,[status(thm)],[])).
% 1.40/1.56 tff(4012,plain,
% 1.40/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c2_1(a2435) | c2_1(a2425) | c3_1(a2425) | (~ndr1_0) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 1.40/1.56 inference(modus_ponens,[status(thm)],[4011, 4010])).
% 1.40/1.56 tff(4013,plain,
% 1.40/1.56 ($false),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[4012, 192, 4006, 3500, 4005, 4004, 4003, 3980, 3499, 3498, 1336, 3986])).
% 1.40/1.56 tff(4014,plain,(hskp5 | hskp1), inference(lemma,lemma(discharge,[]))).
% 1.40/1.56 tff(4015,plain,
% 1.40/1.56 (hskp5),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[4014, 22])).
% 1.40/1.56 tff(4016,plain,
% 1.40/1.56 (c0_1(a2408)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[381, 4015])).
% 1.40/1.56 tff(4017,plain,
% 1.40/1.56 (~c2_1(a2408)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[373, 4015])).
% 1.40/1.56 tff(4018,plain,
% 1.40/1.56 (c3_1(a2408)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[396, 4015])).
% 1.40/1.56 tff(4019,plain,
% 1.40/1.56 (~hskp17),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3852, 4018, 22, 4017, 4016])).
% 1.40/1.56 tff(4020,plain,
% 1.40/1.56 (hskp21 | hskp17),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1804, 192, 3974, 3973, 3972, 1748])).
% 1.40/1.56 tff(4021,plain,
% 1.40/1.56 (hskp21),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[4020, 4019])).
% 1.40/1.56 tff(4022,plain,
% 1.40/1.56 (~c1_1(a2437)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1705, 4021])).
% 1.40/1.56 tff(4023,plain,
% 1.40/1.56 (c2_1(a2437)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1713, 4021])).
% 1.40/1.56 tff(4024,plain,
% 1.40/1.56 (c0_1(a2437)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[1728, 4021])).
% 1.40/1.56 tff(4025,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2437) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c1_1(a2435) | (~c2_1(a2437)) | (~c0_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2437) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c1_1(a2435) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(4026,plain,
% 1.40/1.56 (((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435)) <=> (c1_1(a2437) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c1_1(a2435) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 1.40/1.56 inference(rewrite,[status(thm)],[])).
% 1.40/1.56 tff(4027,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a2437) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c1_1(a2435) | (~c2_1(a2437)) | (~c0_1(a2437))))),
% 1.40/1.56 inference(monotonicity,[status(thm)],[4026])).
% 1.40/1.56 tff(4028,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2437) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c1_1(a2435) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 1.40/1.56 inference(transitivity,[status(thm)],[4027, 4025])).
% 1.40/1.56 tff(4029,plain,
% 1.40/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2413) | c0_1(a2413) | (~c2_1(a2413)) | c2_1(a2435) | c1_1(a2435) | c0_1(a2435))),
% 1.40/1.56 inference(quant_inst,[status(thm)],[])).
% 1.40/1.56 tff(4030,plain,
% 1.40/1.56 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a2437) | c0_1(a2435) | c2_1(a2435) | c0_1(a2413) | c1_1(a2413) | (~ndr1_0) | (~c2_1(a2413)) | c1_1(a2435) | (~c2_1(a2437)) | (~c0_1(a2437))),
% 1.40/1.56 inference(modus_ponens,[status(thm)],[4029, 4028])).
% 1.40/1.56 tff(4031,plain,
% 1.40/1.56 (c1_1(a2435)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[4030, 192, 4024, 4023, 3982, 4022, 3981, 3980, 3978, 3977, 21])).
% 1.40/1.56 tff(4032,plain,
% 1.40/1.56 (hskp18 | hskp17 | (~c1_1(a2435))),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3869, 192, 3981, 3980, 3863])).
% 1.40/1.56 tff(4033,plain,
% 1.40/1.56 (hskp18),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[4032, 4031, 4019])).
% 1.40/1.56 tff(4034,plain,
% 1.40/1.56 (hskp13),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3041, 4033, 22])).
% 1.40/1.56 tff(4035,plain,
% 1.40/1.56 (~c0_1(a2418)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[321, 4034])).
% 1.40/1.56 tff(4036,plain,
% 1.40/1.56 (~c3_1(a2428)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3020, 4033])).
% 1.40/1.56 tff(4037,plain,
% 1.40/1.56 (~c2_1(a2428)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3026, 4033])).
% 1.40/1.56 tff(4038,plain,
% 1.40/1.56 (~c0_1(a2428)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[3032, 4033])).
% 1.40/1.56 tff(4039,plain,
% 1.40/1.56 (c2_1(a2418)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[329, 4034])).
% 1.40/1.56 tff(4040,plain,
% 1.40/1.56 (c1_1(a2418)),
% 1.40/1.56 inference(unit_resolution,[status(thm)],[337, 4034])).
% 1.40/1.56 tff(4041,plain,
% 1.40/1.56 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4042,plain,
% 1.40/1.57 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428)) <=> (c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4043,plain,
% 1.40/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 1.40/1.57 inference(monotonicity,[status(thm)],[4042])).
% 1.40/1.57 tff(4044,plain,
% 1.40/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.57 inference(transitivity,[status(thm)],[4043, 4041])).
% 1.40/1.57 tff(4045,plain,
% 1.40/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2418) | (~c1_1(a2418)) | (~c2_1(a2418)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(4046,plain,
% 1.40/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2418) | (~ndr1_0) | (~c2_1(a2418)) | (~c1_1(a2418)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4045, 4044])).
% 1.40/1.57 tff(4047,plain,
% 1.40/1.57 ($false),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4046, 192, 4006, 4040, 4039, 3980, 4038, 4037, 4036, 4035, 63, 4031])).
% 1.40/1.57 tff(4048,plain,(hskp1), inference(lemma,lemma(discharge,[]))).
% 1.40/1.57 tff(4049,plain,
% 1.40/1.57 (~c3_1(a2403)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[2291, 4048])).
% 1.40/1.57 tff(4050,plain,
% 1.40/1.57 (~c2_1(a2403)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[2297, 4048])).
% 1.40/1.57 tff(4051,plain,
% 1.40/1.57 (c1_1(a2403)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[2305, 4048])).
% 1.40/1.57 tff(4052,plain,
% 1.40/1.57 (hskp23 | c1_1(a2435)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[3816, 192, 4006, 4051, 3980, 4050, 4049, 628])).
% 1.40/1.57 tff(4053,plain,
% 1.40/1.57 (c1_1(a2435)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4052, 629])).
% 1.40/1.57 tff(4054,plain,
% 1.40/1.57 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))),
% 1.40/1.57 inference(bind,[status(th)],[])).
% 1.40/1.57 tff(4055,plain,
% 1.40/1.57 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.40/1.57 inference(quant_intro,[status(thm)],[4054])).
% 1.40/1.57 tff(4056,plain,
% 1.40/1.57 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4057,plain,
% 1.40/1.57 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp7) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))))),
% 1.40/1.57 inference(bind,[status(th)],[])).
% 1.40/1.57 tff(4058,plain,
% 1.40/1.57 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.40/1.57 inference(quant_intro,[status(thm)],[4057])).
% 1.40/1.57 tff(4059,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause191')).
% 1.40/1.57 tff(4060,plain,
% 1.40/1.57 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4059, 4058])).
% 1.40/1.57 tff(4061,plain,
% 1.40/1.57 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4060, 4056])).
% 1.40/1.57 tff(4062,plain,(
% 1.40/1.57 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.40/1.57 inference(skolemize,[status(sab)],[4061])).
% 1.40/1.57 tff(4063,plain,
% 1.40/1.57 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4062, 4055])).
% 1.40/1.57 tff(4064,plain,
% 1.40/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a2427) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c2_1(a2427)) | (~c0_1(a2427)) | (~c3_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a2427) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c2_1(a2427)) | (~c0_1(a2427)) | (~c3_1(a2427)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4065,plain,
% 1.40/1.57 (((~ndr1_0) | (~c3_1(a2427)) | (~c2_1(a2427)) | (~c0_1(a2427)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2427) | (~c0_1(a2427)) | (~c2_1(a2427))) <=> (c1_1(a2427) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c2_1(a2427)) | (~c0_1(a2427)) | (~c3_1(a2427)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4066,plain,
% 1.40/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2427)) | (~c2_1(a2427)) | (~c0_1(a2427)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2427) | (~c0_1(a2427)) | (~c2_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | (c1_1(a2427) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c2_1(a2427)) | (~c0_1(a2427)) | (~c3_1(a2427))))),
% 1.40/1.57 inference(monotonicity,[status(thm)],[4065])).
% 1.40/1.57 tff(4067,plain,
% 1.40/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2427)) | (~c2_1(a2427)) | (~c0_1(a2427)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2427) | (~c0_1(a2427)) | (~c2_1(a2427)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a2427) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c2_1(a2427)) | (~c0_1(a2427)) | (~c3_1(a2427)))),
% 1.40/1.57 inference(transitivity,[status(thm)],[4066, 4064])).
% 1.40/1.57 tff(4068,plain,
% 1.40/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a2427)) | (~c2_1(a2427)) | (~c0_1(a2427)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c1_1(a2427) | (~c0_1(a2427)) | (~c2_1(a2427)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(4069,plain,
% 1.40/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c1_1(W) | (~c0_1(W)) | (~c2_1(W)))) | c1_1(a2427) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c2_1(a2427)) | (~c0_1(a2427)) | (~c3_1(a2427))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4068, 4067])).
% 1.40/1.57 tff(4070,plain,
% 1.40/1.57 (~c0_1(a2427)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4069, 192, 3837, 3836, 4051, 3835, 4050, 4049, 2316])).
% 1.40/1.57 tff(4071,plain,
% 1.40/1.57 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a2427) | (~ndr1_0) | (~c2_1(a2427)) | c0_1(a2427) | (~c3_1(a2427)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a2427) | (~ndr1_0) | (~c2_1(a2427)) | c0_1(a2427) | (~c3_1(a2427)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4072,plain,
% 1.40/1.57 ((hskp5 | (~ndr1_0) | c0_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c1_1(a2427) | c0_1(a2427) | (~c2_1(a2427))) <=> (hskp5 | c1_1(a2427) | (~ndr1_0) | (~c2_1(a2427)) | c0_1(a2427) | (~c3_1(a2427)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4073,plain,
% 1.40/1.57 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c1_1(a2427) | c0_1(a2427) | (~c2_1(a2427)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a2427) | (~ndr1_0) | (~c2_1(a2427)) | c0_1(a2427) | (~c3_1(a2427))))),
% 1.40/1.57 inference(monotonicity,[status(thm)],[4072])).
% 1.40/1.57 tff(4074,plain,
% 1.40/1.57 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c1_1(a2427) | c0_1(a2427) | (~c2_1(a2427)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a2427) | (~ndr1_0) | (~c2_1(a2427)) | c0_1(a2427) | (~c3_1(a2427)))),
% 1.40/1.57 inference(transitivity,[status(thm)],[4073, 4071])).
% 1.40/1.57 tff(4075,plain,
% 1.40/1.57 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2427) | (~c3_1(a2427)) | (~c2_1(a2427)) | c1_1(a2427) | c0_1(a2427) | (~c2_1(a2427)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(4076,plain,
% 1.40/1.57 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a2427) | (~ndr1_0) | (~c2_1(a2427)) | c0_1(a2427) | (~c3_1(a2427))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4075, 4074])).
% 1.40/1.57 tff(4077,plain,
% 1.40/1.57 ($false),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4076, 192, 1955, 3837, 3836, 3835, 1965, 4070])).
% 1.40/1.57 tff(4078,plain,((~hskp17) | hskp5), inference(lemma,lemma(discharge,[]))).
% 1.40/1.57 tff(4079,plain,
% 1.40/1.57 (~hskp17),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4078, 1955])).
% 1.40/1.57 tff(4080,plain,
% 1.40/1.57 (hskp18),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4032, 4079, 4053])).
% 1.40/1.57 tff(4081,plain,
% 1.40/1.57 (~c3_1(a2428)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[3020, 4080])).
% 1.40/1.57 tff(4082,plain,
% 1.40/1.57 (~c2_1(a2428)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[3026, 4080])).
% 1.40/1.57 tff(4083,plain,
% 1.40/1.57 (~c0_1(a2428)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[3032, 4080])).
% 1.40/1.57 tff(4084,assumption,(~c2_1(a2428)), introduced(assumption)).
% 1.40/1.57 tff(4085,assumption,(~c0_1(a2428)), introduced(assumption)).
% 1.40/1.57 tff(4086,plain,
% 1.40/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2428) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2428) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4087,plain,
% 1.40/1.57 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2428) | c1_1(a2428) | c0_1(a2428)) <=> (c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2428) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4088,plain,
% 1.40/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2428) | c1_1(a2428) | c0_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2428) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 1.40/1.57 inference(monotonicity,[status(thm)],[4087])).
% 1.40/1.57 tff(4089,plain,
% 1.40/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2428) | c1_1(a2428) | c0_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2428) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.57 inference(transitivity,[status(thm)],[4088, 4086])).
% 1.40/1.57 tff(4090,plain,
% 1.40/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c2_1(a2403) | c3_1(a2403) | (~c1_1(a2403)) | c2_1(a2428) | c1_1(a2428) | c0_1(a2428))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(4091,plain,
% 1.40/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | c1_1(a2428) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4090, 4089])).
% 1.40/1.57 tff(4092,plain,
% 1.40/1.57 (c1_1(a2428)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4091, 192, 4006, 4051, 3980, 4085, 4084, 4050, 4049, 11, 4053])).
% 1.40/1.57 tff(4093,plain,
% 1.40/1.57 (hskp14 | (~c3_1(a2498))),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[2624, 192, 629, 2594, 2610, 42])).
% 1.40/1.57 tff(4094,plain,
% 1.40/1.57 (~c3_1(a2498)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4093, 2718])).
% 1.40/1.57 tff(4095,plain,
% 1.40/1.57 (hskp6 | c3_1(a2498)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[2615, 192, 629, 2610, 2602, 2087])).
% 1.40/1.57 tff(4096,plain,
% 1.40/1.57 (hskp6),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4095, 4094])).
% 1.40/1.57 tff(4097,plain,
% 1.40/1.57 (c1_1(a2410)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[903, 4096])).
% 1.40/1.57 tff(4098,plain,
% 1.40/1.57 (c0_1(a2410)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[911, 4096])).
% 1.40/1.57 tff(4099,plain,
% 1.40/1.57 (~c3_1(a2410)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[2726, 192, 629, 2718, 4098, 4097, 42])).
% 1.40/1.57 tff(4100,plain,
% 1.40/1.57 (^[U: $i] : refl((hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.40/1.57 inference(bind,[status(th)],[])).
% 1.40/1.57 tff(4101,plain,
% 1.40/1.57 (![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.40/1.57 inference(quant_intro,[status(thm)],[4100])).
% 1.40/1.57 tff(4102,plain,
% 1.40/1.57 (![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4103,plain,
% 1.40/1.57 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp7) <=> ((hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp7))), rewrite(((hskp25 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp7) <=> (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp7) <=> (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.40/1.57 inference(bind,[status(th)],[])).
% 1.40/1.57 tff(4104,plain,
% 1.40/1.57 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp7) <=> ![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.40/1.57 inference(quant_intro,[status(thm)],[4103])).
% 1.40/1.57 tff(4105,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp25) | hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause164')).
% 1.40/1.57 tff(4106,plain,
% 1.40/1.57 (![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4105, 4104])).
% 1.40/1.57 tff(4107,plain,
% 1.40/1.57 (![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4106, 4102])).
% 1.40/1.57 tff(4108,plain,(
% 1.40/1.57 ![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.40/1.57 inference(skolemize,[status(sab)],[4107])).
% 1.40/1.57 tff(4109,plain,
% 1.40/1.57 (![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4108, 4101])).
% 1.40/1.57 tff(4110,plain,
% 1.40/1.57 (~c2_1(a2410)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[895, 4096])).
% 1.40/1.57 tff(4111,plain,
% 1.40/1.57 (((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp7 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp7 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4112,plain,
% 1.40/1.57 ((hskp25 | hskp7 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410))) <=> (hskp25 | hskp7 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4113,plain,
% 1.40/1.57 (((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp7 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp7 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410))))),
% 1.40/1.57 inference(monotonicity,[status(thm)],[4112])).
% 1.40/1.57 tff(4114,plain,
% 1.40/1.57 (((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp7 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))) <=> ((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp7 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.40/1.57 inference(transitivity,[status(thm)],[4113, 4111])).
% 1.40/1.57 tff(4115,plain,
% 1.40/1.57 ((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp25 | hskp7 | (~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(4116,plain,
% 1.40/1.57 ((~![U: $i] : (hskp25 | hskp7 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp25 | hskp7 | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4115, 4114])).
% 1.40/1.57 tff(4117,plain,
% 1.40/1.57 (hskp7),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4116, 192, 889, 4098, 4097, 4110, 4109])).
% 1.40/1.57 tff(4118,plain,
% 1.40/1.57 (((~hskp7) | (~c3_1(a2411))) <=> ((~hskp7) | (~c3_1(a2411)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4119,plain,
% 1.40/1.57 (((~c3_1(a2411)) | (~hskp7)) <=> ((~hskp7) | (~c3_1(a2411)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4120,axiom,((~c3_1(a2411)) | (~hskp7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 1.40/1.57 tff(4121,plain,
% 1.40/1.57 ((~hskp7) | (~c3_1(a2411))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4120, 4119])).
% 1.40/1.57 tff(4122,plain,
% 1.40/1.57 ((~hskp7) | (~c3_1(a2411))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4121, 4118])).
% 1.40/1.57 tff(4123,plain,
% 1.40/1.57 (~c3_1(a2411)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4122, 4117])).
% 1.40/1.57 tff(4124,plain,
% 1.40/1.57 (~c1_1(a2411)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[2827, 4117])).
% 1.40/1.57 tff(4125,plain,
% 1.40/1.57 (c2_1(a2411)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[2835, 4117])).
% 1.40/1.57 tff(4126,plain,
% 1.40/1.57 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a2411) | c3_1(a2411) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c3_1(a2410) | (~c2_1(a2411)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a2411) | c3_1(a2411) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c3_1(a2410) | (~c2_1(a2411)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4127,plain,
% 1.40/1.57 ((hskp14 | (~ndr1_0) | c3_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2411) | c3_1(a2411) | (~c2_1(a2411))) <=> (hskp14 | c1_1(a2411) | c3_1(a2411) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c3_1(a2410) | (~c2_1(a2411)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4128,plain,
% 1.40/1.57 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2411) | c3_1(a2411) | (~c2_1(a2411)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | c1_1(a2411) | c3_1(a2411) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c3_1(a2410) | (~c2_1(a2411))))),
% 1.40/1.57 inference(monotonicity,[status(thm)],[4127])).
% 1.40/1.57 tff(4129,plain,
% 1.40/1.57 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2411) | c3_1(a2411) | (~c2_1(a2411)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a2411) | c3_1(a2411) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c3_1(a2410) | (~c2_1(a2411)))),
% 1.40/1.57 inference(transitivity,[status(thm)],[4128, 4126])).
% 1.40/1.57 tff(4130,plain,
% 1.40/1.57 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2411) | c3_1(a2411) | (~c2_1(a2411)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(4131,plain,
% 1.40/1.57 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp14 | c1_1(a2411) | c3_1(a2411) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c3_1(a2410) | (~c2_1(a2411))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4130, 4129])).
% 1.40/1.57 tff(4132,plain,
% 1.40/1.57 ($false),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4131, 192, 2718, 4125, 4098, 4097, 4124, 4123, 2950, 4099])).
% 1.40/1.57 tff(4133,plain,(hskp14 | hskp25 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.40/1.57 tff(4134,plain,
% 1.40/1.57 (hskp14),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4133, 889, 629])).
% 1.40/1.57 tff(4135,plain,
% 1.40/1.57 (~c3_1(a2420)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[679, 4134])).
% 1.40/1.57 tff(4136,plain,
% 1.40/1.57 (c2_1(a2420)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[687, 4134])).
% 1.40/1.57 tff(4137,plain,
% 1.40/1.57 (c1_1(a2420)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[695, 4134])).
% 1.40/1.57 tff(4138,plain,
% 1.40/1.57 (hskp6),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[2909, 192, 629, 4137, 4136, 4135, 2087])).
% 1.40/1.57 tff(4139,plain,
% 1.40/1.57 (~c2_1(a2410)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[895, 4138])).
% 1.40/1.57 tff(4140,plain,
% 1.40/1.57 (c1_1(a2410)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[903, 4138])).
% 1.40/1.57 tff(4141,plain,
% 1.40/1.57 (c0_1(a2410)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[911, 4138])).
% 1.40/1.57 tff(4142,plain,
% 1.40/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4143,plain,
% 1.40/1.57 (((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))),
% 1.40/1.57 inference(rewrite,[status(thm)],[])).
% 1.40/1.57 tff(4144,plain,
% 1.40/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435))))),
% 1.40/1.57 inference(monotonicity,[status(thm)],[4143])).
% 1.40/1.57 tff(4145,plain,
% 1.40/1.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435)))),
% 1.40/1.57 inference(transitivity,[status(thm)],[4144, 4142])).
% 1.40/1.57 tff(4146,plain,
% 1.40/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2410) | (~c1_1(a2410)) | (~c0_1(a2410)) | c2_1(a2425) | c1_1(a2425) | (~c0_1(a2425)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.40/1.57 inference(quant_inst,[status(thm)],[])).
% 1.40/1.57 tff(4147,plain,
% 1.40/1.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2425) | c2_1(a2410) | (~ndr1_0) | (~c1_1(a2410)) | (~c0_1(a2410)) | c1_1(a2425) | (~c0_1(a2425)) | (~c1_1(a2435))),
% 1.40/1.57 inference(modus_ponens,[status(thm)],[4146, 4145])).
% 1.40/1.57 tff(4148,plain,
% 1.40/1.57 (c1_1(a2425)),
% 1.40/1.57 inference(unit_resolution,[status(thm)],[4147, 192, 3500, 4141, 4140, 3981, 3980, 3499, 4139, 1879, 4053])).
% 1.40/1.57 tff(4149,plain,
% 1.40/1.57 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c2_1(a2435) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c2_1(a2435) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4150,plain,
% 1.40/1.58 ((hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435))) <=> (hskp30 | c2_1(a2435) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4151,plain,
% 1.40/1.58 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | c2_1(a2435) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 1.40/1.58 inference(monotonicity,[status(thm)],[4150])).
% 1.40/1.58 tff(4152,plain,
% 1.40/1.58 (((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c2_1(a2435) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.58 inference(transitivity,[status(thm)],[4151, 4149])).
% 1.40/1.58 tff(4153,plain,
% 1.40/1.58 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp30 | (~ndr1_0) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c2_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(4154,plain,
% 1.40/1.58 ((~![V: $i, U: $i] : (hskp30 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp30 | c2_1(a2435) | c3_1(a2425) | (~ndr1_0) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[4153, 4152])).
% 1.40/1.58 tff(4155,plain,
% 1.40/1.58 (hskp30 | (~c1_1(a2425)) | (~c1_1(a2435))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4154, 192, 4006, 3500, 3980, 3498, 564])).
% 1.40/1.58 tff(4156,plain,
% 1.40/1.58 (hskp30),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4155, 4148, 4053])).
% 1.40/1.58 tff(4157,plain,
% 1.40/1.58 ((~hskp11) | hskp23 | (~c1_1(a2425))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[715, 3499, 3498])).
% 1.40/1.58 tff(4158,plain,
% 1.40/1.58 (~hskp11),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4157, 4148, 629])).
% 1.40/1.58 tff(4159,assumption,(hskp30), introduced(assumption)).
% 1.40/1.58 tff(4160,plain,
% 1.40/1.58 (c3_1(a2450)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[582, 4159])).
% 1.40/1.58 tff(4161,plain,
% 1.40/1.58 (c1_1(a2450)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[590, 4159])).
% 1.40/1.58 tff(4162,plain,
% 1.40/1.58 (c0_1(a2450)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[598, 4159])).
% 1.40/1.58 tff(4163,plain,
% 1.40/1.58 (hskp19 | c2_1(a2450)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[1140, 192, 889, 3790, 3787, 106])).
% 1.40/1.58 tff(4164,plain,
% 1.40/1.58 (c2_1(a2450)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4163, 43])).
% 1.40/1.58 tff(4165,plain,
% 1.40/1.58 (^[U: $i] : refl((hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))),
% 1.40/1.58 inference(bind,[status(th)],[])).
% 1.40/1.58 tff(4166,plain,
% 1.40/1.58 (![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 1.40/1.58 inference(quant_intro,[status(thm)],[4165])).
% 1.40/1.58 tff(4167,plain,
% 1.40/1.58 (![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4168,plain,
% 1.40/1.58 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp15))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) <=> (hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp11) <=> ((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp11))), rewrite(((hskp15 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U))) | hskp11) <=> (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp11) <=> (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.40/1.58 inference(bind,[status(th)],[])).
% 1.40/1.58 tff(4169,plain,
% 1.40/1.58 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp11) <=> ![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 1.40/1.58 inference(quant_intro,[status(thm)],[4168])).
% 1.40/1.58 tff(4170,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp15) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause171')).
% 1.40/1.58 tff(4171,plain,
% 1.40/1.58 (![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[4170, 4169])).
% 1.40/1.58 tff(4172,plain,
% 1.40/1.58 (![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[4171, 4167])).
% 1.40/1.58 tff(4173,plain,(
% 1.40/1.58 ![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 1.40/1.58 inference(skolemize,[status(sab)],[4172])).
% 1.40/1.58 tff(4174,plain,
% 1.40/1.58 (![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[4173, 4166])).
% 1.40/1.58 tff(4175,plain,
% 1.40/1.58 (((~![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)))) <=> ((~![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp11 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4176,plain,
% 1.40/1.58 ((~![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(4177,plain,
% 1.40/1.58 ((~![U: $i] : (hskp15 | hskp11 | (~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)))) | hskp15 | hskp11 | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[4176, 4175])).
% 1.40/1.58 tff(4178,plain,
% 1.40/1.58 (hskp15 | (~c2_1(a2450))),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4177, 192, 307, 3787, 3786, 4174])).
% 1.40/1.58 tff(4179,plain,
% 1.40/1.58 (hskp15),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4178, 4164])).
% 1.40/1.58 tff(4180,plain,
% 1.40/1.58 (~c2_1(a2422)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[528, 4179])).
% 1.40/1.58 tff(4181,plain,
% 1.40/1.58 (c3_1(a2422)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[514, 4179])).
% 1.40/1.58 tff(4182,plain,
% 1.40/1.58 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a2422) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | c0_1(a2422) | (~c3_1(a2422)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a2422) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | c0_1(a2422) | (~c3_1(a2422)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4183,plain,
% 1.40/1.58 ((hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2422) | c0_1(a2422) | (~c3_1(a2422))) <=> (hskp12 | c2_1(a2422) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | c0_1(a2422) | (~c3_1(a2422)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4184,plain,
% 1.40/1.58 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2422) | c0_1(a2422) | (~c3_1(a2422)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c2_1(a2422) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | c0_1(a2422) | (~c3_1(a2422))))),
% 1.40/1.58 inference(monotonicity,[status(thm)],[4183])).
% 1.40/1.58 tff(4185,plain,
% 1.40/1.58 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2422) | c0_1(a2422) | (~c3_1(a2422)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a2422) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | c0_1(a2422) | (~c3_1(a2422)))),
% 1.40/1.58 inference(transitivity,[status(thm)],[4184, 4182])).
% 1.40/1.58 tff(4186,plain,
% 1.40/1.58 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2422) | c0_1(a2422) | (~c3_1(a2422)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(4187,plain,
% 1.40/1.58 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c2_1(a2422) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | c0_1(a2422) | (~c3_1(a2422))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[4186, 4185])).
% 1.40/1.58 tff(4188,plain,
% 1.40/1.58 (c0_1(a2422)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4187, 192, 308, 3790, 3787, 3786, 4181, 4180, 766])).
% 1.40/1.58 tff(4189,plain,
% 1.40/1.58 (c1_1(a2422)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[522, 4179])).
% 1.40/1.58 tff(4190,plain,
% 1.40/1.58 ($false),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[2658, 192, 889, 43, 4189, 4180, 106, 4188])).
% 1.40/1.58 tff(4191,plain,(hskp19 | hskp25 | hskp12 | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2450)) | hskp11), inference(lemma,lemma(discharge,[]))).
% 1.40/1.58 tff(4192,plain,
% 1.40/1.58 (hskp19),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4191, 4162, 308, 889, 4161, 4160, 307])).
% 1.40/1.58 tff(4193,plain,
% 1.40/1.58 (~c0_1(a2432)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[297, 4192])).
% 1.40/1.58 tff(4194,plain,
% 1.40/1.58 (c1_1(a2432)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[305, 4192])).
% 1.40/1.58 tff(4195,plain,
% 1.40/1.58 (~c2_1(a2432)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[314, 192, 308, 307, 4194, 4193, 278])).
% 1.40/1.58 tff(4196,plain,
% 1.40/1.58 (c3_1(a2432)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[822, 4192])).
% 1.40/1.58 tff(4197,plain,
% 1.40/1.58 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2432)) | c2_1(a2432))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2432)) | c2_1(a2432))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4198,plain,
% 1.40/1.58 ((hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432))) <=> (hskp12 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2432)) | c2_1(a2432))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4199,plain,
% 1.40/1.58 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2432)) | c2_1(a2432)))),
% 1.40/1.58 inference(monotonicity,[status(thm)],[4198])).
% 1.40/1.58 tff(4200,plain,
% 1.40/1.58 (((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432)))) <=> ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2432)) | c2_1(a2432))),
% 1.40/1.58 inference(transitivity,[status(thm)],[4199, 4197])).
% 1.40/1.58 tff(4201,plain,
% 1.40/1.58 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp12 | (~ndr1_0) | (~c3_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2450)) | c2_1(a2432) | c0_1(a2432) | (~c3_1(a2432)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(4202,plain,
% 1.40/1.58 ((~![V: $i, U: $i] : (hskp12 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp12 | c0_1(a2432) | (~ndr1_0) | (~c3_1(a2450)) | (~c0_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2432)) | c2_1(a2432)),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[4201, 4200])).
% 1.40/1.58 tff(4203,plain,
% 1.40/1.58 ($false),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4202, 192, 308, 4162, 4161, 4160, 4196, 4193, 766, 4195])).
% 1.40/1.58 tff(4204,plain,((~hskp30) | hskp12 | hskp11 | hskp25), inference(lemma,lemma(discharge,[]))).
% 1.40/1.58 tff(4205,plain,
% 1.40/1.58 (hskp12),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4204, 4158, 4156, 889])).
% 1.40/1.58 tff(4206,plain,
% 1.40/1.58 (~c1_1(a2417)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[217, 4205])).
% 1.40/1.58 tff(4207,plain,
% 1.40/1.58 (~c0_1(a2417)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[223, 4205])).
% 1.40/1.58 tff(4208,assumption,(~c3_1(a2428)), introduced(assumption)).
% 1.40/1.58 tff(4209,plain,
% 1.40/1.58 (c3_1(a2417)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[231, 4205])).
% 1.40/1.58 tff(4210,plain,
% 1.40/1.58 (c3_1(a2450)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[582, 4156])).
% 1.40/1.58 tff(4211,plain,
% 1.40/1.58 (c1_1(a2450)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[590, 4156])).
% 1.40/1.58 tff(4212,plain,
% 1.40/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2417)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2417)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4213,plain,
% 1.40/1.58 (((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428)) <=> (c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2417)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4214,plain,
% 1.40/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2417))))),
% 1.40/1.58 inference(monotonicity,[status(thm)],[4213])).
% 1.40/1.58 tff(4215,plain,
% 1.40/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2417)))),
% 1.40/1.58 inference(transitivity,[status(thm)],[4214, 4212])).
% 1.40/1.58 tff(4216,plain,
% 1.40/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c1_1(a2417) | c0_1(a2417) | (~c3_1(a2417)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(4217,plain,
% 1.40/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c3_1(a2417))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[4216, 4215])).
% 1.40/1.58 tff(4218,plain,
% 1.40/1.58 (~c2_1(a2450)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4217, 192, 4211, 4210, 4209, 4085, 4084, 4208, 4207, 4206, 2530])).
% 1.40/1.58 tff(4219,plain,
% 1.40/1.58 (c0_1(a2450)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[598, 4156])).
% 1.40/1.58 tff(4220,plain,
% 1.40/1.58 (~c2_1(a2417)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[786, 192, 4219, 4211, 4210, 3500, 4209, 3499, 3498, 4206, 554])).
% 1.40/1.58 tff(4221,plain,
% 1.40/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2428)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2428)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4222,plain,
% 1.40/1.58 (((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2428) | c3_1(a2428) | (~c1_1(a2428)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417)) <=> (c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2428)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4223,plain,
% 1.40/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2428) | c3_1(a2428) | (~c1_1(a2428)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2428))))),
% 1.40/1.58 inference(monotonicity,[status(thm)],[4222])).
% 1.40/1.58 tff(4224,plain,
% 1.40/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2428) | c3_1(a2428) | (~c1_1(a2428)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2428)))),
% 1.40/1.58 inference(transitivity,[status(thm)],[4223, 4221])).
% 1.40/1.58 tff(4225,plain,
% 1.40/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2428) | c3_1(a2428) | (~c1_1(a2428)) | c2_1(a2417) | c1_1(a2417) | c0_1(a2417))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(4226,plain,
% 1.40/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c2_1(V) | c3_1(V) | (~c1_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a2428) | c3_1(a2428) | c0_1(a2417) | c1_1(a2417) | (~ndr1_0) | (~c3_1(a2450)) | c2_1(a2450) | (~c1_1(a2450)) | c2_1(a2417) | (~c1_1(a2428))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[4225, 4224])).
% 1.40/1.58 tff(4227,plain,
% 1.40/1.58 ($false),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4226, 192, 4211, 4210, 4084, 4208, 4207, 4206, 11, 4220, 4218, 4092])).
% 1.40/1.58 tff(4228,plain,(hskp25 | c2_1(a2428) | c3_1(a2428) | c0_1(a2428) | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.40/1.58 tff(4229,plain,
% 1.40/1.58 (hskp25),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4228, 4082, 4081, 4083, 629])).
% 1.40/1.58 tff(4230,plain,
% 1.40/1.58 (~c0_1(a2478)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[120, 4229])).
% 1.40/1.58 tff(4231,plain,
% 1.40/1.58 (c2_1(a2478)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[114, 4229])).
% 1.40/1.58 tff(4232,plain,
% 1.40/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2478) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c1_1(a2478)) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2478) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4233,plain,
% 1.40/1.58 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428)) <=> (c0_1(a2478) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4234,plain,
% 1.40/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2478) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c1_1(a2478)) | (~c2_1(a2478))))),
% 1.40/1.58 inference(monotonicity,[status(thm)],[4233])).
% 1.40/1.58 tff(4235,plain,
% 1.40/1.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2478) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c1_1(a2478)) | (~c2_1(a2478)))),
% 1.40/1.58 inference(transitivity,[status(thm)],[4234, 4232])).
% 1.40/1.58 tff(4236,plain,
% 1.40/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2478) | (~c1_1(a2478)) | (~c2_1(a2478)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(4237,plain,
% 1.40/1.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2478) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c1_1(a2478)) | (~c2_1(a2478))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[4236, 4235])).
% 1.40/1.58 tff(4238,plain,
% 1.40/1.58 (~c1_1(a2478)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4237, 192, 4231, 4006, 4230, 3980, 4083, 4082, 4081, 63, 4053])).
% 1.40/1.58 tff(4239,plain,
% 1.40/1.58 (hskp21),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4020, 4079])).
% 1.40/1.58 tff(4240,plain,
% 1.40/1.58 (~c1_1(a2437)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[1705, 4239])).
% 1.40/1.58 tff(4241,plain,
% 1.40/1.58 (~c3_1(a2478)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[126, 4229])).
% 1.40/1.58 tff(4242,plain,
% 1.40/1.58 (c2_1(a2437)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[1713, 4239])).
% 1.40/1.58 tff(4243,plain,
% 1.40/1.58 (c0_1(a2437)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[1728, 4239])).
% 1.40/1.58 tff(4244,plain,
% 1.40/1.58 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c3_1(a2478) | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a2478) | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4245,plain,
% 1.40/1.58 ((hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478))) <=> (hskp3 | c3_1(a2478) | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4246,plain,
% 1.40/1.58 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | c3_1(a2478) | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.40/1.58 inference(monotonicity,[status(thm)],[4245])).
% 1.40/1.58 tff(4247,plain,
% 1.40/1.58 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a2478) | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.58 inference(transitivity,[status(thm)],[4246, 4244])).
% 1.40/1.58 tff(4248,plain,
% 1.40/1.58 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp3 | (~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | c3_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.58 inference(quant_inst,[status(thm)],[])).
% 1.40/1.58 tff(4249,plain,
% 1.40/1.58 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp3 | c3_1(a2478) | c1_1(a2437) | (~ndr1_0) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.40/1.58 inference(modus_ponens,[status(thm)],[4248, 4247])).
% 1.40/1.58 tff(4250,plain,
% 1.40/1.58 (hskp3),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[4249, 192, 4231, 4243, 4242, 4241, 4240, 1687, 4238])).
% 1.40/1.58 tff(4251,plain,
% 1.40/1.58 (~c3_1(a2405)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[1203, 4250])).
% 1.40/1.58 tff(4252,plain,
% 1.40/1.58 (c2_1(a2405)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[1228, 4250])).
% 1.40/1.58 tff(4253,plain,
% 1.40/1.58 (c0_1(a2405)),
% 1.40/1.58 inference(unit_resolution,[status(thm)],[1211, 4250])).
% 1.40/1.58 tff(4254,plain,
% 1.40/1.58 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp7 | c0_1(a2435) | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp7 | c0_1(a2435) | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4255,plain,
% 1.40/1.58 ((hskp7 | (~ndr1_0) | c3_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c0_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435))) <=> (hskp7 | c0_1(a2435) | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.58 inference(rewrite,[status(thm)],[])).
% 1.40/1.58 tff(4256,plain,
% 1.40/1.58 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c0_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp7 | c0_1(a2435) | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c1_1(a2435)) | (~c3_1(a2435))))),
% 1.40/1.58 inference(monotonicity,[status(thm)],[4255])).
% 1.40/1.59 tff(4257,plain,
% 1.40/1.59 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c0_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp7 | c0_1(a2435) | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[4256, 4254])).
% 1.40/1.59 tff(4258,plain,
% 1.40/1.59 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c3_1(a2405) | (~c2_1(a2405)) | (~c0_1(a2405)) | c0_1(a2435) | (~c1_1(a2435)) | (~c3_1(a2435)))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(4259,plain,
% 1.40/1.59 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)) | (~c3_1(V)))) | hskp7 | c0_1(a2435) | c3_1(a2405) | (~ndr1_0) | (~c0_1(a2405)) | (~c2_1(a2405)) | (~c1_1(a2435)) | (~c3_1(a2435))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[4258, 4257])).
% 1.40/1.59 tff(4260,plain,
% 1.40/1.59 (hskp7),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4259, 192, 4006, 4253, 4252, 3981, 4251, 4063, 4053])).
% 1.40/1.59 tff(4261,plain,
% 1.40/1.59 (~c1_1(a2411)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[2827, 4260])).
% 1.40/1.59 tff(4262,plain,
% 1.40/1.59 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a2478) | c0_1(a2435) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2478) | c0_1(a2435) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4263,plain,
% 1.40/1.59 ((hskp4 | (~ndr1_0) | c0_1(a2435) | (~c3_1(a2435)) | (~c1_1(a2435)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478))) <=> (hskp4 | c0_1(a2478) | c0_1(a2435) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4264,plain,
% 1.40/1.59 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2435) | (~c3_1(a2435)) | (~c1_1(a2435)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | c0_1(a2478) | c0_1(a2435) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[4263])).
% 1.40/1.59 tff(4265,plain,
% 1.40/1.59 (((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2435) | (~c3_1(a2435)) | (~c1_1(a2435)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))) <=> ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2478) | c0_1(a2435) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[4264, 4262])).
% 1.40/1.59 tff(4266,plain,
% 1.40/1.59 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp4 | (~ndr1_0) | c0_1(a2435) | (~c3_1(a2435)) | (~c1_1(a2435)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(4267,plain,
% 1.40/1.59 ((~![V: $i, U: $i] : (hskp4 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp4 | c0_1(a2478) | c0_1(a2435) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[4266, 4265])).
% 1.40/1.59 tff(4268,plain,
% 1.40/1.59 (hskp4),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4267, 192, 4231, 4006, 4230, 3981, 982, 4053, 4238])).
% 1.40/1.59 tff(4269,plain,
% 1.40/1.59 (~c2_1(a2407)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[1416, 4268])).
% 1.40/1.59 tff(4270,plain,
% 1.40/1.59 (~c1_1(a2407)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[1410, 4268])).
% 1.40/1.59 tff(4271,plain,
% 1.40/1.59 (c0_1(a2407)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[1949, 4268])).
% 1.40/1.59 tff(4272,plain,
% 1.40/1.59 (hskp22),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[1501, 192, 1955, 4271, 4270, 4269, 1495])).
% 1.40/1.59 tff(4273,plain,
% 1.40/1.59 (~c2_1(a2453)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[1456, 4272])).
% 1.40/1.59 tff(4274,plain,
% 1.40/1.59 (~c1_1(a2453)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[1475, 4272])).
% 1.40/1.59 tff(4275,plain,
% 1.40/1.59 (~c0_1(a2453)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[1462, 4272])).
% 1.40/1.59 tff(4276,plain,
% 1.40/1.59 (c2_1(a2411)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[2835, 4260])).
% 1.40/1.59 tff(4277,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2437) | c1_1(a2411) | (~ndr1_0) | c0_1(a2411) | (~c2_1(a2411)) | (~c2_1(a2437)) | (~c0_1(a2437)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2437) | c1_1(a2411) | (~ndr1_0) | c0_1(a2411) | (~c2_1(a2411)) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4278,plain,
% 1.40/1.59 (((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453)) <=> (c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2437) | c1_1(a2411) | (~ndr1_0) | c0_1(a2411) | (~c2_1(a2411)) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4279,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2437) | c1_1(a2411) | (~ndr1_0) | c0_1(a2411) | (~c2_1(a2411)) | (~c2_1(a2437)) | (~c0_1(a2437))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[4278])).
% 1.40/1.59 tff(4280,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2437) | c1_1(a2411) | (~ndr1_0) | c0_1(a2411) | (~c2_1(a2411)) | (~c2_1(a2437)) | (~c0_1(a2437)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[4279, 4277])).
% 1.40/1.59 tff(4281,plain,
% 1.40/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2437) | (~c2_1(a2437)) | (~c0_1(a2437)) | c1_1(a2411) | c0_1(a2411) | (~c2_1(a2411)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(4282,plain,
% 1.40/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2437) | c1_1(a2411) | (~ndr1_0) | c0_1(a2411) | (~c2_1(a2411)) | (~c2_1(a2437)) | (~c0_1(a2437))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[4281, 4280])).
% 1.40/1.59 tff(4283,plain,
% 1.40/1.59 (c0_1(a2411)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4282, 192, 4243, 4242, 4276, 4275, 4274, 4273, 4240, 4261, 21])).
% 1.40/1.59 tff(4284,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c1_1(a2478) | (~c2_1(a2478)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4285,plain,
% 1.40/1.59 (((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453)) <=> (c0_1(a2478) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4286,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a2478) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c1_1(a2478) | (~c2_1(a2478))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[4285])).
% 1.40/1.59 tff(4287,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c1_1(a2478) | (~c2_1(a2478)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[4286, 4284])).
% 1.40/1.59 tff(4288,plain,
% 1.40/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a2411) | (~c2_1(a2411)) | (~c0_1(a2411)) | c1_1(a2478) | c0_1(a2478) | (~c2_1(a2478)) | c2_1(a2453) | c1_1(a2453) | c0_1(a2453))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(4289,plain,
% 1.40/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a2478) | c0_1(a2453) | c1_1(a2453) | c2_1(a2453) | c1_1(a2411) | (~ndr1_0) | (~c0_1(a2411)) | (~c2_1(a2411)) | c1_1(a2478) | (~c2_1(a2478))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[4288, 4287])).
% 1.40/1.59 tff(4290,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4289, 192, 4231, 4276, 4230, 4275, 4274, 4273, 4261, 21, 4238, 4283])).
% 1.40/1.59 tff(4291,plain,(hskp5 | hskp23), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(4292,plain,
% 1.40/1.59 (hskp5),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4291, 629])).
% 1.40/1.59 tff(4293,plain,
% 1.40/1.59 (~c2_1(a2408)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[373, 4292])).
% 1.40/1.59 tff(4294,plain,
% 1.40/1.59 (c3_1(a2408)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[396, 4292])).
% 1.40/1.59 tff(4295,plain,
% 1.40/1.59 (c1_1(a2408)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[2335, 192, 629, 4294, 4051, 4293, 4050, 4049, 628])).
% 1.40/1.59 tff(4296,plain,
% 1.40/1.59 (c0_1(a2408)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[381, 4292])).
% 1.40/1.59 tff(4297,plain,
% 1.40/1.59 ((~c1_1(a2408)) | c1_1(a2425)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[2280, 192, 3500, 4296, 3981, 3980, 3499, 4293, 1879, 4053])).
% 1.40/1.59 tff(4298,plain,
% 1.40/1.59 (c1_1(a2425)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4297, 4295])).
% 1.40/1.59 tff(4299,plain,
% 1.40/1.59 (hskp30 | (~c1_1(a2408)) | (~c1_1(a2425))),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[644, 192, 3500, 4294, 3498, 4293, 564])).
% 1.40/1.59 tff(4300,plain,
% 1.40/1.59 (hskp30),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4299, 4295, 4298])).
% 1.40/1.59 tff(4301,plain,
% 1.40/1.59 (c3_1(a2450)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[582, 4300])).
% 1.40/1.59 tff(4302,plain,
% 1.40/1.59 (c1_1(a2450)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[590, 4300])).
% 1.40/1.59 tff(4303,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4304,plain,
% 1.40/1.59 (((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4305,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[4304])).
% 1.40/1.59 tff(4306,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[4305, 4303])).
% 1.40/1.59 tff(4307,plain,
% 1.40/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(4308,plain,
% 1.40/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c3_1(a2450)) | (~c2_1(a2450)) | (~c1_1(a2450)) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[4307, 4306])).
% 1.40/1.59 tff(4309,plain,
% 1.40/1.59 (~c2_1(a2450)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4308, 192, 4302, 4301, 3500, 2628, 3498, 888, 882, 1076, 4298])).
% 1.40/1.59 tff(4310,plain,
% 1.40/1.59 (hskp12 | (~c1_1(a2408))),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[773, 192, 4006, 4296, 4294, 3981, 3980, 766])).
% 1.40/1.59 tff(4311,plain,
% 1.40/1.59 (hskp12),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4310, 4295])).
% 1.40/1.59 tff(4312,plain,
% 1.40/1.59 (~c1_1(a2417)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[217, 4311])).
% 1.40/1.59 tff(4313,plain,
% 1.40/1.59 (c3_1(a2417)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[231, 4311])).
% 1.40/1.59 tff(4314,plain,
% 1.40/1.59 (c0_1(a2450)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[598, 4300])).
% 1.40/1.59 tff(4315,plain,
% 1.40/1.59 (~c2_1(a2417)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[786, 192, 4314, 4302, 4301, 3500, 4313, 3499, 3498, 4312, 554])).
% 1.40/1.59 tff(4316,plain,
% 1.40/1.59 (~c0_1(a2417)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[223, 4311])).
% 1.40/1.59 tff(4317,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[794, 192, 4302, 4301, 3499, 3498, 4316, 4312, 11, 4315, 4309, 4298])).
% 1.40/1.59 tff(4318,plain,(hskp23), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(4319,plain,
% 1.40/1.59 (hskp15),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[506, 4318])).
% 1.40/1.59 tff(4320,plain,
% 1.40/1.59 (~c2_1(a2422)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[528, 4319])).
% 1.40/1.59 tff(4321,plain,
% 1.40/1.59 (c3_1(a2422)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[514, 4319])).
% 1.40/1.59 tff(4322,plain,
% 1.40/1.59 (c1_1(a2422)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[522, 4319])).
% 1.40/1.59 tff(4323,plain,
% 1.40/1.59 (c1_1(a2435)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[2467, 192, 4322, 4321, 4051, 3981, 3980, 4320, 4050, 4049, 11])).
% 1.40/1.59 tff(4324,plain,
% 1.40/1.59 (hskp18),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4032, 4079, 4323])).
% 1.40/1.59 tff(4325,plain,
% 1.40/1.59 (~c3_1(a2428)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[3020, 4324])).
% 1.40/1.59 tff(4326,plain,
% 1.40/1.59 (~c2_1(a2428)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[3026, 4324])).
% 1.40/1.59 tff(4327,plain,
% 1.40/1.59 (~c0_1(a2428)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[3032, 4324])).
% 1.40/1.59 tff(4328,plain,
% 1.40/1.59 (~c0_1(a2455)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[480, 4318])).
% 1.40/1.59 tff(4329,plain,
% 1.40/1.59 (c2_1(a2455)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[496, 4318])).
% 1.40/1.59 tff(4330,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2455) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c2_1(a2455)) | (~c1_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2455) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4331,plain,
% 1.40/1.59 (((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428)) <=> (c0_1(a2455) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4332,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2455) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c2_1(a2455)) | (~c1_1(a2455))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[4331])).
% 1.40/1.59 tff(4333,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2455) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[4332, 4330])).
% 1.40/1.59 tff(4334,plain,
% 1.40/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2435)) | c2_1(a2435) | (~c1_1(a2435)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2428) | c0_1(a2428) | c3_1(a2428))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(4335,plain,
% 1.40/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2455) | c2_1(a2435) | c0_1(a2428) | c2_1(a2428) | c3_1(a2428) | (~ndr1_0) | (~c1_1(a2435)) | (~c3_1(a2435)) | (~c2_1(a2455)) | (~c1_1(a2455))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[4334, 4333])).
% 1.40/1.59 tff(4336,plain,
% 1.40/1.59 (~c1_1(a2455)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4335, 192, 4329, 4006, 4328, 3980, 4327, 4326, 4325, 63, 4323])).
% 1.40/1.59 tff(4337,plain,
% 1.40/1.59 (c3_1(a2455)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[488, 4318])).
% 1.40/1.59 tff(4338,plain,
% 1.40/1.59 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4339,plain,
% 1.40/1.59 ((hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455))) <=> (hskp5 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4340,plain,
% 1.40/1.59 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[4339])).
% 1.40/1.59 tff(4341,plain,
% 1.40/1.59 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455))),
% 1.40/1.59 inference(transitivity,[status(thm)],[4340, 4338])).
% 1.40/1.59 tff(4342,plain,
% 1.40/1.59 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c0_1(a2455) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455) | c0_1(a2455) | (~c2_1(a2455)))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(4343,plain,
% 1.40/1.59 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c0_1(a2455) | (~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | c1_1(a2455)),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[4342, 4341])).
% 1.40/1.59 tff(4344,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4343, 192, 1955, 4329, 4337, 4328, 1965, 4336])).
% 1.40/1.59 tff(4345,plain,(hskp5), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(4346,plain,
% 1.40/1.59 (~c2_1(a2408)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[373, 4345])).
% 1.40/1.59 tff(4347,plain,
% 1.40/1.59 (c0_1(a2408)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[381, 4345])).
% 1.40/1.59 tff(4348,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2408) | (~c0_1(a2408)) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2408) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4349,plain,
% 1.40/1.59 (((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435))) <=> (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2408) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4350,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | (c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2408) | (~c0_1(a2408)) | (~c1_1(a2435))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[4349])).
% 1.40/1.59 tff(4351,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2408) | (~c0_1(a2408)) | (~c1_1(a2435)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[4350, 4348])).
% 1.40/1.59 tff(4352,plain,
% 1.40/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a2403) | (~c1_1(a2403)) | (~c0_1(a2403)) | c2_1(a2408) | c1_1(a2408) | (~c0_1(a2408)) | c2_1(a2435) | c0_1(a2435) | (~c1_1(a2435)))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(4353,plain,
% 1.40/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c2_1(W) | c0_1(W) | (~c1_1(W)))) | c0_1(a2435) | c2_1(a2435) | c2_1(a2408) | c2_1(a2403) | (~ndr1_0) | (~c1_1(a2403)) | (~c0_1(a2403)) | c1_1(a2408) | (~c0_1(a2408)) | (~c1_1(a2435))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[4352, 4351])).
% 1.40/1.59 tff(4354,plain,
% 1.40/1.59 ((~c0_1(a2403)) | c1_1(a2408)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4353, 192, 4347, 4051, 3981, 3980, 4346, 4050, 1879, 4323])).
% 1.40/1.59 tff(4355,plain,
% 1.40/1.59 (~c0_1(a2403)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4354, 1])).
% 1.40/1.59 tff(4356,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2455) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2455)) | (~c1_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2455) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4357,plain,
% 1.40/1.59 (((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403)) <=> (c0_1(a2455) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4358,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a2455) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2455)) | (~c1_1(a2455))))),
% 1.40/1.59 inference(monotonicity,[status(thm)],[4357])).
% 1.40/1.59 tff(4359,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2455) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.40/1.59 inference(transitivity,[status(thm)],[4358, 4356])).
% 1.40/1.59 tff(4360,plain,
% 1.40/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | (~c3_1(a2422)) | c2_1(a2422) | (~c1_1(a2422)) | c0_1(a2455) | (~c1_1(a2455)) | (~c2_1(a2455)) | c2_1(a2403) | c0_1(a2403) | c3_1(a2403))),
% 1.40/1.59 inference(quant_inst,[status(thm)],[])).
% 1.40/1.59 tff(4361,plain,
% 1.40/1.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)) | (~c2_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a2455) | c2_1(a2422) | c2_1(a2403) | c3_1(a2403) | (~ndr1_0) | c0_1(a2403) | (~c1_1(a2422)) | (~c3_1(a2422)) | (~c2_1(a2455)) | (~c1_1(a2455))),
% 1.40/1.59 inference(modus_ponens,[status(thm)],[4360, 4359])).
% 1.40/1.59 tff(4362,plain,
% 1.40/1.59 (c0_1(a2403) | (~c1_1(a2455))),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4361, 192, 4329, 4322, 4321, 4328, 4320, 4050, 4049, 63])).
% 1.40/1.59 tff(4363,plain,
% 1.40/1.59 (~c1_1(a2455)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4362, 4355])).
% 1.40/1.59 tff(4364,plain,
% 1.40/1.59 (c3_1(a2408)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[396, 4345])).
% 1.40/1.59 tff(4365,plain,
% 1.40/1.59 (hskp29),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[3518, 192, 4329, 4347, 4364, 4328, 1039, 1, 4363])).
% 1.40/1.59 tff(4366,plain,
% 1.40/1.59 (c3_1(a2409)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[1064, 4365])).
% 1.40/1.59 tff(4367,plain,
% 1.40/1.59 (c0_1(a2409)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[1675, 4365])).
% 1.40/1.59 tff(4368,plain,
% 1.40/1.59 (~c1_1(a2409)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[3527, 192, 4367, 4366, 4329, 4337, 3500, 3499, 3498, 554, 4363])).
% 1.40/1.59 tff(4369,plain,
% 1.40/1.59 (c2_1(a2409)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[1056, 4365])).
% 1.40/1.59 tff(4370,plain,
% 1.40/1.59 ($false),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[2441, 192, 4367, 4369, 4366, 4051, 4050, 4049, 2316, 4368])).
% 1.40/1.59 tff(4371,plain,(c1_1(a2408)), inference(lemma,lemma(discharge,[]))).
% 1.40/1.59 tff(4372,plain,
% 1.40/1.59 ((~c1_1(a2408)) | c1_1(a2425)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[2280, 192, 3500, 4347, 3981, 3980, 3499, 4346, 1879, 4323])).
% 1.40/1.59 tff(4373,plain,
% 1.40/1.59 (c1_1(a2425)),
% 1.40/1.59 inference(unit_resolution,[status(thm)],[4372, 4371])).
% 1.40/1.59 tff(4374,plain,
% 1.40/1.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.59 tff(4375,plain,
% 1.40/1.59 (((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414))) <=> (c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.40/1.59 inference(rewrite,[status(thm)],[])).
% 1.40/1.60 tff(4376,plain,
% 1.40/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455))))),
% 1.40/1.60 inference(monotonicity,[status(thm)],[4375])).
% 1.40/1.60 tff(4377,plain,
% 1.40/1.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)))),
% 1.40/1.60 inference(transitivity,[status(thm)],[4376, 4374])).
% 1.40/1.60 tff(4378,plain,
% 1.40/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455)) | c3_1(a2425) | (~c1_1(a2425)) | (~c0_1(a2425)) | c1_1(a2414) | c3_1(a2414) | (~c0_1(a2414)))),
% 1.40/1.60 inference(quant_inst,[status(thm)],[])).
% 1.40/1.60 tff(4379,plain,
% 1.40/1.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c1_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c3_1(a2425) | c1_1(a2414) | c3_1(a2414) | (~ndr1_0) | (~c0_1(a2414)) | (~c1_1(a2425)) | (~c0_1(a2425)) | (~c3_1(a2455)) | (~c2_1(a2455)) | (~c1_1(a2455))),
% 1.40/1.60 inference(modus_ponens,[status(thm)],[4378, 4377])).
% 1.40/1.60 tff(4380,plain,
% 1.40/1.60 ((~c1_1(a2425)) | (~c1_1(a2455))),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[4379, 192, 4329, 4337, 3500, 2628, 3498, 888, 882, 1076])).
% 1.40/1.60 tff(4381,plain,
% 1.40/1.60 (~c1_1(a2455)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[4380, 4373])).
% 1.40/1.60 tff(4382,plain,
% 1.40/1.60 (hskp30 | (~c1_1(a2408)) | (~c1_1(a2425))),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[644, 192, 3500, 4364, 3498, 4346, 564])).
% 1.40/1.60 tff(4383,plain,
% 1.40/1.60 (hskp30),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[4382, 4371, 4373])).
% 1.40/1.60 tff(4384,plain,
% 1.40/1.60 (c3_1(a2450)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[582, 4383])).
% 1.40/1.60 tff(4385,plain,
% 1.40/1.60 (c1_1(a2450)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[590, 4383])).
% 1.40/1.60 tff(4386,plain,
% 1.40/1.60 (c0_1(a2450)),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[598, 4383])).
% 1.40/1.60 tff(4387,plain,
% 1.40/1.60 ($false),
% 1.40/1.60 inference(unit_resolution,[status(thm)],[605, 192, 4386, 4385, 4384, 4329, 4337, 3500, 3499, 3498, 554, 4381])).
% 1.40/1.60 % SZS output end Proof
% 1.40/1.60 % E exiting
%------------------------------------------------------------------------------